Universal Approximation Using Radial-Basis-Function Networks

Adaptive Dynamic Surface Control of Epileptor Model Based on Nonlinear Luenberger State Observer

Epilepsy is a prevalent neurological disorder characterized by recurrent seizures, which are sudden bursts of electrical activity in the brain. The Epileptor model is a computational model specifically created to replicate the complex dynamics of epileptic seizures. The parameters of the Epileptor model can be adjusted to simulate activities associated with some seizure classes seen in patients. Due to the closeness of this model to nonlinear systems with nonstrict feedback form and the existence of uncertainties in the model, an adaptive dynamic surface controller is chosen for control of the system. Considering that the states in the Epileptor model are not measurable and the only measurable output is the Local Field Potentials signal, a nonlinear Luenberger state observer is developed to estimate the system states. It is the first time that the Luenberger state observer is used for the Epileptor model. In this approach, Radial Basis Neural Networks are utilized to estimate the system's nonlinear dynamics. The stability of our proposed controller along with the observer is proved, and the performance is shown using simulation. Simulation results show that by using the suggested method, the output and states of the, system track their reference, value with an acceptable error.

Chaotic time series classification by means of reservoir-based convolutional neural networks

We propose a novel Reservoir Computing (RC) based classification method that distinguishes between different chaotic time series. Our method is composed of two steps: (i) we use the reservoir as a feature extracting machine that captures the salient features of time series data; (ii) the readout layer of the reservoir is subsequently fed into a Convolutional Neural Network (CNN) to facilitate classification and recognition. One of the notable advantages is that the readout layer, as obtained by randomly generated empirical hyper-parameters within the RC module, provides sufficient information for the CNN to accomplish the classification tasks effectively. The quality of extracted features by RC is independently evaluated by the root mean square error, which measures how well the training signal may be reconstructed from the input time series. Furthermore, we propose two ways to implement the RC module, namely, a single shallow RC and parallel RC configurations, to further improve the classification accuracy. The important roles of RC in feature extraction are demonstrated by comparing the results when the CNN is provided with either ordinal pattern probability features or unprocessed raw time series directly, both of which perform worse than RC-based method. In addition to CNN, we show that the readout of RC is good for other classification tools as well. The successful classification of electroencephalogram recordings of different brain states suggests that our RC-based classification tools can be used for experimental studies.

Selective Memory Recursive Least Squares: Recast Forgetting Into Memory in RBF Neural Network-Based Real-Time Learning

In radial basis function neural network (RBFNN)-based real-time learning tasks, forgetting mechanisms are widely used such that the neural network can keep its sensitivity to new data. However, with forgetting mechanisms, some useful knowledge will get lost simply because they are learned a long time ago, which we refer to as the passive knowledge forgetting phenomenon. To address this problem, this article proposes a real-time training method named selective memory recursive least squares (SMRLS) in which the classical forgetting mechanisms are recast into a memory mechanism. Different from the forgetting mechanism, which mainly evaluates the importance of samples according to the time when samples are collected, the memory mechanism evaluates the importance of samples through both temporal and spatial distribution of samples. With SMRLS, the input space of the RBFNN is evenly divided into a finite number of partitions, and a synthesized objective function is developed using synthesized samples from each partition. In addition to the current approximation error, the neural network also updates its weights according to the recorded data from the partition being visited. Compared with classical training methods including the forgetting factor recursive least squares (FFRLS) and stochastic gradient descent (SGD) methods, SMRLS achieves improved learning speed and generalization capability, which are demonstrated by corresponding simulation results.

Topical drug formulation for enhanced permeation: A comparison of Bayesian optimisation and response surface methodology with an ibuprofen-loaded poloxamer 407-based formulations case study

Topical skin products aim to address aesthetic, protective, and/or therapeutic needs through interaction with the human epidermal system. Traditionally, formulation development relies on empirical knowledge and trial-and-error experiments. In this paper, we introduced the Bayesian optimisation method and compared it with the traditional response surface methodology (RSM) for topical drug formulation. The objective was to optimise the formulation composition of ibuprofen gel-like to achieve a maximum flux through in vitro permeation tests (IVPTs). As a model system, poloxamer 407, ethanol, and propylene glycol (PG) were selected as the key excipients, whose concentrations were optimised. Strat-M membrane, serving as a surrogate for human skin, and Franz cell diffusion were employed in IVPTs. Two sets of experiments were conducted under identical conditions for 30 h. Under the RSM approach, the optimised ibuprofen gel-like formulation was identified with a poloxamer 407: ethanol: PG ratio of 20:20:10, achieving a measured permeation flux of 11.28 ± 0.35 μg cm-2h-1. In comparison, Bayesian optimisation, after four iterations, yielded an optimised formulation with a ratio of 20.95:19.44:12.14, resulting in a permeation flux of 14.15 ± 0.77 μg cm-2h-1. These findings highlight the potential of Bayesian optimisation as an effective tool for improving topical drug formulations.

Adaptive formation learning control for cooperative AUVs under complete uncertainty

Introduction

This paper addresses the critical need for adaptive formation control in Autonomous Underwater Vehicles (AUVs) without requiring knowledge of system dynamics or environmental data. Current methods, often assuming partial knowledge like known mass matrices, limit adaptability in varied settings.

Methods

We proposed two-layer framework treats all system dynamics, including the mass matrix, as entirely unknown, achieving configuration-agnostic control applicable to multiple underwater scenarios. The first layer features a cooperative estimator for inter-agent communication independent of global data, while the second employs a decentralized deterministic learning (DDL) controller using local feedback for precise trajectory control. The framework's radial basis function neural networks (RBFNN) store dynamic information, eliminating the need for relearning after system restarts.

Results

This robust approach addresses uncertainties from unknown parametric values and unmodeled interactions internally, as well as external disturbances such as varying water currents and pressures, enhancing adaptability across diverse environments.

Discussion

Comprehensive and rigorous mathematical proofs are provided to confirm the stability of the proposed controller, while simulation results validate each agent's control accuracy and signal boundedness, confirming the framework's stability and resilience in complex scenarios.

