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Physics-informed neural networks (PINNs) have been widely used to solve partial differential equations in a forward and inverse manner using deep neural networks. However, training these networks can be challenging for multiscale problems.…

Physics-informed neural networks (PINNs) provide a framework to build surrogate models for dynamical systems governed by differential equations. During the learning process, PINNs incorporate a physics-based regularization term within the…

Several recent works in scientific machine learning have revived interest in the application of neural networks to partial differential equations (PDEs). A popular approach is to aggregate the residual form of the governing PDE and its…

Physics-Informed Neural Networks (PINNs) show significant potential for solving inverse problems, especially when observations are limited and sparse, provided that the relevant physical equations are known. We use PINNs to estimate smooth…

Physics-Informed Neural Networks (PINNs) have demonstrated considerable success in solving complex fluid dynamics problems. However, their performance often deteriorates in regimes characterized by steep gradients, intricate boundary…

Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding physical laws directly into neural network training. However, solving high-fidelity PDEs remains…

Physics-Informed Neural Networks (PINNs), which incorporate PDEs as soft constraints, train with a composite loss function that contains multiple training point types: different types of collocation points chosen during training to enforce…

In a more connected world, modeling multi-agent systems with hyperbolic partial differential equations (PDEs) offers a compact, physics-consistent description of collective dynamics. However, classical control tools need adaptation for…

Parameter estimation for differential equations from measured data is an inverse problem prevalent across quantitative sciences. Physics-Informed Neural Networks (PINNs) have emerged as effective tools for solving such problems, especially…

In recent years, scientific machine learning, particularly physic-informed neural networks (PINNs), has introduced new innovative methods to understanding the differential equations that describe power system dynamics, providing a more…

In this study, the capabilities of the Physics-Informed Neural Network (PINN) method are investigated for three major tasks: modeling, simulation, and optimization in the context of the heat conduction problem. In the modeling phase, the…

Physics-Informed Neural Networks (PINNs) solve partial differential equations (PDEs) by embedding governing equations and boundary/initial conditions into the loss function. However, enforcing Dirichlet boundary conditions accurately…

Initial boundary value problems arise commonly in applications with engineering and natural systems governed by nonlinear partial differential equations (PDEs). Operator learning is an emerging field for solving these equations by using a…

We consider a subclass of $n$-player stochastic games, in which players have their own internal state/action spaces while they are coupled through their payoff functions. It is assumed that players' internal chains are driven by independent…

Physics-informed neural networks (PINNs) are a promising approach that combines the power of neural networks with the interpretability of physical modeling. PINNs have shown good practical performance in solving partial differential…

We consider the approximation of a class of dynamic partial differential equations (PDE) of second order in time by the physics-informed neural network (PINN) approach, and provide an error analysis of PINN for the wave equation, the…

Optimal and safety-critical control are fundamental problems for stochastic systems, and are widely considered in real-world scenarios such as robotic manipulation and autonomous driving. In this paper, we consider the problem of…

Physics-informed neural networks (PINNs) offer a novel AI-driven framework for integrating physical laws directly into neural network models, facilitating the solution of complex multiphysics problems in materials engineering. This study…

Complex physical systems are often described by partial differential equations (PDEs) that depend on parameters such as the Reynolds number in fluid mechanics. In applications such as design optimization or uncertainty quantification,…

We propose characteristics-informed neural networks (CINN), a simple and efficient machine learning approach for solving forward and inverse problems involving hyperbolic PDEs. Like physics-informed neural networks (PINN), CINN is a…