Coupling an agent-based model and an ensemble Kalman filter for real-time crowd modelling

Agent-based modelling has emerged as a powerful tool for modelling systems that are driven by discrete, heterogeneous individuals and has proven particularly popular in the realm of pedestrian simulation. However, real-time agent-based simulations face the challenge that they will diverge from the real system over time. This paper addresses this challenge by integrating the ensemble Kalman filter (EnKF) with an agent-based crowd model to enhance its accuracy in real time. Using the example of Grand Central Station in New York, we demonstrate how our approach can update the state of an agent-based model in real time, aligning it with the evolution of the actual system. The findings reveal that the EnKF can substantially improve the accuracy of agent-based pedestrian simulations by assimilating data as they evolve. This approach not only offers efficiency advantages over existing methods but also presents a more realistic representation of a complex environment than most previous attempts. The potential applications of this method span the management of public spaces under 'normality' to exceptional circumstances such as disaster response, marking a significant advancement for real-time agent-based modelling applications.

Bayesian Data Assimilation of Temperature Dependence of Solid-Liquid Interfacial Properties of Nickel

Temperature dependence of solid–liquid interfacial properties during crystal growth in nickel was investigated by ensemble Kalman filter (EnKF)-based data assimilation, in which the phase-field simulation was combined with atomic configurations of molecular dynamics (MD) simulation. Negative temperature dependence was found in the solid–liquid interfacial energy, the kinetic coefficient, and their anisotropy parameters from simultaneous estimation of four parameters. On the other hand, it is difficult to obtain a concrete value for the anisotropy parameter of solid–liquid interfacial energy since this factor is less influential for the MD simulation of crystal growth at high undercooling temperatures. The present study is significant in shedding light on the high potential of Bayesian data assimilation as a novel methodology of parameter estimation of practical materials an out of equilibrium condition.

KFGRNI: A robust method to inference gene regulatory network from time-course gene data based on ensemble Kalman filter

A central problem of systems biology is the reconstruction of Gene Regulatory Networks (GRNs) by the use of time series data. Although many attempts have been made to design an efficient method for GRN inference, providing a best solution is still a challenging task. Existing noise, low number of samples, and high number of nodes are the main reasons causing poor performance of existing methods. The present study applies the ensemble Kalman filter algorithm to model a GRN from gene time series data. The inference of a GRN is decomposed with p genes into p subproblems. In each subproblem, the ensemble Kalman filter algorithm identifies the weight of interactions for each target gene. With the use of the ensemble Kalman filter, the expression pattern of the target gene is predicted from the expression patterns of all the remaining genes. The proposed method is compared with several well-known approaches. The results of the evaluation indicate that the proposed method improves inference accuracy and demonstrates better regulatory relations with noisy data.

Development and Evaluation of an Ensemble-Based Data Assimilation System for Regional Reanalysis Over the Tibetan Plateau and Surrounding Regions

The Tibetan Plateau is regarded as the Earth's Third Pole, which is the source region of several major rivers that impact more 20% the world population. This high-altitude region is reported to have been undergoing much greater rate of weather changes under global warming, but the existing reanalysis products are inadequate for depicting the state of the atmosphere, particularly with regard to the amount of precipitation and its diurnal cycle. An ensemble Kalman filter (EnKF) data assimilation system based on the limited-area Weather Research and Forecasting (WRF) model was evaluated for use in developing a regional reanalysis over the Tibetan Plateau and the surrounding regions. A 3-month prototype reanalysis over the summer months (June-August) of 2015 using WRF-EnKF at a 30-km grid spacing to assimilate nonradiance observations from the Global Telecommunications System was developed and evaluated against independent sounding and satellite observations in comparison to the ERA-Interim and fifth European Centre for Medium-Range Weather Forecasts Reanalysis (ERA5) global reanalysis. Results showed that both the posterior analysis and the subsequent 6- to 12-hr WRF forecasts of the prototype regional reanalysis compared favorably with independent sounding observations, satellite-based precipitation versus those from ERA-Interim and ERA5 during the same period. In particular, the prototype regional reanalysis had clear advantages over the global reanalyses of ERA-Interim and ERA5 in the analysis accuracy of atmospheric humidity, as well as in the subsequent downscale-simulated precipitation intensity, spatial distribution, diurnal evolution, and extreme occurrence.

Multiple Target Tracking Based on Multiple Hypotheses Tracking and Modified Ensemble Kalman Filter in Multi-Sensor Fusion

In multi-sensor fusion (MSF), the integration of multi-sensor observation data with different observation errors to achieve more accurate positioning of the target has always been a research focus. In this study, a modified ensemble Kalman filter (EnKF) is presented to substitute the traditional Kalman filter (KF) in the multiple hypotheses tracking (MHT) to deal with the high nonlinearity that always shows up in multiple target tracking (MTT) problems. In addition, the multi-source observation data fusion is also realized by using the modified EnKF, which enables the low-precision observation data to be corrected by high-precision observation data, and the accuracy of the corrected data can be calibrated by the statistical information provided by the EnKF. Numerical studies are given to demonstrate the effectiveness of our proposed method and the results show that the MHT-EnKF method can achieve remarkable enhancement in dealing with nonlinear movement variation and positioning accuracy for MTT problems in MSF scenario.