Global Fast Terminal Fuzzy Sliding Mode Control of Quadrotor UAV Based on RBF Neural Network

In this paper, a global fast terminal fuzzy sliding mode control scheme based on the radial basis function (RBF) neural network is proposed for quadrotor unmanned aerial vehicle systems in the presence of external disturbances, system model uncertainty, and time-varying mass. Firstly, the dynamic model of the quadrotor is divided into two subsystems, i.e., an outer-loop control subsystem and an inner-loop control subsystem. Secondly, an adaptive sliding mode controller is used to control the outer-loop control subsystem, which includes the adaptive laws estimating the time-varying mass and external disturbances. In the inner-loop control subsystem, a global fast terminal fuzzy sliding mode controller, which is based on the RBF neural network, is designed to control the attitude of a quadrotor. In this method, the system model uncertainty is approximated using the RBF neural network. Simultaneously, an adaptive fuzzy controller is introduced to estimate the switching gain and eliminate external disturbances, and the chattering phenomenon is eliminated effectively. Finally, simulations are provided to demonstrate the effectiveness of the proposed control scheme.

Extreme Fuzzy Broad Learning System: Algorithm, Frequency Principle, and Applications in Classification and Regression

As an effective alternative to deep neural networks, broad learning system (BLS) has attracted more attention due to its efficient and outstanding performance and shorter training process in classification and regression tasks. Nevertheless, the performance of BLS will not continue to increase, but even decrease, as the number of nodes reaches the saturation point and continues to increase. In addition, the previous research on neural networks usually ignored the reason for the good generalization of neural networks. To solve these problems, this article first proposes the Extreme Fuzzy BLS (E-FBLS), a novel cascaded fuzzy BLS, in which multiple fuzzy BLS blocks are grouped or cascaded together. Moreover, the original data is input to each FBLS block rather than the previous blocks. In addition, we use residual learning to illustrate the effectiveness of E-FBLS. From the frequency domain perspective, we also discover the existence of the frequency principle in E-FBLS, which can provide good interpretability for the generalization of the neural network. Experimental results on classical classification and regression datasets show that the accuracy of the proposed E-FBLS is superior to traditional BLS in handling classification and regression tasks. The accuracy improves when the number of blocks increases to some extent. Moreover, we verify the frequency principle of E-FBLS that E-FBLS can obtain the low-frequency components quickly, while the high-frequency components are gradually adjusted as the number of FBLS blocks increases.

Adaptive Event-Triggered Bipartite Formation for Multiagent Systems via Reinforcement Learning

This article investigates the online learning and energy-efficient control issues for nonlinear discrete-time multiagent systems (MASs) with unknown dynamics models and antagonistic interactions. First, a distributed combined measurement error function is formulated using the signed graph theory to transfer the bipartite formation issue into a consensus issue. Then, an enhanced linearization controller model for the controlled MASs is developed by employing dynamic linearization technology. After that, an online learning adaptive event-triggered (ET) actor-critic neural network (AC-NN) framework for the MASs to implement bipartite formation control tasks is proposed by employing the optimized NNs and designed adaptive ET mechanism. Moreover, the convergence of the designed formation control framework is strictly proved by the constructed Lyapunov functions. Finally, simulation and experimental studies further demonstrate the effectiveness of the proposed algorithm.

Optimized distributed formation control using identifier-critic-actor reinforcement learning for a class of stochastic nonlinear multi-agent systems

This article is to propose an adaptive reinforcement learning (RL)-based optimized distributed formation control for the unknown stochastic nonlinear single-integrator dynamic multi-agent system (MAS). For solving the issue of unknown dynamic, an adaptive identifier neural network (NN) is developed to determine the stochastic MAS under expectation sense. And then, for deriving the optimized formation control, the RL is putted into effect via constructing a pair of critic and actor NNs. With regard of the traditional RL optimal controls, their algorithm exists the inherent complexity, because their adaptive RL algorithm are derived from negative gradient of the square of Hamilton-Jacobi-Bellman (HJB) equation. As a result, these methods are difficultly extended to stochastic dynamical systems. However, since this adaptive RL laws are derived from a simple positive function rather than the square of HJB equation, it can make optimal control with simple algorithm. Therefore, this optimized formation scheme can be smoothly performed to the stochastic MAS. Finally, according to theorem proof and computer simulation, the optimized method can realize the required control objective.

Nonlinear model predictive control of a conductance-based neuron model via data-driven forecasting

Objective. Precise control of neural systems is essential to experimental investigations of how the brain controls behavior and holds the potential for therapeutic manipulations to correct aberrant network states. Model predictive control, which employs a dynamical model of the system to find optimal control inputs, has promise for dealing with the nonlinear dynamics, high levels of exogenous noise, and limited information about unmeasured states and parameters that are common in a wide range of neural systems. However, the challenge still remains of selecting the right model, constraining its parameters, and synchronizing to the neural system.Approach. As a proof of principle, we used recent advances in data-driven forecasting to construct a nonlinear machine-learning model of a Hodgkin-Huxley type neuron when only the membrane voltage is observable and there are an unknown number of intrinsic currents.Main Results. We show that this approach is able to learn the dynamics of different neuron types and can be used with model predictive control (MPC) to force the neuron to engage in arbitrary, researcher-defined spiking behaviors.Significance.To the best of our knowledge, this is the first application of nonlinear MPC of a conductance-based model where there is only realistically limited information about unobservable states and parameters.

Soil data augmentation and model construction based on spectral difference and content difference

Soil analysis makes for developing precision agriculture and monitoring land quality, while the models available for spectroscopy-based chemometrics are constrained by limited samples from small areas. The paper proposed sample expansion and model construction based on spectral difference and content difference, realizing data augmentation and deep learning applied to original samples with limited numbers. The spectral subtraction based on maximum or minimum values exploited the maximum or minimum values to acquire the spectral difference and content difference, which provided a new data form for model construction. Keeping enhanced samples whose spectral difference and content difference were all zero was useful for improving model performance. Augmentation of all data or training data based on maximum or minimum values-based spectral subtraction, which sorted the contents and made them the maximum or minimum values in sequence, achieved sample expansion by the spectral difference and content difference. The model utilized the random vector functional link (RVFL) network, extreme learning machine (ELM), and one-dimensional convolutional neural network (1D CNN), which could predict the content of new samples through ensemble averaging when predicting content difference. The experimental result showed the model of the spectral subtraction based on maximum or minimum values had a similar performance to that of the original samples. Augmentation of all data improved model performance by only RVFL and ELM. Augmentation of training data verified 1D CNN was better than RVFL and ELM. The paper implements a new data augmentation method and applies CNN to original samples with inadequate numbers, which lays the foundation for an improved model and applying spectral preprocessing.

