Related papers: NUNO: A General Framework for Learning Parametric …
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…
Solving cell problems in homogenization is hard, and available deep-learning frameworks fail to match the speed and generality of traditional computational frameworks. More to the point, it is generally unclear what to expect of…
Supervised learning in function spaces is an emerging area of machine learning research with applications to the prediction of complex physical systems such as fluid flows, solid mechanics, and climate modeling. By directly learning maps…
Supervised deep learning methods typically require large datasets and high-quality labels to achieve reliable predictions. However, their performance often degrades when trained on imperfect labels. To address this challenge, we propose a…
Pansharpening aims to synthesize high-resolution multispectral (HR-MS) images by fusing the spatial textures of panchromatic (PAN) images with the spectral information of low-resolution multispectral (LR-MS) images. While recent deep…
Deep operator network (DeepONet) has shown significant promise as surrogate models for systems governed by partial differential equations (PDEs), enabling accurate mappings between infinite-dimensional function spaces. However, when applied…
Neural operators generalize classical neural networks to maps between infinite-dimensional spaces, e.g., function spaces. Prior works on neural operators proposed a series of novel methods to learn such maps and demonstrated unprecedented…
A Fourier neural operator (FNO) is one of the physics-inspired machine learning methods. In particular, it is a neural operator. In recent times, several types of neural operators have been developed, e.g., deep operator networks, Graph…
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 extend data-driven models to map between infinite-dimensional functional spaces. While these operators perform effectively in either the time or frequency domain, their performance may be limited when applied to…
Surrogate models are critical for accelerating computationally expensive simulations in science and engineering, particularly for solving parametric partial differential equations (PDEs). Developing practical surrogate models poses…
We propose the *State Space Neural Operator* (SS-NO), a compact architecture for learning solution operators of time-dependent partial differential equations (PDEs). Our formulation extends structured state space models (SSMs) to joint…
Computationally efficient surrogates for parametrized physical models play a crucial role in science and engineering. Operator learning provides data-driven surrogates that map between function spaces. However, instead of full-field…
Fourier Neural Operator (FNO) is a powerful and popular operator learning method. However, FNO is mainly used in forward prediction, yet a great many applications rely on solving inverse problems. In this paper, we propose an invertible…
Engineering design problems often involve solving parametric Partial Differential Equations (PDEs) under variable PDE parameters and domain geometry. Recently, neural operators have shown promise in learning PDE operators and quickly…
In this work, we propose a concise neural operator architecture for operator learning. Drawing an analogy with a conventional fully connected neural network, we define the neural operator as follows: the output of the $i$-th neuron in a…
Data-driven methods have emerged as powerful tools for modeling the responses of complex nonlinear materials directly from experimental measurements. Among these methods, the data-driven constitutive models present advantages in physical…
We propose the geometry-informed neural operator (GINO), a highly efficient approach to learning the solution operator of large-scale partial differential equations with varying geometries. GINO uses a signed distance function and…
This work introduces a neural operator based surrogate modeling framework for neutron transport computation. Two architectures, the Deep Operator Network (DeepONet) and the Fourier Neural Operator (FNO), were trained for fixed source…
We introduce MENO (''Matrix Exponential-based Neural Operator''), a hybrid surrogate modeling framework for efficiently solving stiff systems of ordinary differential equations (ODEs) that exhibit a sparse nonlinear structure. In such…