Related papers: Adaptive Physics-Informed Neural Networks for Mark…

In this paper we develop a neural network for the numerical simulation of time-dependent linear transport equations with diffusive scaling and uncertainties. The goal of the network is to resolve the computational challenges of…

Model Predictive Control (MPC) is a method to control nonlinear systems with guaranteed stability and constraint satisfaction but suffers from high computation times. Approximate MPC (AMPC) with neural networks (NNs) has emerged to address…

This research presents the development of an innovative algorithm tailored for the adaptive sampling of residual points within the framework of Physics-Informed Neural Networks (PINNs). By addressing the limitations inherent in existing…

Approximate model-predictive control (AMPC) aims to imitate an MPC's behavior with a neural network, removing the need to solve an expensive optimization problem at runtime. However, during deployment, the parameters of the underlying MPC…

Physics-informed neural networks (PINNs) effectively embed physical principles into machine learning, but often struggle with complex or alternating geometries. We propose a novel method for integrating geometric transformations within…

Physics-informed Neural Network (PINN) is a promising tool that has been applied in a variety of physical phenomena described by partial differential equations (PDE). However, it has been observed that PINNs are difficult to train in…

Physics-Informed Neural Networks (PINNs) have recently been proposed to solve scientific and engineering problems, where physical laws are introduced into neural networks as prior knowledge. With the embedded physical laws, PINNs enable the…

Physics-Informed Neural Networks (PINNs) have emerged recently as a promising application of deep neural networks to the numerical solution of nonlinear partial differential equations (PDEs). However, it has been recognized that adaptive…

Physics-informed neural networks (PINN) is a machine learning (ML)-based method to solve partial differential equations that has gained great popularity due to the fast development of ML libraries in the last few years. The…

The physics informed neural networks (PINNs) has been widely utilized to numerically approximate PDE problems. While PINNs has achieved good results in producing solutions for many partial differential equations, studies have shown that it…

Bayesian Physics Informed Neural Networks (BPINN) have attracted considerable attention for inferring the system states and physical parameters of differential equations according to noisy observations. However, in practice, Hamiltonian…

Physics-informed neural networks (PINNs) are revolutionizing science and engineering practice by bringing together the power of deep learning to bear on scientific computation. In forward modeling problems, PINNs are meshless partial…

Physics-informed neural networks (PINNs) integrate fundamental physical principles with advanced data-driven techniques, driving significant advancements in scientific computing. However, PINNs face persistent challenges with stiffness in…

Parameter estimation remains a challenging task across many areas of engineering. Because data acquisition can often be costly, limited, or prone to inaccuracies (noise, uncertainty) it is crucial to identify sensor configurations that…

The numerical approximation of partial differential equations (PDEs) using neural networks has seen significant advancements through Physics-Informed Neural Networks (PINNs). Despite their straightforward optimization framework and…

Physics-Informed Neural Networks (PINN) are a machine learning tool that can be used to solve direct and inverse problems related to models described by Partial Differential Equations. This paper proposes an adaptive inverse PINN applied to…

In the following article we consider approximate Bayesian parameter inference for observation driven time series models. Such statistical models appear in a wide variety of applications, including econometrics and applied mathematics. This…

Numerical modeling errors are unavoidable in finite element analysis. The presence of model errors inherently reflects both model accuracy and uncertainty. To date there have been few methods for explicitly quantifying errors at points of…

Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving partial differential equations (PDEs) by embedding the governing physics into the loss function associated with a deep neural network. In this work, a…

Physics-Informed Neural Networks (PINNs) have emerged as a tool for approximating the solution of Partial Differential Equations (PDEs) in both forward and inverse problems. PINNs minimize a loss function which includes the PDE residual…