Optimized ensemble deep learning framework for scalable forecasting of dynamics containing extreme events

Extreme events in the Higgs oscillator: A dynamical study and forecasting approach

Many dynamical systems exhibit unexpected large amplitude excursions in the chronological progression of a state variable. In the present work, we consider the dynamics associated with the one-dimensional Higgs oscillator, which is realized through gnomonic projection of a harmonic oscillator defined on a spherical space of constant curvature onto a Euclidean plane, which is tangent to the spherical space. While studying the dynamics of such a Higgs oscillator subjected to damping and an external forcing, various bifurcation phenomena, such as symmetry breaking, period doubling, and intermittency crises are encountered. As the driven parameter increases, the route to chaos takes place via intermittency crisis, and we also identify the occurrence of extreme events due to the interior crisis. The study of probability distribution also confirms the occurrence of extreme events. Finally, we train the long short-term memory neural network model with the time-series data to forecast extreme events.

Time-series-analysis-based detection of critical transitions in real-world non-autonomous systems

Real-world non-autonomous systems are open, out-of-equilibrium systems that evolve in and are driven by temporally varying environments. Such systems can show multiple timescale and transient dynamics together with transitions to very different and, at times, even disastrous dynamical regimes. Since such critical transitions disrupt the systems' intended or desired functionality, it is crucial to understand the underlying mechanisms, to identify precursors of such transitions, and to reliably detect them in time series of suitable system observables to enable forecasts. This review critically assesses the various steps of investigation involved in time-series-analysis-based detection of critical transitions in real-world non-autonomous systems: from the data recording to evaluating the reliability of offline and online detections. It will highlight pros and cons to stimulate further developments, which would be necessary to advance understanding and forecasting nonlinear behavior such as critical transitions in complex systems.

Extreme rotational events in a forced-damped nonlinear pendulum

Since Galileo's time, the pendulum has evolved into one of the most exciting physical objects in mathematical modeling due to its vast range of applications for studying various oscillatory dynamics, including bifurcations and chaos, under various interests. This well-deserved focus aids in comprehending various oscillatory physical phenomena that can be reduced to the equations of the pendulum. The present article focuses on the rotational dynamics of the two-dimensional forced-damped pendulum under the influence of the ac and dc torque. Interestingly, we are able to detect a range of the pendulum's length for which the angular velocity exhibits a few intermittent extreme rotational events that deviate significantly from a certain well-defined threshold. The statistics of the return intervals between these extreme rotational events are supported by our data to be spread exponentially at a specific pendulum's length beyond which the external dc and ac torque are no longer sufficient for a full rotation around the pivot. The numerical results show a sudden increase in the size of the chaotic attractor due to interior crisis, which is the source of instability that is responsible for triggering large amplitude events in our system. We also notice the occurrence of phase slips with the appearance of extreme rotational events when the phase difference between the instantaneous phase of the system and the externally applied ac torque is observed.

Annotation-free glioma grading from pathological images using ensemble deep learning

Glioma grading is critical for treatment selection, and the fine classification between glioma grades II and III is still a pathological challenge. Traditional systems based on a single deep learning (DL) model can only show relatively low accuracy in distinguishing glioma grades II and III. Introducing ensemble DL models by combining DL and ensemble learning techniques, we achieved annotation-free glioma grading (grade II or III) from pathological images. We established multiple tile-level DL models using residual network ResNet-18 architecture and then used DL models as component classifiers to develop ensemble DL models to achieve patient-level glioma grading. Whole-slide images of 507 subjects with low-grade glioma (LGG) from the Cancer Genome Atlas (TCGA) were included. The 30 DL models exhibited an average area under the curve (AUC) of 0.7991 in patient-level glioma grading. Single DL models showed large variation, and the median between-model cosine similarity was 0.9524, significantly smaller than the threshold of 1.0. The ensemble model based on logistic regression (LR) methods with a 14-component DL classifier (LR-14) demonstrated a mean patient-level accuracy and AUC of 0.8011 and 0.8945, respectively. Our proposed LR-14 ensemble DL model achieved state-of-the-art performance in glioma grade II and III classifications based on unannotated pathological images.

Extreme transient dynamics

We study the extreme transient dynamics of four self-excited pendula coupled via the movable beam. A slight difference in the pendula lengths induces the appearance of traveling phase behavior, within which the oscillators synchronize, but the phases between the nodes change in time. We discuss various scenarios of traveling states (involving different pendula) and their properties, comparing them with classical synchronization patterns of phase-locking. The research investigates the problem of transient dynamics preceding the stabilization of the network on a final synchronous attractor, showing that the width of transient windows can become extremely long. The relation between the behavior of the system within the transient regime and its initial conditions is examined and described. Our results include both identical and non-identical pendula masses, showing that the distribution of the latter ones is related to the transients. The research performed in this paper underlines possible transient problems occurring during the analysis of the systems when the slow evolution of the dynamics can be misinterpreted as the final behavior.