Higher-order interactions between hippocampal CA1 neurons are disrupted in amnestic mice

Across systems, higher-order interactions between components govern emergent dynamics. Here we tested whether contextual threat memory retrieval in mice relies on higher-order interactions between dorsal CA1 hippocampal neurons requiring learning-induced dendritic spine plasticity. We compared population-level Ca2+ transients as wild-type mice (with intact learning-induced spine plasticity and memory) and amnestic mice (TgCRND8 mice with high levels of amyloid-β and deficits in learning-induced spine plasticity and memory) were tested for memory. Using machine-learning classifiers with different capacities to use input data with complex interactions, our findings indicate complex neuronal interactions in the memory representation of wild-type, but not amnestic, mice. Moreover, a peptide that partially restored learning-induced spine plasticity also restored the statistical complexity of the memory representation and memory behavior in Tg mice. These findings provide a previously missing bridge between levels of analysis in memory research, linking receptors, spines, higher-order neuronal dynamics and behavior.

Learning active subspaces and discovering important features with Gaussian radial basis functions neural networks

Providing a model that achieves a strong predictive performance and is simultaneously interpretable by humans is one of the most difficult challenges in machine learning research due to the conflicting nature of these two objectives. To address this challenge, we propose a modification of the radial basis function neural network model by equipping its Gaussian kernel with a learnable precision matrix. We show that precious information is contained in the spectrum of the precision matrix that can be extracted once the training of the model is completed. In particular, the eigenvectors explain the directions of maximum sensitivity of the model revealing the active subspace and suggesting potential applications for supervised dimensionality reduction. At the same time, the eigenvectors highlight the relationship in terms of absolute variation between the input and the latent variables, thereby allowing us to extract a ranking of the input variables based on their importance to the prediction task enhancing the model interpretability. We conducted numerical experiments for regression, classification, and feature selection tasks, comparing our model against popular machine learning models, the state-of-the-art deep learning-based embedding feature selection techniques, and a transformer model for tabular data. Our results demonstrate that the proposed model does not only yield an attractive prediction performance compared to the competitors but also provides meaningful and interpretable results that potentially could assist the decision-making process in real-world applications. A PyTorch implementation of the model is available on GitHub at the following link.1.

Deep radial basis function networks with subcategorization for mitosis detection in breast histopathology images

Due to the intra-class diversity of mitotic cells and the morphological overlap with similarly looking imposters, automatic mitosis detection in histopathology slides is still a challenging task. In this paper, we propose a novel mitosis detection model in a weakly supervised way, which consists of a candidate proposal network and a verification network. The candidate proposal network based on patch learning aims to separate both mitotic cells and their mimics from the background as candidate objects, which substantially reduces missed detections in the screening process of candidates. These obtained candidate results are then fed into the verification network for mitosis refinement. The verification network adopts an RBF-based subcategorization scheme to deal with the problems of high intra-class variability of mitosis and the mimics with similar appearance. We utilize the RBF centers to define subcategories containing mitotic cells with similar properties and capture representative RBF center locations through joint training of classification and clustering. Due to the lower intra-class variation within a subcategory, the localized feature space at subcategory level can better characterize a certain type of mitotic figures and can provide a better similarity measurement for distinguishing mitotic cells from nonmitotic cells. Our experiments manifest that this subcategorization scheme helps improve the performance of mitosis detection and achieves state-of-the-art results on the publicly available mitosis datasets using only weak labels.

Graph Embedded Ensemble Deep Randomized Network for Diagnosis of Alzheimer's Disease

Randomized shallow/deep neural networks with closed form solution avoid the shortcomings that exist in the back propagation (BP) based trained neural networks. Ensemble deep random vector functional link (edRVFL) network utilize the strength of two growing fields, i.e., deep learning and ensemble learning. However, edRVFL model doesn't consider the geometrical relationship of the data while calculating the final output parameters corresponding to each layer considered as base model. In the literature, graph embedded frameworks have been successfully used to describe the geometrical relationship within data. In this paper, we propose an extended graph embedded RVFL (EGERVFL) model that, unlike standard RVFL, employs both intrinsic and penalty subspace learning (SL) criteria under the graph embedded framework in its optimization process to calculate the model's output parameters. The proposed shallow EGERVFL model has only single hidden layer and hence, has less representation learning. Therefore, we further develop an ensemble deep EGERVFL (edEGERVFL) model that can be considered a variant of edRVFL model. Unlike edRVFL, the proposed edEGERVFL model solves graph embedded based optimization problem in each layer and hence, has better generalization performance than edRVFL model. We evaluated the proposed approaches for the diagnosis of Alzheimer's disease and furthermore on UCI datasets. The experimental results demonstrate that the proposed models perform better than baseline models. The source code of the proposed models is available at https://github.com/mtanveer1/.

Unraveling biochemical spatial patterns: Machine learning approaches to the inverse problem of stationary Turing patterns

The diffusion-driven Turing instability is a potential mechanism for spatial pattern formation in numerous biological and chemical systems. However, engineering these patterns and demonstrating that they are produced by this mechanism is challenging. To address this, we aim to solve the inverse problem in artificial and experimental Turing patterns. This task is challenging since patterns are often corrupted by noise and slight changes in initial conditions can lead to different patterns. We used both least squares to explore the problem and physics-informed neural networks to build a noise-robust method. We elucidate the functionality of our network in scenarios mimicking biological noise levels and showcase its application using an experimentally obtained chemical pattern. The findings reveal the significant promise of machine learning in steering the creation of synthetic patterns in bioengineering, thereby advancing our grasp of morphological intricacies within biological systems while acknowledging existing limitations.

