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Deep Operator Network (DeepONet), a recently introduced deep learning operator network, approximates linear and nonlinear solution operators by taking parametric functions (infinite-dimensional objects) as inputs and mapping them to…

Neural operators have emerged as a powerful tool for learning the mapping between infinite-dimensional parameter and solution spaces of partial differential equations (PDEs). In this work, we focus on multiscale PDEs that have important…

We introduce Equivariant Neural Eikonal Solvers, a novel framework that integrates Equivariant Neural Fields (ENFs) with Neural Eikonal Solvers. Our approach employs a single neural field where a unified shared backbone is conditioned on…

In computational physics, a longstanding challenge lies in finding numerical solutions to partial differential equations (PDEs). Recently, research attention has increasingly focused on Neural Operator methods, which are notable for their…

Designing a convolution for a spherical neural network requires a delicate tradeoff between efficiency and rotation equivariance. DeepSphere, a method based on a graph representation of the sampled sphere, strikes a controllable balance…

Solving high-dimensional partial differential equations (PDEs) efficiently requires handling multi-scale features across varying resolutions. To address this challenge, we present the Multiwavelet-based Multigrid Neural Operator (M2NO), a…

Neural networks (NNs) have been widely used to solve partial differential equations (PDEs) in the applications of physics, biology, and engineering. One effective approach for solving PDEs with a fixed differential operator is learning…

We have studied possible applications of a particular pseudo-differential algebra in singular analysis for the construction of fundamental solutions and Green's functions of a certain class of elliptic partial differential operators. The…

Learning the mapping between two function spaces has garnered considerable research attention. However, learning the solution operator of partial differential equations (PDEs) remains a challenge in scientific computing. Fourier neural…

Deep neural network (DNN) and auto differentiation have been widely used in computational physics to solve variational problems. When DNN is used to represent the wave function to solve quantum many-body problems using variational…

In scientific machine learning (SciML), a key challenge is learning unknown, evolving physical processes and making predictions across spatio-temporal scales. For example, in real-world manufacturing problems like additive manufacturing,…

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…

We explore artificial neural networks as a tool for the reconstruction of spectral functions from imaginary time Green's functions, a classic ill-conditioned inverse problem. Our ansatz is based on a supervised learning framework in which…

This work studies machine learning for electron density prediction, which is fundamental for understanding chemical systems and density functional theory (DFT) simulations. To this end, we introduce the Gaussian plane-wave neural operator…

Hyperspectral single image super-resolution (SISR) is a challenging task due to the difficulty of restoring fine spatial details while preserving spectral fidelity across a wide range of wavelengths, which limits the performance of…

Convolutional neural networks (CNNs) have achieved remarkable performance in hyperspectral image (HSI) classification over the last few years. Despite the progress that has been made, rich and informative spectral information of HSI has…

Omnidirectional images and spherical representations of $3D$ shapes cannot be processed with conventional 2D convolutional neural networks (CNNs) as the unwrapping leads to large distortion. Using fast implementations of spherical and…

To separate seismic interference (SI) noise while ensuring high signal fidelity, we propose a deep neural network (DNN)-based workflow applied to common shot gathers (CSGs). In our design, a small subset of the entire to-be-processed data…

This paper introduces a data-driven operator learning method for multiscale partial differential equations, with a particular emphasis on preserving high-frequency information. Drawing inspiration from the representation of multiscale…

The well-known governing physics in science and engineering is often based on certain assumptions and approximations. Therefore, analyses and designs carried out based on these equations are also approximate. The emergence of data-driven…