Related papers: A neural operator-based surrogate solver for free-…
We propose an extended Fourier neural operator (FNO) architecture for learning state and linear quadratic additive optimal control of systems governed by partial differential equations. Using the Ehrenpreis-Palamodov fundamental principle,…
Recent advancements in operator-type neural networks have shown promising results in approximating the solutions of spatiotemporal Partial Differential Equations (PDEs). However, these neural networks often entail considerable training…
The inverse medium problem, inherently ill-posed and nonlinear, presents significant computational challenges. This study introduces a novel approach by integrating a Neumann series structure within a neural network framework to effectively…
This note introduces a regression technique for finding a class of nonlinear integro-differential operators from data. The method parametrizes the spatial operator with neural networks and Fourier transforms such that it can fit a class of…
Neural operators have emerged as a powerful, data-driven paradigm for learning solution operators of partial differential equations (PDEs). State-of-the-art architectures, such as the Fourier Neural Operator (FNO), have achieved remarkable…
Efficient and accurate spectral solvers for nonlocal models in any spatial dimension are presented. The approach we pursue is based on the Fourier multipliers of nonlocal Laplace operators introduced in a previous work. It is demonstrated…
Neural operators are a new type of models that can map between function spaces, allowing trained models to emulate the solution operators of partial differential equations (PDEs). This paper proposes a multigrid Fourier neural operator…
Neural operators, which emerge as implicit solution operators of hidden governing equations, have recently become popular tools for learning responses of complex real-world physical systems. Nevertheless, the majority of neural operator…
The numerical solution of partial differential equations (PDEs) is fundamental to scientific and engineering computing. In the presence of strong anisotropy, material heterogeneity, and complex geometries, however, classical iterative…
Designing universal artificial intelligence (AI) solver for partial differential equations (PDEs) is an open-ended problem and a significant challenge in science and engineering. Currently, data-driven solvers have achieved great success,…
In many mechanistic medical, biological, physical and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs) can make simulations impractically slow. Biological models require the…
A surrogate model approximates the outputs of a solver of Partial Differential Equations (PDEs) with a low computational cost. In this article, we propose a method to build learning-based surrogates in the context of parameterized PDEs,…
Neural networks have become a powerful tool as surrogate models to provide numerical solutions for scientific problems with increased computational efficiency. This efficiency can be advantageous for numerically challenging problems where…
Surrogate models for partial-differential equations are widely used in the design of meta-materials to rapidly evaluate the behavior of composable components. However, the training cost of accurate surrogates by machine learning can rapidly…
A plethora of next-generation all-optical devices based on exciton-polaritons have been proposed in latest years, including prototypes of transistors, switches, analogue quantum simulators and others. However, for such systems consisting of…
The spatiotemporal resolution of Partial Differential Equations (PDEs) plays important roles in the mathematical description of the world's physical phenomena. In general, scientists and engineers solve PDEs numerically by the use of…
Learning partial differential equations' (PDEs) solution operators is an essential problem in machine learning. However, there are several challenges for learning operators in practical applications like the irregular mesh, multiple input…
Neural networks have promise as surrogate partial differential equation (PDE) solvers, but it remains a challenge to use these concepts to solve problems with high accuracy and scalability. In this work, we show that neural network…
Neural surrogate solvers can estimate solutions to partial differential equations in physical problems more efficiently than standard numerical methods, but require extensive high-resolution training data. In this paper, we break this…
Scientific machine learning is increasingly being spoken of as universal emulators for classical numerical solvers for multi-scale partial differential equations, but most apparent successes can be explained by facts that also define their…