Distributed Adaptive Formation Tracking for a Class of Uncertain Nonlinear Multiagent Systems: Guaranteed Connectivity Under Moving Obstacles

This article explores a guaranteed network connectivity problem during moving obstacle avoidance within a distributed formation tracking framework for uncertain nonlinear multiagent systems with range constraints. We investigate this problem based on a new adaptive distributed design using nonlinear errors and auxiliary signals. Within the detection range, each agent regards other agents and static or dynamic objects as obstacles. The nonlinear error variables for formation tracking and collision avoidance are presented, and the auxiliary signals in formation tracking errors are introduced to maintain network connectivity under the avoidance mechanism. The adaptive formation controllers using command-filtered backstepping are constructed to ensure closed-loop stability with collision avoidance and preserved connectivity. Compared with the previous formation results, the resulting features are as follows: 1) the nonlinear error function for the avoidance mechanism is considered an error variable, and an adaptive tuning mechanism for estimating the dynamic obstacle velocity is derived in a Lyapunov-based control design procedure; 2) network connectivity during dynamic obstacle avoidance is preserved by constructing the auxiliary signals; and 3) owing to neural networks-based compensating variables, the bounding conditions of time derivatives of virtual controllers are not required in the stability analysis.

Neural Network Boundary Approximation for Uncertain Nonlinear Spatiotemporal Systems and Its Application of Tracking Control

This brief addresses the neural network (NN) approximation problem for uncertain nonlinear systems with time-varying parameters (that is, unknown nonlinear spatiotemporal systems). Due to the fact that the unknown spatiotemporal functions cannot be directly approximated by NNs, a so-called time-varying parameter extraction is given to separate time-varying parameters from uncertain nonlinear spatiotemporal functions. By using the supremum of Euler norm of the extracted time-varying parameters, the nonlinear spatiotemporal function is mapped to an unknown state-based boundary function, which can be approximated by NNs. Based on the time-varying parameter extraction, an adaptive neural tracking control law is designed for uncertain strict-feedback nonlinear spatiotemporal systems, which guarantees the convergence of the tracking error with a trajectory performance. The effectiveness of the designed method is verified by simulations.

Learning Traveling Solitary Waves Using Separable Gaussian Neural Networks

In this paper, we apply a machine-learning approach to learn traveling solitary waves across various physical systems that are described by families of partial differential equations (PDEs). Our approach integrates a novel interpretable neural network (NN) architecture, called Separable Gaussian Neural Networks (SGNN) into the framework of Physics-Informed Neural Networks (PINNs). Unlike the traditional PINNs that treat spatial and temporal data as independent inputs, the present method leverages wave characteristics to transform data into the so-called co-traveling wave frame. This reformulation effectively addresses the issue of propagation failure in PINNs when applied to large computational domains. Here, the SGNN architecture demonstrates robust approximation capabilities for single-peakon, multi-peakon, and stationary solutions (known as "leftons") within the (1+1)-dimensional, b-family of PDEs. In addition, we expand our investigations, and explore not only peakon solutions in the ab-family but also compacton solutions in (2+1)-dimensional, Rosenau-Hyman family of PDEs. A comparative analysis with multi-layer perceptron (MLP) reveals that SGNN achieves comparable accuracy with fewer than a tenth of the neurons, underscoring its efficiency and potential for broader application in solving complex nonlinear PDEs.

Learning in Deep Radial Basis Function Networks

Learning in neural networks with locally-tuned neuron models such as radial Basis Function (RBF) networks is often seen as instable, in particular when multi-layered architectures are used. Furthermore, universal approximation theorems for single-layered RBF networks are very well established; therefore, deeper architectures are theoretically not required. Consequently, RBFs are mostly used in a single-layered manner. However, deep neural networks have proven their effectiveness on many different tasks. In this paper, we show that deeper RBF architectures with multiple radial basis function layers can be designed together with efficient learning schemes. We introduce an initialization scheme for deep RBF networks based on k-means clustering and covariance estimation. We further show how to make use of convolutions to speed up the calculation of the Mahalanobis distance in a partially connected way, which is similar to the convolutional neural networks (CNNs). Finally, we evaluate our approach on image classification as well as speech emotion recognition tasks. Our results show that deep RBF networks perform very well, with comparable results to other deep neural network types, such as CNNs.

Hyperdimensional computing with holographic and adaptive encoder

Introduction

Brain-inspired computing has become an emerging field, where a growing number of works focus on developing algorithms that bring machine learning closer to human brains at the functional level. As one of the promising directions, Hyperdimensional Computing (HDC) is centered around the idea of having holographic and high-dimensional representation as the neural activities in our brains. Such representation is the fundamental enabler for the efficiency and robustness of HDC. However, existing HDC-based algorithms suffer from limitations within the encoder. To some extent, they all rely on manually selected encoders, meaning that the resulting representation is never adapted to the tasks at hand.

Methods

In this paper, we propose FLASH, a novel hyperdimensional learning method that incorporates an adaptive and learnable encoder design, aiming at better overall learning performance while maintaining good properties of HDC representation. Current HDC encoders leverage Random Fourier Features (RFF) for kernel correspondence and enable locality-preserving encoding. We propose to learn the encoder matrix distribution via gradient descent and effectively adapt the kernel for a more suitable HDC encoding.

Results

Our experiments on various regression datasets show that tuning the HDC encoder can significantly boost the accuracy, surpassing the current HDC-based algorithm and providing faster inference than other baselines, including RFF-based kernel ridge regression.

Discussion

The results indicate the importance of an adaptive encoder and customized high-dimensional representation in HDC.

Quantized-output-feedback practical prescribed-time design strategy for decentralized tracking of a class of interconnected nonlinear systems with unknown interaction delays

This paper proposes a decentralized practical prescribed-time (PT) tracking design using quantized output feedback (QOF) for uncertain interconnected lower-triangular systems with unknown time-delay interconnections. The local output signals are assumed to be only measured and quantized for the PT tracker design under a band-limited network. By employing a PT-dependent scaling function, a decentralized memoryless PT observer based on quantized local outputs is developed to estimate local unmeasurable state variables. Owing to output quantization, the available output feedback signals become discontinuous. As a result, the tracking error between the actual (i.e., unquantized) local output and the local desired signal cannot be utilized in the local virtual controller. To address this issue, a novel adaptive compensation mechanism is derived to design the local PT neural network tracking laws using only quantized local outputs and estimated states. The proposed PT tracking controller does not require information on the interconnected nonlinear functions and interaction delays. During the Lyapunov stability analysis, the boundary layer error decomposition approach is employed to address the issue of non-differentiability in the local virtual control laws. The proposed QOF control system achieves practical PT stability. It is shown that the settling time of local tracking errors can be predetermined, regardless of the design parameters and initial conditions. Finally, the proposed QOF decentralization strategy is supported with illustrative examples and a comparison to demonstrate its benefits.