State and Parameter Estimation from Observed Signal Increments

The success of the ensemble Kalman filter has triggered a strong interest in expanding its scope beyond classical state estimation problems. In this paper, we focus on continuous-time data assimilation where the model and measurement errors are correlated and both states and parameters need to be identified. Such scenarios arise from noisy and partial observations of Lagrangian particles which move under a stochastic velocity field involving unknown parameters. We take an appropriate class of McKean-Vlasov equations as the starting point to derive ensemble Kalman-Bucy filter algorithms for combined state and parameter estimation. We demonstrate their performance through a series of increasingly complex multi-scale model systems.

Predictability and identifiability assessment of models for prostate cancer under androgen suppression therapy

The past two decades have seen the development of numerous mathematical models to study various aspects of prostate cancer in clinical settings. These models often contain large sets of parameters and rely on limited data sets for validation. The quantitative analysis of the dynamics of prostate cancer under treatment may be hindered by the lack of identifiability of the parameters from the available data, which limits the predictive ability of the model. Using three ordinary differential equation models as case studies, we carry out a numerical investigation of the identifiability and uncer- tainty quantification of the model parameters. In most cases, the parameters are not identifiable from time series of prostate-specific antigen, which is used as a clinical proxy for tumor progression. It may not be possible to define a finite confidence bound on an unidentifiable parameter, and the relative uncertainties in even identifiable parameters may be large in some cases. The Fisher information ma- trix may be used to determine identifiable parameter subsets for a given model. The use of biological constraints and additional types of measurements, should they become available, may reduce these uncertainties. Ensemble Kalman filtering may provide clinically useful, short-term predictions of pa- tient outcomes from imperfect models, though care must be taken when estimating "patient-specific" parameters. Our results demonstrate the importance of parameter identifiability in the validation and predictive ability of mathematical models of prostate tumor treatment. Observing-system simulation experiments, widely used in meteorology, may prove useful in the development of biomathematical models intended for future clinical application.

Backward sensitivity analysis and reduced-order covariance estimation in noninvasive parameter identification for cerebral arteries

Using a previously developed inversion platform for functional cerebral medical imaging with ensemble Kalman filters, this work analyzes the sensitivity of the results with respect to different parameters entering the physical model and inversion procedure, such as the inlet flow rate from the heart, the choice of the boundary conditions, and the nonsymmetry in the network terminations. It also proposes an alternative low complexity construction for the covariance matrix of the hemodynamic parameters of a network of arteries including the circle of Willis. The platform takes as input patient-specific blood flow rates extracted from magnetic resonance angiography and magnetic resonance imaging (dicom files) and is applied to several available patients data. The paper presents full analysis of the results for one of these patients, including a sensitivity study with respect to the proximal and distal boundary conditions. The results notably show that the uncertainties on the inlet flow rate led to uncertainties of the same order of magnitude in the estimated parameters (blood pressure and elastic parameters) and that three-lumped parameters boundary conditions are necessary for a correct retrieval of the target signals.

Feedback control of an HBV model based on ensemble kalman filter and differential evolution

In this paper, we derive efficient drug treatment strategies for hepatitis B virus (HBV) infection by formulating a feedback control problem. We introduce and analyze a dynamic mathematical model that describes the HBV infection during antiviral therapy. We determine the reproduction number and then conduct a qualitative analysis of the model using the number. A control problem is considered to minimize the viral load with consideration for the treatment costs. In order to reflect the status of patients at both the initial time and the follow-up visits, we consider the feedback control problem based on the ensemble Kalman filter (EnKF) and differential evolution (DE). EnKF is employed to estimate full information of the state from incomplete observation data. We derive a piecewise constant drug schedule by applying DE algorithm. Numerical simulations are performed using various weights in the objective functional to suggest optimal treatment strategies in different situations.

Concrete ensemble Kalman filters with rigorous catastrophic filter divergence

The ensemble Kalman filter and ensemble square root filters are data assimilation methods used to combine high-dimensional, nonlinear dynamical models with observed data. Ensemble methods are indispensable tools in science and engineering and have enjoyed great success in geophysical sciences, because they allow for computationally cheap low-ensemble-state approximation for extremely high-dimensional turbulent forecast models. From a theoretical perspective, the dynamical properties of these methods are poorly understood. One of the central mysteries is the numerical phenomenon known as catastrophic filter divergence, whereby ensemble-state estimates explode to machine infinity, despite the true state remaining in a bounded region. In this article we provide a breakthrough insight into the phenomenon, by introducing a simple and natural forecast model that transparently exhibits catastrophic filter divergence under all ensemble methods and a large set of initializations. For this model, catastrophic filter divergence is not an artifact of numerical instability, but rather a true dynamical property of the filter. The divergence is not only validated numerically but also proven rigorously. The model cleanly illustrates mechanisms that give rise to catastrophic divergence and confirms intuitive accounts of the phenomena given in past literature.