Related papers: PAS-Net: Physics-informed Adaptive Scale Deep Oper…

Physics-informed neural networks (PINNs) have attracted attention as an alternative approach to solve partial differential equations using a deep neural network (DNN). Their simplicity and capability allow them to solve inverse problems for…

The physics informed neural network (PINN) is a promising method for solving time-evolution partial differential equations (PDEs). However, the standard PINN method may fail to solve the PDEs with strongly nonlinear characteristics or those…

We present our progress on the application of physics informed deep learning to reservoir simulation problems. The model is a neural network that is jointly trained to respect governing physical laws and match boundary conditions. The…

Deep neural networks that approximate nonlinear function-to-function mappings, i.e., operators, which are called DeepONet, have been demonstrated in recent articles to be capable of encoding entire PDE control methodologies, such as…

Neural surrogates for stiff differential-algebraic equations (DAEs) face two barriers: soft-constraint methods leave algebraic residuals that stiffness amplifies into errors, and hard-constraint methods require trajectory data from stiff…

Regular physics-informed neural networks (PINNs) predict the solution of partial differential equations using sparse labeled data but only over a single domain. On the other hand, fully supervised learning models are first trained usually…

Neural network based data-driven operator learning schemes have shown tremendous potential in computational mechanics. DeepONet is one such neural network architecture which has gained widespread appreciation owing to its excellent…

The fundamental computational issues in Bayesian inverse problems (BIP) governed by partial differential equations (PDEs) stem from the requirement of repeated forward model evaluations. A popular strategy to reduce such costs is to replace…

In recent years, the researches about solving partial differential equations (PDEs) based on artificial neural network have attracted considerable attention. In these researches, the neural network models are usually designed depend on…

Data-driven models for predicting dynamic responses of linear and nonlinear systems are of great importance due to their wide application from probabilistic analysis to inverse problems such as system identification and damage diagnosis. In…

Physics-informed neural networks (PINNs) have been widely applied in different fields due to their effectiveness in solving partial differential equations (PDEs). However, the accuracy and efficiency of PINNs need to be considerably…

Accurate temporal extrapolation remains a fundamental challenge for neural operators modeling dynamical systems, where predictions must extend far beyond the training horizon. Conventional DeepONet approaches rely on two limited paradigms:…

In this study, we investigate how the updating of weights during forward operation and the computation of gradients during backpropagation impact the optimization process, training procedure, and overall performance of the neural network,…

In the pursuit of accurate experimental and computational data while minimizing effort, there is a constant need for high-fidelity results. However, achieving such results often requires significant computational resources. To address this…

This work proposes a wavelet-based physics-informed quantum neural network framework to efficiently address multiscale partial differential equations that involve sharp gradients, stiffness, rapid local variations, and highly oscillatory…

This work demonstrates that neural operator learning provides a powerful and flexible framework for building fast, accurate emulators of moving boundary systems, enabling their integration into digital twin platforms. To this end, a Deep…

Recent studies have demonstrated the success of deep learning in solving forward and inverse problems in engineering and scientific computing domains, such as physics-informed neural networks (PINNs). Source inversion problems under sparse…

Deep neural networks (DNNs) have been widely applied to solve real-world regression problems. However, selecting optimal network structures remains a significant challenge. This study addresses this issue by linking neuron selection in DNNs…

Deep learning has been shown to be an effective tool in solving partial differential equations (PDEs) through physics-informed neural networks (PINNs). PINNs embed the PDE residual into the loss function of the neural network, and have been…

Physics-informed neural networks (PINNs) have recently emerged as a promising way to compute the solutions of partial differential equations (PDEs) using deep neural networks. However, despite their significant success in various fields, it…