Automated 2D and 3D finite element overclosure adjustment and mesh morphing using generalized regression neural networks

Computer representations of three-dimensional (3D) geometries are crucial for simulating systems and processes in engineering and science. In medicine, and more specifically, biomechanics and orthopaedics, obtaining and using 3D geometries is critical to many workflows. However, while many tools exist to obtain 3D geometries of organic structures, little has been done to make them usable for their intended medical purposes. Furthermore, many of the proposed tools are proprietary, limiting their use. This work introduces two novel algorithms based on Generalized Regression Neural Networks (GRNN) and 4 processes to perform mesh morphing and overclosure adjustment. These algorithms were implemented, and test cases were used to validate them against existing algorithms to demonstrate improved performance. The resulting algorithms demonstrate improvements to existing techniques based on Radial Basis Function (RBF) networks by converting to GRNN-based implementations. Implementations in MATLAB of these algorithms and the source code are publicly available at the following locations: https://github.com/thor-andreassen/femors; https://simtk.org/projects/femors-rbf; https://www.mathworks.com/matlabcentral/fileexchange/120353-finite-element-morphing-overclosure-reduction-and-slicing.

Dynamic learning from adaptive neural control for full-state constrained strict-feedback nonlinear systems

This study focuses on the learning and control issues of strict-feedback systems with full-state constraints. To achieve learning capability under constraints, transformation mapping is utilized to convert the original system with full-state constraints into a quasi-pure-feedback unconstrained system. Utilizing the system transformation technique, only a single neural network (NN) is required to identify the unknown dynamics within the transformed system. Combining the dynamic surface control design, a novel adaptive neural control scheme is developed to ensure that all closed-loop signals are uniformly bounded, and every system state remains within the predefined constraint range. In addition, the precise convergence of NN weights is further transformed into an exponential stability problem for a category of linear time-varying systems under persistent excitation conditions. Subsequently, the converged NN weights are efficiently stored and utilized to create a learning controller to achieve better control performance while abiding by the full-state constraints. The viability of this control strategy is demonstrated via simulations.

Protein-protein and protein-nucleic acid binding site prediction via interpretable hierarchical geometric deep learning

Identification of protein-protein and protein-nucleic acid binding sites provides insights into biological processes related to protein functions and technical guidance for disease diagnosis and drug design. However, accurate predictions by computational approaches remain highly challenging due to the limited knowledge of residue binding patterns. The binding pattern of a residue should be characterized by the spatial distribution of its neighboring residues combined with their physicochemical information interaction, which yet cannot be achieved by previous methods. Here, we design GraphRBF, a hierarchical geometric deep learning model to learn residue binding patterns from big data. To achieve it, GraphRBF describes physicochemical information interactions by designing an enhanced graph neural network and characterizes residue spatial distributions by introducing a prioritized radial basis function neural network. After training and testing, GraphRBF shows great improvements over existing state-of-the-art methods and strong interpretability of its learned representations. Applying GraphRBF to the SARS-CoV-2 omicron spike protein, it successfully identifies known epitopes of the protein. Moreover, it predicts multiple potential binding regions for new nanobodies or even new drugs with strong evidence. A user-friendly online server for GraphRBF is freely available at http://liulab.top/GraphRBF/server.

Nearly optimal fault-tolerant constrained tracking for multi-axis servo system via practical terminal sliding mode and adaptive dynamic programming

In this paper, a nearly optimal tracking control is proposed for n-links robotic manipulators subject to parameter uncertainties, time-profile failures, and input saturation constraints. Firstly, the practical terminal sliding-mode (PTSM) manifold with a linear additional term is proposed to combine the system states related to joint rotation, such that the controlled states quickly fall into a tiny neighborhood of the equilibrium once they reach the PTSM manifold. Secondly, a nearly optimal sliding-mode reaching law is designed by using the adaptive dynamic programming (ADP) technique. Benefiting from a non-quadratic positive defined mapping of the proposed performance index, which relates to the derivative of the sliding-mode function, reduced-order system dynamics can be constrained to a desired region. For the bounded actuator fault caused by various inducements such as the power supply fluctuation and the wear of parts, a radial basis function neural network (RBFNN) is introduced to compensate for this, and the input saturation constraints of the controlled plant are also compensated at the same time. Innovatively, the node weights of RBFNN are updated by the critic network of the ADP framework, such that the integrity of the proposed control strategy is improved. Simulations verify the main conclusions.

Fractional order fast terminal sliding mode control scheme for tracking control of robot manipulators

In this study, a fractional order fast terminal sliding mode control strategy is developed to address the trajectory tracking problem that arises when robot manipulators are subjected to uncertainties and external disturbances. A novel fractional order fast terminal sliding surface is proposed to achieve rapid finite time convergence and the explicit expression for the settling time is also formulated. To manage uncertainties, chattering phenomenon, singularities, large control gains, etc., a new fractional order fast terminal sliding mode control scheme is developed based on the proposed sliding surface. The radial basis function neural network is used in the proposed control strategy to approximate the nonlinearities and modeling errors of the robot dynamics in real time. The reconstruction error of neural network and upper bound on disturbances are handled by the adaptive compensator. The Lyapunov technique is used to examine the stability of the proposed control strategy. The proposed control technique improves the efficiency of the controller and allows for the asymptotic error convergence to occur in a finite amount of time. To compare the effectiveness of the proposed scheme to various existing control approaches, numerical simulation studies are also conducted.

Decentralized Adaptive Neural Inverse Optimal Control of Nonlinear Interconnected Systems

Existing methods on decentralized optimal control of continuous-time nonlinear interconnected systems require a complicated and time-consuming iteration on finding the solution of Hamilton-Jacobi-Bellman (HJB) equations. In order to overcome this limitation, in this article, a decentralized adaptive neural inverse approach is proposed, which ensures the optimized performance but avoids solving HJB equations. Specifically, a new criterion of inverse optimal practical stabilization is proposed, based on which a new direct adaptive neural strategy and a modified tuning functions method are proposed to design a decentralized inverse optimal controller. It is proven that all the closed-loop signals are bounded and the goal of inverse optimality with respect to the cost functional is achieved. Illustrative examples validate the performance of the methods presented.

