Related papers: Generalized Spherical Neural Operators: Green's Fu…
Fourier neural operators (FNOs) provide a mesh-independent way to learn solution operators for partial differential equations, yet their efficacy for magnetized turbulence is largely unexplored. Here we train an FNO surrogate for the 2-D…
Effectively predicting molecular interactions has the potential to accelerate molecular dynamics by multiple orders of magnitude and thus revolutionize chemical simulations. Graph neural networks (GNNs) have recently shown great successes…
We apply the generalized method of separation of variables (GMSV) to solve boundary value problems for the Laplace operator in three-dimensional domains with disconnected spherical boundaries (i.e., an arbitrary configuration of…
A variety of infinitely wide neural architectures (e.g., dense NNs, CNNs, and transformers) induce Gaussian process (GP) priors over their outputs. These relationships provide both an accurate characterization of the prior predictive…
High-frequency features are critical in multiscale phenomena such as turbulent flows and phase transitions, since they encode essential physical information. The recently proposed Wavelet Neural Operator (WNO) utilizes wavelets'…
Neural operators generalize neural networks to learn mappings between function spaces from data. They are commonly used to learn solution operators of parametric partial differential equations (PDEs) or propagators of time-dependent PDEs.…
This article introduces GIT-Net, a deep neural network architecture for approximating Partial Differential Equation (PDE) operators, inspired by integral transform operators. GIT-NET harnesses the fact that differential operators commonly…
In this work, we introduce a planning neural operator (PNO) for predicting the value function of a motion planning problem. We recast value function approximation as learning a single operator from the cost function space to the value…
Neural operators have emerged as a powerful data-driven paradigm for solving partial differential equations (PDEs), while their accuracy and scalability are still limited, particularly on irregular domains where fluid flows exhibit rich…
Neural operators have been applied in various scientific fields, such as solving parametric partial differential equations, dynamical systems with control, and inverse problems. However, challenges arise when dealing with input functions…
Normalization Layers (NLs) are widely used in modern deep-learning architectures. Despite their apparent simplicity, their effect on optimization is not yet fully understood. This paper introduces a spherical framework to study the…
In-context operator learning enables neural networks to infer solution operators from contextual examples without weight updates. While prior work has demonstrated the effectiveness of this paradigm in leveraging vast datasets, a systematic…
Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert…
Neural operators are becoming the default tools to learn solutions to governing partial differential equations (PDEs) in weather and ocean forecasting applications. Despite early promising achievements, significant challenges remain,…
Convolutional neural networks (CNNs) constructed natively on the sphere have been developed recently and shown to be highly effective for the analysis of spherical data. While an efficient framework has been formulated, spherical CNNs are…
In recent years, Neural Operators(NO) have gradually emerged as a popular approach for solving Partial Differential Equations (PDEs). However, their application to large-scale engineering tasks suffers from significant computational…
Neural operators have achieved significant success in modern scientific computing due to their flexibility and strong generalization capabilities. Existing models, however, primarily rely on first-order kernel integral approximations, which…
We propose the Factorized Fourier Neural Operator (F-FNO), a learning-based approach for simulating partial differential equations (PDEs). Starting from a recently proposed Fourier representation of flow fields, the F-FNO bridges the…
Energy efficiency remains a critical challenge in deploying physics-informed operator learning models for computational mechanics and scientific computing, particularly in power-constrained settings such as edge and embedded devices, where…
Recent advances in scientific machine learning (SciML) have enabled neural operators (NOs) to serve as powerful surrogates for modeling the dynamic evolution of physical systems governed by partial differential equations (PDEs). While…