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Physics-informed neural networks (PINNs) are able to solve partial differential equations (PDEs) by incorporating the residuals of the PDEs into their loss functions. Variational Physics-Informed Neural Networks (VPINNs) and hp-VPINNs use…

Partial differential equations (PDEs) are central to scientific modeling. Modern workflows increasingly rely on learning-based components to support model reuse, inference, and integration across large computational processes. Despite the…

The use of deep learning methods in scientific computing represents a potential paradigm shift in engineering problem solving. One of the most prominent developments is Physics-Informed Neural Networks (PINNs), in which neural networks are…

In the field of pharmacokinetics and pharmacodynamics (PKPD) modeling, which plays a pivotal role in the drug development process, traditional models frequently encounter difficulties in fully encapsulating the complexities of drug…

We formulate and study a class of two-player zero-sum stochastic dynamic games with partial and asymmetric information. Information asymmetry introduces fundamental challenges involving \emph{belief representation} and \emph{theory of mind}…

Partial differential equations (PDEs) provide a mathematical foundation for simulating and understanding intricate behaviors in both physical sciences and engineering. With the growing capabilities of deep learning, data$-$driven approaches…

In this study, we propose a new numerical scheme for physics-informed neural networks (PINNs) that enables precise and inexpensive solution for partial differential equations (PDEs) in case of arbitrary geometries while strictly enforcing…

In this paper, numerical methods using Physics-Informed Neural Networks (PINNs) are presented with the aim to solve higher-order ordinary differential equations (ODEs). Indeed, this deep-learning technique is successfully applied for…

The physics-informed neural network (PINN) is effective in solving the partial differential equation (PDE) by capturing the physics constraints as a part of the training loss function through the Automatic Differentiation (AD). This study…

Inferring biophysical parameters and hidden state variables from partial and noisy observations is a fundamental challenge in computational neuroscience. This problem is particularly difficult for fast - slow spiking and bursting models,…

In this study, we introduce a method based on Separable Physics-Informed Neural Networks (SPINNs) for effectively solving the BGK model of the Boltzmann equation. While the mesh-free nature of PINNs offers significant advantages in handling…

Throughout many fields, practitioners often rely on differential equations to model systems. Yet, for many applications, the theoretical derivation of such equations and/or accurate resolution of their solutions may be intractable. Instead,…

This paper presents a comprehensive review of the design of experiments used in the surrogate models. In particular, this study demonstrates the necessity of the design of experiment schemes for the Physics-Informed Neural Network (PINN),…

Policy gradient methods enjoy strong practical performance in numerous tasks in reinforcement learning. Their theoretical understanding in multiagent settings, however, remains limited, especially beyond two-player competitive and potential…

We study the numerical approximation of a time-dependent variational mean field game system with local couplings and either periodic or Neumann boundary conditions. Following a variational approach, we employ a finite difference…

Physics-Informed Neural Networks (PINNs) recast PDE solving as an optimisation problem in function space by minimising a residual-based objective, yet many applications require additional derivative-based relations that are just as…

Physics-Informed Neural Networks (PINN) has evolved into a powerful tool for solving partial differential equations, which has been applied to various fields such as energy, environment, en-gineering, etc. When utilizing PINN to solve…

We study a class of two-player zero-sum stochastic games known as \textit{blind stochastic games}, where players neither observe the state nor receive any information about it during the game. A central concept for analyzing long-duration…

We consider a stochastic differential game in the context of forward-backward stochastic differential equations, where one player implements an impulse control while the opponent controls the system continuously. Utilizing the notion of…

Accurately simulating systems governed by PDEs, such as voltage fields in cardiac electrophysiology (EP) modelling, remains a significant modelling challenge. Traditional numerical solvers are computationally expensive and sensitive to…