An effective AI model for automatically detecting arteriovenous fistula stenosis

In this study, a novel artificial intelligence (AI) model is proposed to detect stenosis in arteriovenous fistulas (AVFs) using inexpensive and non-invasive audio recordings. The proposed model is a combination of two new input features based on short-time Fourier transform (STFT) and sample entropy, as well as two associated classification models (ResNet50 and ANN). The model's hyper-parameters were optimized through the use of the design of the experiment (DOE). The proposed AI model demonstrates high performance with all essential metrics, including sensitivity, specificity, accuracy, precision, and F1-score, exceeding 0.90 at detecting stenosis greater than 50%. These promising results suggest that our approach can lead to new insights and knowledge in this field. Moreover, the robust performance of our model, combined with the affordability of the audio recording device, makes it a valuable tool for detecting AVF stenosis in home-care settings.

Adaptive closed-loop paradigm of electrophysiology for neuron models

The traditional electrophysiological experiments based on an open-loop paradigm are relatively complicated and limited when facing an individual neuron with uncertain nonlinear factors. Emerging neural technologies enable tremendous growth in experimental data leading to the curse of high-dimensional data, which obstructs the mechanism exploration of spiking activities in the neurons. In this work, we propose an adaptive closed-loop electrophysiology simulation experimental paradigm based on a Radial Basis Function neural network and a highly nonlinear unscented Kalman filter. On account of the complex nonlinear dynamic characteristics of the real neurons, the proposed simulation experimental paradigm could fit the unknown neuron models with different channel parameters and different structures (i.e. single or multiple compartments), and further compute the injected stimulus in time according to the arbitrary desired spiking activities of the neurons. However, the hidden electrophysiological states of the neurons are difficult to be measured directly. Thus, an extra Unscented Kalman filter modular is incorporated in the closed-loop electrophysiology experimental paradigm. The numerical results and theoretical analyses demonstrate that the proposed adaptive closed-loop electrophysiology simulation experimental paradigm achieves desired spiking activities arbitrarily and the hidden dynamics of the neurons are visualized by the unscented Kalman filter modular. The proposed adaptive closed-loop simulation experimental paradigm can avoid the inefficiency of data at increasingly greater scales and enhance the scalability of electrophysiological experiments, thus speeding up the discovery cycle on neuroscience.

Deterministic learning-based neural control for output-constrained strict-feedback nonlinear systems

This paper studies learning from adaptive neural control of output-constrained strict-feedback uncertain nonlinear systems. To overcome the constraint restriction and achieve learning from the closed-loop control process, there are several significant steps. Firstly, a state transformation is introduced to convert the original constrained system output into an unconstrained one. Then an equivalent n-order affine nonlinear system is constructed based on the transformed unconstrained output state in norm form by the system transformation method. By combining dynamic surface control (DSC) technique, an adaptive neural control scheme is proposed for the transformed system. Then all closed-loop signals are uniformly ultimately bounded and the system output tracks the expected trajectory well with satisfying the constraint requirement. Secondly, the partial persistent excitation condition of the radial basis function neural network (RBF NN) could be verified to achieve. Therefore, the uncertain dynamics can be precisely approximated by RBF NN. Subsequently, the learning ability of RBF NN is achieved, and the knowledge acquired from the neural control process is stored in the form of constant neural networks (NNs). By reutilizing the knowledge, a novel learning controller is established to improve the control performance when facing the similar or same control task. The proposed learning control (LC) scheme can avoid repeating the online adaptation of neural weight estimates, which saves computing resources and improves transient performance. Meanwhile, the LC method significantly raises the tracking accuracy and the speed of error convergence while satisfying of the constraint condition simultaneously. Simulation studies demonstrate the efficiency of this proposed control scheme.

Development of prediction models for one-year brain tumour survival using machine learning: a comparison of accuracy and interpretability

BACKGROUND AND OBJECTIVE

Prediction of survival in patients diagnosed with a brain tumour is challenging because of heterogeneous tumour behaviours and treatment response. Advances in machine learning have led to the development of clinical prognostic models, but due to the lack of model interpretability, integration into clinical practice is almost non-existent. In this retrospective study, we compare five classification models with varying degrees of interpretability for the prediction of brain tumour survival greater than one year following diagnosis.

METHODS

1028 patients aged ≥16 years with a brain tumour diagnosis between April 2012 and April 2020 were included in our study. Three intrinsically interpretable 'glass box' classifiers (Bayesian Rule Lists [BRL], Explainable Boosting Machine [EBM], and Logistic Regression [LR]), and two 'black box' classifiers (Random Forest [RF] and Support Vector Machine [SVM]) were trained on electronic patients records for the prediction of one-year survival. All models were evaluated using balanced accuracy (BAC), F1-score, sensitivity, specificity, and receiver operating characteristics. Black box model interpretability and misclassified predictions were quantified using SHapley Additive exPlanations (SHAP) values and model feature importance was evaluated by clinical experts.

RESULTS

The RF model achieved the highest BAC of 78.9%, closely followed by SVM (77.7%), LR (77.5%) and EBM (77.1%). Across all models, age, diagnosis (tumour type), functional features, and first treatment were top contributors to the prediction of one year survival. We used EBM and SHAP to explain model misclassifications and investigated the role of feature interactions in prognosis.

CONCLUSION

Interpretable models are a natural choice for the domain of predictive medicine. Intrinsically interpretable models, such as EBMs, may provide an advantage over traditional clinical assessment of brain tumour prognosis by weighting potential risk factors and their interactions that may be unknown to clinicians. An agreement between model predictions and clinical knowledge is essential for establishing trust in the models decision making process, as well as trust that the model will make accurate predictions when applied to new data.

