Related papers: CoPhy-PGNN: Learning Physics-guided Neural Network…
Combining machine learning with physics is a trending approach for discovering unknown dynamics, and one of the most intensively studied frameworks is the physics-informed neural network (PINN). However, PINN often fails to optimize the…
Physics-Informed Neural Networks (PINNs) have become a promising research direction in the field of solving Partial Differential Equations (PDEs). Dealing with singular perturbation problems continues to be a difficult challenge in the…
Physics-informed neural networks (PINNs) have garnered significant interest for their potential in solving partial differential equations (PDEs) that govern a wide range of physical phenomena. By incorporating physical laws into the…
The application of deep learning methods to speed up the resolution of challenging power flow problems has recently shown very encouraging results. However, power system dynamics are not snap-shot, steady-state operations. These dynamics…
Physics-Informed Neural Networks (PINNs) are a class of deep neural networks that are trained, using automatic differentiation, to compute the response of systems governed by partial differential equations (PDEs). The training of PINNs is…
Neural networks, especially the recent proposed neural operator models, are increasingly being used to find the solution operator of differential equations. Compared to traditional numerical solvers, they are much faster and more efficient…
Physics-informed neural networks (PINNs) and their variants have been very popular in recent years as algorithms for the numerical simulation of both forward and inverse problems for partial differential equations. This article aims to…
The computational demands of deep learning motivate the investigation of alternative approaches to computation. One alternative is physical neural networks~(PNNs), in which learning and inference are performed directly via physical…
Given their ability to effectively learn non-linear mappings and perform fast inference, deep neural networks (NNs) have been proposed as a viable alternative to traditional simulation-driven approaches for solving high-dimensional…
Neural networks can be used to learn the solution of partial differential equations (PDEs) on arbitrary domains without requiring a computational mesh. Common approaches integrate differential operators in training neural networks using a…
The utilization of Deep Neural Networks (DNNs) in physical science and engineering applications has gained traction due to their capacity to learn intricate functions. While large datasets are crucial for training DNN models in fields like…
Physics-informed neural networks (PINNs) train a single neural approximation by minimizing multiple physics- and data-derived losses, but the gradients of these losses often interfere and can stall optimization. Existing remedies typically…
Physics-informed neural networks (PINNs) have emerged as promising surrogate modes for solving partial differential equations (PDEs). Their effectiveness lies in the ability to capture solution-related features through neural networks.…
Graph Neural Networks (GNNs) are a powerful representational tool for solving problems on graph-structured inputs. In almost all cases so far, however, they have been applied to directly recovering a final solution from raw inputs, without…
Energy-based models, a.k.a. energy networks, perform inference by optimizing an energy function, typically parametrized by a neural network. This allows one to capture potentially complex relationships between inputs and outputs. To learn…
The Physics-Informed Neural Network (PINN) approach is a new and promising way to solve partial differential equations using deep learning. The $L^2$ Physics-Informed Loss is the de-facto standard in training Physics-Informed Neural…
Physics-informed neural networks (PINNs) have shown remarkable prospects in solving forward and inverse problems involving partial differential equations (PDEs). However, PINNs still face the challenge of high computational cost in solving…
Physics-informed neural networks (PINNs) commonly address ill-posed inverse problems by uncovering unknown physics. This study presents a novel unsupervised learning framework that identifies spatial subdomains with specific governing…
Physics Informed Machine Learning has emerged as a popular approach for modeling and simulation in digital twins, enabling the generation of accurate models of processes and behaviors in real-world systems. However, existing methods either…
A physics-informed neural network (PINN) uses physics-augmented loss functions, e.g., incorporating the residual term from governing partial differential equations (PDEs), to ensure its output is consistent with fundamental physics laws.…