Extreme events in a complex network: Interplay between degree distribution and repulsive interaction

The role of topological heterogeneity in the origin of extreme events in a network is investigated here. The dynamics of the oscillators associated with the nodes are assumed to be identical and influenced by mean-field repulsive interactions. An interplay of topological heterogeneity and the repulsive interaction between the dynamical units of the network triggers extreme events in the nodes when each node succumbs to such events for discretely different ranges of repulsive coupling. A high degree node is vulnerable to weaker repulsive interactions, while a low degree node is susceptible to stronger interactions. As a result, the formation of extreme events changes position with increasing strength of repulsive interaction from high to low degree nodes. Extreme events at any node are identified with the appearance of occasional large-amplitude events (amplitude of the temporal dynamics) that are larger than a threshold height and rare in occurrence, which we confirm by estimating the probability distribution of all events. Extreme events appear at any oscillator near the boundary of transition from rotation to libration at a critical value of the repulsive coupling strength. To explore the phenomenon, a paradigmatic second-order phase model is used to represent the dynamics of the oscillator associated with each node. We make an annealed network approximation to reduce our original model and, thereby, confirm the dual role of the repulsive interaction and the degree of a node in the origin of extreme events in any oscillator associated with a node.

Deep learning for Covid-19 forecasting: State-of-the-art review

The Covid-19 pandemic has galvanized scientists to apply machine learning methods to help combat the crisis. Despite the significant amount of research there exists no comprehensive survey devoted specifically to examining deep learning methods for Covid-19 forecasting. In this paper, we fill the gap in the literature by reviewing and analyzing the current studies that use deep learning for Covid-19 forecasting. In our review, all published papers and preprints, discoverable through Google Scholar, for the period from Apr 1, 2020 to Feb 20, 2022 which describe deep learning approaches to forecasting Covid-19 were considered. Our search identified 152 studies, of which 53 passed the initial quality screening and were included in our survey. We propose a model-based taxonomy to categorize the literature. We describe each model and highlight its performance. Finally, the deficiencies of the existing approaches are identified and the necessary improvements for future research are elucidated. The study provides a gateway for researchers who are interested in forecasting Covid-19 using deep learning.

Time series forecasting for tuberculosis incidence employing neural network models

Every effort aimed at stopping the expansion of Tuberculosis is important to national programs' struggle to combat this disease. Different computational tools have been proposed in order to design new strategies that allow managing potential patients and thus providing the correct treatment. In this work, artificial neural networks were used for time series forecasting, which were trained with information on reported cases obtained from the national vigilance institution in Colombia. Three neural models were proposed in order to determine the best one according to their forecasting performance. The first approach employed a nonlinear autoregressive model, the second proposal used a recurrent neural network, and the third proposal was based on radial basis functions. The results are presented in terms of the mean average percentage error, which indicates that the models based on traditional methods show better performance compared to connectionist ones. These models contribute to obtaining dynamic information about incidence, thus providing extra-help for health authorities to propose more strategies to control the disease's spread.

Role of assortativity in predicting burst synchronization using echo state network

In this study, we use a reservoir computing based echo state network (ESN) to predict the collective burst synchronization of neurons. Specifically, we investigate the ability of ESN in predicting the burst synchronization of an ensemble of Rulkov neurons placed on a scale-free network. We have shown that a limited number of nodal dynamics used as input in the machine can capture the real trend of burst synchronization in this network. Further, we investigate the proper selection of nodal inputs of degree-degree (positive and negative) correlated networks. We show that for a disassortative network, selection of different input nodes based on degree has no significant role in the machine's prediction. However, in the case of assortative network, training the machine with the information (i.e., time series) of low degree nodes gives better results in predicting the burst synchronization. The results are found to be consistent with the investigation carried out with a continuous time Hindmarsh-Rose neuron model. Furthermore, the role of hyperparameters like spectral radius and leaking parameter of ESN on the prediction process has been examined. Finally, we explain the underlying mechanism responsible for observing these differences in the prediction in a degree correlated network.

Data driven soliton solution of the nonlinear Schrödinger equation with certain P T-symmetric potentials via deep learning

We investigate the physics informed neural network method, a deep learning approach, to approximate soliton solution of the nonlinear Schrödinger equation with parity time symmetric potentials. We consider three different parity time symmetric potentials, namely, Gaussian, periodic, and Rosen-Morse potentials. We use the physics informed neural network to solve the considered nonlinear partial differential equation with the above three potentials. We compare the predicted result with the actual result and analyze the ability of deep learning in solving the considered partial differential equation. We check the ability of deep learning in approximating the soliton solution by taking the squared error between real and predicted values. Further, we examine the factors that affect the performance of the considered deep learning method with different activation functions, namely, ReLU, sigmoid, and tanh. We also use a new activation function, namely, sech, which is not used in the field of deep learning, and analyze whether this new activation function is suitable for the prediction of soliton solution of the nonlinear Schrödinger equation for the aforementioned parity time symmetric potentials. In addition to the above, we present how the network's structure and the size of the training data influence the performance of the physics informed neural network. Our results show that the constructed deep learning model successfully approximates the soliton solution of the considered equation with high accuracy.