Tracking Control of Self-Restructuring Systems: A Low-Complexity Neuroadaptive PID Approach With Guaranteed Performance

This article investigates the tracking control problem for a class of self-restructuring systems. Different from existing studies on systems with fixed structure, this work focuses on systems with varying structures, arising from, for instance, biological self-developing, unconsciously switching, or unexpected subsystem failure. As the resultant dynamic model is complicated and uncertain, any model-based control is too costly and seldom practical. Here, we explore a nonmodel-based low-complexity proportional-integral-derivative (PID) control. Unlike traditional PID with fixed gains, the proposed one is embedded with neural-network (NN)-based self-tuning adaptive gains, where the tuning strategy is analytically built upon system stability and performance specifications, such that transient behavior and steady-state performance are ensured. Both square and nonsquare systems are addressed by using the matrix decomposition technique. The benefits and feasibility of the proposed control method are also validated and confirmed by the simulations.

Two-Stage Data-Driven Evolutionary Optimization for High-Dimensional Expensive Problems

Surrogate-assisted evolutionary algorithms (SAEAs) have been widely used for solving complex and computationally expensive optimization problems. However, most of the existing algorithms converge slowly in the later stage. This article proposes a novel two-stage data-driven evolutionary optimization (TS-DDEO) that meets the requirements of early exploration and later exploitation. In the first stage, a surrogate-assisted hierarchical particle swarm optimization method is used to find a promising area from the entire search space. In the second stage, we propose a best-data-driven optimization (BDDO) method with a strong exploitation ability to accelerate the optimization process. BDDO has a real-time update mechanism for the surrogate model and population and uses a predefined number of ranking-top solutions to update population and surrogates. BDDO combines three surrogate-assisted evolutionary sampling strategies: 1) surrogate-assisted differential evolution sampling; 2) surrogate-assisted local search; and 3) a surrogate-assisted full-crossover (FC) strategy which is proposed to integrate existing best genotypes in the population. Experiments and analysis have validated the effectiveness of the two-stage framework, the BDDO method, and the FC strategy. Moreover, the proposed algorithm is compared with five state-of-the-art SAEAs on high-dimensional benchmark functions. The result shows that TS-DDEO performs better both in effectiveness and robustness.

Segmentation by test-time optimization for CBCT-based adaptive radiation therapy

PURPOSE

Online adaptive radiotherapy (ART) requires accurate and efficient auto-segmentation of target volumes and organs-at-risk (OARs) in mostly cone-beam computed tomography (CBCT) images, which often have severe artifacts and lack soft-tissue contrast, making direct segmentation very challenging. Propagating expert-drawn contours from the pretreatment planning CT through traditional or deep learning (DL)-based deformable image registration (DIR) can achieve improved results in many situations. Typical DL-based DIR models are population based, that is, trained with a dataset for a population of patients, and so they may be affected by the generalizability problem.

METHODS

In this paper, we propose a method called test-time optimization (TTO) to refine a pretrained DL-based DIR population model, first for each individual test patient, and then progressively for each fraction of online ART treatment. Our proposed method is less susceptible to the generalizability problem and thus can improve overall performance of different DL-based DIR models by improving model accuracy, especially for outliers. Our experiments used data from 239 patients with head-and-neck squamous cell carcinoma to test the proposed method. First, we trained a population model with 200 patients and then applied TTO to the remaining 39 test patients by refining the trained population model to obtain 39 individualized models. We compared each of the individualized models with the population model in terms of segmentation accuracy.

RESULTS

The average improvement of the Dice similarity coefficient (DSC) and 95% Hausdorff distance (HD95) of segmentation can be up to 0.04 (5%) and 0.98 mm (25%), respectively, with the individualized models compared to the population model over 17 selected OARs and a target of 39 patients. Although the average improvement may seem mild, we found that the improvement for outlier patients with structures of large anatomical changes is significant. The number of patients with at least 0.05 DSC improvement or 2 mm HD95 improvement by TTO averaged over the 17 selected structures for the state-of-the-art architecture VoxelMorph is 10 out of 39 test patients. By deriving the individualized model using TTO from the pretrained population model, TTO models can be ready in about 1 min. We also generated the adapted fractional models for each of the 39 test patients by progressively refining the individualized models using TTO to CBCT images acquired at later fractions of online ART treatment. When adapting the individualized model to a later fraction of the same patient, the model can be ready in less than a minute with slightly improved accuracy.

CONCLUSIONS

The proposed TTO method is well suited for online ART and can boost segmentation accuracy for DL-based DIR models, especially for outlier patients where the pretrained models fail.

Deterministic learning-based neural network control with adaptive phase compensation

Under the persistent excitation (PE) condition, the real dynamics of the nonlinear system can be obtained through the deterministic learning-based radial basis function neural network (RBFNN) control. However, in this scheme, the learning speed and accuracy are limited by the tradeoff between the PE levels and the approximation capabilities of the neural network (NN). Inspired by the frequency domain phase compensation of linear time-invariant (LTI) systems, this paper presents an adaptive phase compensator employing the pure time delay to improve the performance of the deterministic learning-based adaptive feedforward control with the reference input known a priori. When the adaptive phase compensation is applied to the hidden layer of the RBFNN, the nonlinear approximation capability of the RBFNN is effectively improved such that both the learning performance (learning speed and accuracy) and the control performance of the deterministic learning-based control scheme are improved. Theoretical analysis is conducted to prove the stability of the proposed learning control scheme for a class of systems which are affine in the control. Simulation studies demonstrate the effectiveness of the proposed phase compensation method.

Adaptive-observer-based consensus tracking with fault-tolerant network connectivity of uncertain time-delay nonlinear multiagent systems with actuator and communication faults

In this study, a distributed output-feedback design approach for ensuring fault-tolerant initial network connectivity and preselected-time consensus tracking performance is proposed for a class of uncertain time-delay nonlinear multiagent systems (TDNMSs) with unexpected actuator and communication faults. It is assumed that time-varying state delays and system nonlinearities in TDNMSs are unknown. The main contribution of this study is to provide a delay-independent output-feedback control strategy to address a fault-tolerant initial connectivity preservation problem in the consensus tracking field. A local delay-independent adaptive state observer using neural networks is designed for each follower, and the boundedness of local observation errors is proved by constructing a Lyapunov-Krasovskii functional and adaptive tuning laws. Then, the local nonlinear relative output errors using a time-varying function with a preselected convergence time are derived to design simple local delay-independent trackers. The stability of the proposed consensus tracking system is analyzed, and simulation comparison results demonstrate the validity of the proposed strategy.

