Related papers: Hyena Neural Operator for Partial Differential Equ…
Fourier Neural Operators are deep learning models that learn mappings between function spaces and can be used to learn and solve partial differential equations (PDEs), in some cases significantly faster than traditional PDE solvers. Within…
Partial differential equations (PDEs) are indispensable for modeling many physical phenomena and also commonly used for solving image processing tasks. In the latter area, PDE-based approaches interpret image data as discretizations of…
The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy,…
Processing global geometric context while preserving equivariance is crucial when modeling biological, chemical, and physical systems. Yet, this is challenging due to the computational demands of equivariance and global context at scale.…
Numerical simulations of seismic wave propagation in heterogeneous 3D media are central to investigating subsurface structures and understanding earthquake processes, yet are computationally expensive for large problems. This is…
Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks. As promising surrogate solvers of partial differential equations (PDEs) for real-time prediction, deep neural…
In this paper, we propose Neumann Series Neural Operator (NSNO) to learn the solution operator of Helmholtz equation from inhomogeneity coefficients and source terms to solutions. Helmholtz equation is a crucial partial differential…
Fourier Neural Operators (FNO) offer a principled approach to solving challenging partial differential equations (PDE) such as turbulent flows. At the core of FNO is a spectral layer that leverages a discretization-convergent representation…
This study presents a novel unsupervised convolutional Neural Network (NN) architecture with nonlocal interactions for solving Partial Differential Equations (PDEs). The nonlocal Peridynamic Differential Operator (PDDO) is employed as a…
Neural operators (NO) are discretization invariant deep learning methods with functional output and can approximate any continuous operator. NO have demonstrated the superiority of solving partial differential equations (PDEs) over other…
We introduce a practical method to enforce partial differential equation (PDE) constraints for functions defined by neural networks (NNs), with a high degree of accuracy and up to a desired tolerance. We develop a differentiable…
To approximate solutions of complex nonlinear partial differential equations remains a computational challenge, especially for sets of equations relevant in industry, such as Euler or Navier-Stokes equations. Even the most sophisticated…
Recent advances in the theory of Neural Operators (NOs) have enabled fast and accurate computation of the solutions to complex systems described by partial differential equations (PDEs). Despite their great success, current NO-based…
Deep Operator Networks are emerging as fundamental tools among various neural network types to learn mappings between function spaces, and have recently gained attention due to their ability to approximate nonlinear operators. In…
Neural operators, which aim to approximate mappings between infinite-dimensional function spaces, have been widely applied in the simulation and prediction of physical systems. However, the limited representational capacity of network…
We present a novel graph transformer framework, HAMLET, designed to address the challenges in solving partial differential equations (PDEs) using neural networks. The framework uses graph transformers with modular input encoders to directly…
Multiscale modeling is an effective approach for investigating multiphysics systems with largely disparate size features, where models with different resolutions or heterogeneous descriptions are coupled together for predicting the system's…
Deep convolutional neural networks (DCNNs) are a class of artificial neural networks, primarily for computer vision tasks such as segmentation and classification. Many nonlinear operations, such as activation functions and pooling…
In this paper, inspired by the multigrid method, we propose a multi-level deep framework for deep solvers. Overall, it divides the entire training process into different levels of training. At each level of training, an adaptive sampling…
The solution of partial differential equations (PDEs) plays a central role in numerous applications in science and engineering, particularly those involving multiphase flow in porous media. Complex, nonlinear systems govern these problems…