Related papers: Physics-informed deep learning and compressive col…

Deep operator networks (DeepONets) represent a powerful class of data-driven methods for operator learning, demonstrating strong approximation capabilities for a wide range of linear and nonlinear operators. They have shown promising…

We consider the approximation of initial/boundary value problems involving, possibly high-dimensional, dissipative evolution partial differential equations (PDEs) using a deep neural network framework. More specifically, we first propose…

In this work, we study physics-informed neural networks (PINNs) constrained by partial differential equations (PDEs) and their application in approximating PDEs with two characteristic scales. From a continuous perspective, our formulation…

In this paper, we study the linear transport model by adopting the deep learning method, in particular the deep neural network (DNN) approach. While the interest of using DNN to study partial differential equations is arising, here we adapt…

We present the partial evolutionary tensor neural networks (pETNNs), a novel framework for solving time-dependent partial differential equations with high accuracy and capable of handling high-dimensional problems. Our architecture…

A recent paper by Davies et al (2021) describes how deep learning (DL) technology was used to find plausible hypotheses that have led to two original mathematical results: one in knot theory, one in representation theory. I argue here that…

In this paper, we construct approximated solutions of Differential Equations (DEs) using the Deep Neural Network (DNN). Furthermore, we present an architecture that includes the process of finding model parameters through experimental data,…

Spectral methods are an important part of scientific computing's arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the…

Numerical experiments indicate that deep learning algorithms overcome the curse of dimensionality when approximating solutions of semilinear PDEs. For certain linear PDEs and semilinear PDEs with gradient-independent nonlinearities this has…

In this paper we establish a connection between non-convex optimization methods for training deep neural networks and nonlinear partial differential equations (PDEs). Relaxation techniques arising in statistical physics which have already…

Recent work in deep learning focuses on solving physical systems in the Ordinary Differential Equation or Partial Differential Equation. This current work proposed a variant of Convolutional Neural Networks (CNNs) that can learn the hidden…

Physics-informed neural networks (PINNs) have been demonstrated to be efficient in solving partial differential equations (PDEs) from a variety of experimental perspectives. Some recent studies have also proposed PINN algorithms for PDEs on…

In an ever expanding set of research and application areas, deep neural networks (DNNs) set the bar for algorithm performance. However, depending upon additional constraints such as processing power and execution time limits, or…

Deep neural networks (DNNs), especially physics-informed neural networks (PINNs), have recently become a new popular method for solving forward and inverse problems governed by partial differential equations (PDEs). However, these methods…

Deep learning (DL) relies heavily on data, and the quality of data influences its performance significantly. However, obtaining high-quality, well-annotated datasets can be challenging or even impossible in many real-world applications,…

Recently, researchers have utilized neural networks to accurately solve partial differential equations (PDEs), enabling the mesh-free method for scientific computation. Unfortunately, the network performance drops when encountering a high…

In certain practical engineering applications, there is an urgent need to perform repetitive solving of partial differential equations (PDEs) in a short period. This paper primarily considers three scenarios requiring extensive repetitive…

Simulation of multiphase flow in porous media is crucial for the effective management of subsurface energy and environment related activities. The numerical simulators used for modeling such processes rely on spatial and temporal…

In this paper, we introduce Deep Probabilistic Ensembles (DPEs), a scalable technique that uses a regularized ensemble to approximate a deep Bayesian Neural Network (BNN). We do so by incorporating a KL divergence penalty term into the…

We present a novel framework combining Deep Operator Networks (DeepONets) with Physics-Informed Neural Networks (PINNs) to solve partial differential equations (PDEs) and estimate their unknown parameters. By integrating data-driven…