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  1. We present an efficient probabilistic solver for time-dependent nonlinear partial differential equations.We formulate our method as the maximum a posteriori solver for a constrained risk problem on a reproducing kernel Hilbert space induced by a spatio-temporal Gaussian process prior. We show that for a suitable choice of temporal kernels, the risk objective can be minimized efficiently via a Gauss–Newton algorithm cor- responding to an iterated extended Kalman smoother (IEKS). Furthermore, by leveraging a parallel-in-time implementation of IEKS, our algorithm can take advantage of massively parallel graphical processing units to achieve logarithmic instead of linear scaling with time. We validate our method numerically on popular benchmark problems. 
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    Free, publicly-accessible full text available September 22, 2025
  2. PSO-PINN is a class of algorithms for training physics-informed neural networks (PINN) using particle swarm optimization (PSO). PSO-PINN can mitigate the well-known difficulties presented by gradient descent training of PINNs when dealing with PDEs with irregular solutions. Additionally, PSO-PINN is an ensemble approach to PINN that yields reproducible predictions with quantified uncertainty. In this paper, we introduce Multi-Objective PSO-PINN, which treats PINN training as a multi-objective problem. The proposed multi-objective PSO-PINN represents a new paradigm in PINN training, which thus far has relied on scalarizations of the multi-objective loss function. A full multi-objective approach allows on-the-fly compromises in the trade-off among the various components of the PINN loss function. Experimental results with a diffusion PDE problem demonstrate the promise of this methodology. 
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  3. null (Ed.)
    We present PALLAS, a practical method for gene regulatory network (GRN) inference from time series data, which employs penalized maximum likelihood and particle swarms for optimization. PALLAS is based on the Partially-Observable Boolean Dynamical System (POBDS) model and thus does not require ad-hoc binarization of the data. The penalty in the likelihood is a LASSO regularization term, which encourages the resulting network to be sparse. PALLAS is able to scale to networks of realistic size under no prior knowledge, by virtue of a novel continuous-discrete Fish School Search particle swarm algorithm for efficient simultaneous maximization of the penalized likelihood over the discrete space of networks and the continuous space of observational parameters. The performance of PALLAS is demonstrated by a comprehensive set of experiments using synthetic data generated from real and artificial networks, as well as real time series microarray and RNA-seq data, where it is compared to several other well-known methods for gene regulatory network inference. The results show that PALLAS can infer GRNs more accurately than other methods, while being capable of working directly on gene expression data, without need of ad-hoc binarization. PALLAS is a fully-fledged program, written in python, and available on GitHub (https://github.com/yukuntan92/PALLAS). 
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  4. null (Ed.)

    Mathematical models are widely recognized as an important tool for analyzing and understanding the dynamics of infectious disease outbreaks, predict their future trends, and evaluate public health intervention measures for disease control and elimination. We propose a novel stochastic metapopulation state-space model for COVID-19 transmission, which is based on a discrete-time spatio-temporal susceptible, exposed, infected, recovered, and deceased (SEIRD) model. The proposed framework allows the hidden SEIRD states and unknown transmission parameters to be estimated from noisy, incomplete time series of reported epidemiological data, by application of unscented Kalman filtering (UKF), maximum-likelihood adaptive filtering, and metaheuristic optimization. Experiments using both synthetic data and real data from the Fall 2020 COVID-19 wave in the state of Texas demonstrate the effectiveness of the proposed model.

     
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  6. Background: Single-cell gene expression measurements offer opportunities in deriving mechanistic understanding of complex diseases, including cancer. However, due to the complex regulatory machinery of the cell, gene regulatory network (GRN) model inference based on such data still manifests significant uncertainty. Results:The goal of this paper is to develop optimal classification of single-cell trajectories accounting for potential model uncertainty. Partially-observed Boolean dynamical systems (POBDS) are used for modeling gene regulatory networks observed through noisy gene-expression data. We derive the exact optimal Bayesian classifier (OBC) for binary classification of single-cell trajectories. The application of the OBC becomes impractical for large GRNs, due to computational and memory requirements. To address this, we introduce a particle-based single-cell classification method that is highly scalable for large GRNs with much lower complexity than the optimal solution. Conclusion:The performance of the proposed particle-based method is demonstrated through numerical experiments using a POBDS model of the well-known T-cell large granular lymphocyte (T-LGL) leukemia network with noisy time-series gene-expression 
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  7. We propose a Bayesian decision making framework for control of Markov Decision Processes (MDPs) with unknown dynamics and large, possibly continuous, state, action, and parameter spaces in data-poor environments. Most of the existing adaptive controllers for MDPs with unknown dynamics are based on the reinforcement learning framework and rely on large data sets acquired by sustained direct interaction with the system or via a simulator. This is not feasible in many applications, due to ethical, economic, and physical constraints. The proposed framework addresses the data poverty issue by decomposing the problem into an offline planning stage that does not rely on sustained direct interaction with the system or simulator and an online execution stage. In the offline process, parallel Gaussian process temporal difference (GPTD) learning techniques are employed for near-optimal Bayesian approximation of the expected discounted reward over a sample drawn from the prior distribution of unknown parameters. In the online stage, the action with the maximum expected return with respect to the posterior distribution of the parameters is selected. This is achieved by an approximation of the posterior distribution using a Markov Chain Monte Carlo (MCMC) algorithm, followed by constructing multiple Gaussian processes over the parameter space for efficient prediction of the means of the expected return at the MCMC sample. The effectiveness of the proposed framework is demonstrated using a simple dynamical system model with continuous state and action spaces, as well as a more complex model for a metastatic melanoma gene regulatory network observed through noisy synthetic gene expression data. 
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