Related papers: Physics-Informed Neural Network Policy Iteration: …
We propose and analyze a numerical algorithm for solving a class of optimal control problems for learning-informed semilinear partial differential equations. The latter is a class of PDEs with constituents that are in principle unknown and…
This study investigates the potential accuracy boundaries of physics-informed neural networks, contrasting their approach with previous similar works and traditional numerical methods. We find that selecting improved optimization algorithms…
In recent years, Scientific Machine Learning (SciML) methods for solving partial differential equations (PDEs) have gained increasing popularity. Within such a paradigm, Physics-Informed Neural Networks (PINNs) are novel deep learning…
We propose the first learning scheme for functional differential equations (FDEs). FDEs play a fundamental role in physics, mathematics, and optimal control. However, the numerical analysis of FDEs has faced challenges due to its…
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…
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,…
Predicting outcomes and planning interactions with the physical world are long-standing goals for machine learning. A variety of such tasks involves continuous physical systems, which can be described by partial differential equations…
Quantum control is a ubiquitous research field that has enabled physicists to delve into the dynamics and features of quantum systems, delivering powerful applications for various atomic, optical, mechanical, and solid-state systems. In…
Physics-Informed Neural Networks (PINNs) are a powerful class of numerical solvers for partial differential equations, employing deep neural networks with successful applications across a diverse set of problems. However, their…
Physics-Informed Neural Networks (PINNs) have been widely used to obtain solutions to various physical phenomena modeled as Differential Equations. As PINNs are not naturally equipped with mechanisms for Uncertainty Quantification, some…
We study sparse solutions of optimal control problems governed by PDEs with uncertain coefficients. We propose two formulations, one where the solution is a deterministic control optimizing the mean objective, and a formulation aiming at…
Deep learning methods have gained considerable interest in the numerical solution of various partial differential equations (PDEs). One particular focus is physics-informed neural networks (PINN), which integrate physical principles into…
We prove a priori and a posteriori error estimates for physics-informed neural networks (PINNs) for linear PDEs. We analyze elliptic equations in primal and mixed form, elasticity, parabolic, hyperbolic and Stokes equations; and a PDE…
We investigate the inverse problem for Partial Differential Equations (PDEs) in scenarios where the parameters of the given PDE dynamics may exhibit changepoints at random time. We employ Physics-Informed Neural Networks (PINNs) - universal…
We propose a physics-informed neural networks (PINNs) framework to solve the infinite-horizon optimal control problem of nonlinear systems. In particular, since PINNs are generally able to solve a class of partial differential equations…
We propose new machine learning schemes for solving high dimensional nonlinear partial differential equations (PDEs). Relying on the classical backward stochastic differential equation (BSDE) representation of PDEs, our algorithms estimate…
Physics-Informed Neural Network (PINN) is a novel multi-task learning framework useful for solving physical problems modeled using differential equations (DEs) by integrating the knowledge of physics and known constraints into the…
We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…
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…
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…