Observer-based dynamical pattern recognition via deterministic learning

In this paper, based on the sampled-data observer and the deterministic learning theory, a rapid dynamical pattern recognition approach is proposed for univariate time series composed of the output signals of the dynamical systems. Specifically, locally-accurate identification of inherent dynamics of univariate time series is first achieved by using the sampled-data observer and the radial basis function (RBF) networks. The dynamical estimators embedded with the learned knowledge are then designed by resorting to the sampled-data observer. It is proved that generated estimator residuals can reflect the difference between the system dynamics of the training and test univariate time series. Finally, a recognition decision-making scheme is proposed based on the residual norms of the dynamical estimators. Through rigorous analysis, recognition conditions are given to guarantee the accurate recognition of the dynamical pattern of the test univariate time series. The significance of this paper lies in that the difficult problems of dynamical modeling and rapid recognition for univariate time series are solved by incorporating the sampled-data observer design and the deterministic learning theory. The effectiveness of the proposed approach is confirmed by a numerical example and compressor stall warning experiments.

Intelligent decision support tool for optimizing stochastic inventory systems under uncertainty

Pricing and production policies play a key role in ensuring the added value of supply chain systems. For perishable inventory management, the pricing and production lines must be manipulated dynamically since several uncertainties are involved in the system’s behavior. This study discusses the impact of dynamic pricing and production policies on an uncertain stochastic inventory system with perishable products. The mathematical model of the inventory management system under external disturbance is formulated using a continuous differential equation in which the price and production rates are considered as control factors to optimize total profits, which is described as an objective function. An analytical solution for the optimal pricing and production rate was obtained using the Hamilton-Jacobi-Bellman equation. The unknown disturbance was approximated using an intelligent approach called radial basis function neural network. Finally, extensive numerical simulations were presented to validate the theoretical results and optimization solutions (including the efficiency of the approximation of the unknown disturbance) for the dynamic pricing and production management strategy of an uncertain stochastic inventory system against volatile markets. The performance of the proposed method was analyzed under different stock level conditions, which highlighted the importance of keeping the inventory levels at an optimal range to ensure the profitability of business operations. This management strategy can assist a business with solutions for inventory policies while supporting decision-making processes to facilitate coping with production management disruptions.

A Radial Basis Function Neural Network for Stochastic Frontier Analyses of General Multivariate Production and Cost Functions

Production function techniques often impose functional form and other restrictions that limit their applicability. One common limitation in popular production function techniques is the requirement that all inputs and outputs must be positive numbers. There is a need to develop a production function analysis technique that is less restrictive in the assumptions it makes, and inputs it can process. This paper proposes such a general technique by linking fields of neural networks and econometrics. Specifically, two radial basis function (RBF) neural networks are proposed for stochastic production and cost frontier analyses. The functional forms of production and cost functions are considered unknown except that they are multivariate. Using simulated and real-world datasets, experiments are performed, and results are provided. The results illustrate that the proposed technique has broad applicability and performs equal to or better than the traditional stochastic frontier analysis technique.

Gradient Descent-Barzilai Borwein-Based Neural Network Tracking Control for Nonlinear Systems With Unknown Dynamics

In this article, a combined gradient descent-Barzilai Borwein (GD-BB) algorithm and radial basis function neural network (RBFNN) output tracking control strategy was proposed for a family of nonlinear systems with unknown drift function and control input gain function. In such a method, a neural network (NN) is used to approximate the controller directly. The main merits of the proposed strategy are given as follows: first, not only the NN parameters, such as weights, centers, and widths but also the learning rates of NN parameter updating laws are updated online via the proposed learning algorithm based on Barzilai-Borwein technique; and second, the controller design process can be further simplified, the controller parameters that should be tuned can be greatly reduced. Theoretical analysis about the stability of the closed-loop system is manifested. In addition, simulations were conducted on a numerical discrete time system and an inverted pendulum system to validate the presented control strategy.

Constrained attitude tracking control and active sloshing suppression for liquid-filled spacecraft

This paper is concerned with the attitude tracking control problem of liquid-filled spacecraft with large liquid sloshing. In existing work, the force and torque generated by liquid sloshing are usually treated as external disturbances which are assumed not coupled with spacecraft states and slow-varying. This assumption is inconsistent with the situation of large liquid sloshing. Besides, no special measures are taken to suppress liquid sloshing. In this paper, a novel constrained attitude tracking control and active sloshing suppression scheme is proposed, which considers the force and torque generated by liquid sloshing as nonlinear functions of spacecraft states and suppresses liquid sloshing by limiting the magnitudes of angular velocity, control torque and its changing rate. Three filters and two auxiliary subsystems are constructed to deal with state and input constraints. A neural network is employed to approximate the torque and force caused by liquid sloshing and a nonlinear disturbance observer is designed to estimate the external disturbance. The proposed constrained attitude control method is independent of modeling accuracy, uses only easily measurable feedback signals and does not require high computational cost.

Cerebellum as a kernel machine: A novel perspective on expansion recoding in granule cell layer

Sensorimotor information provided by mossy fibers (MF) is mapped to high-dimensional space by a huge number of granule cells (GrC) in the cerebellar cortex's input layer. Significant studies have demonstrated the computational advantages and primary contributor of this expansion recoding. Here, we propose a novel perspective on the expansion recoding where each GrC serve as a kernel basis function, thereby the cerebellum can operate like a kernel machine that implicitly use high dimensional (even infinite) feature spaces. We highlight that the generation of kernel basis function is indeed biologically plausible scenario, considering that the key idea of kernel machine is to memorize important input patterns. We present potential regimes for developing kernels under constrained resources and discuss the advantages and disadvantages of each regime using various simulation settings.

Use RBF as a Sampling Method in Multistart Global Optimization Method

In this paper, a new sampling technique is proposed that can be used in the Multistart global optimization technique as well as techniques based on it. The new method takes a limited number of samples from the objective function and then uses them to train an Radial Basis Function (RBF) neural network. Subsequently, several samples were taken from the artificial neural network this time, and those with the smallest network value in them are used in the global optimization method. The proposed technique was applied to a wide range of objective functions from the relevant literature and the results were extremely promising.