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Memory complexity and data scarcity have so far prohibited learning solution operators of partial differential equations (PDEs) at high resolutions. We address these limitations by introducing a new data efficient and highly parallelizable…
The UNet-enhanced Fourier Neural Operator (UFNO) extends the Fourier Neural Operator (FNO) by incorporating a parallel UNet pathway, enabling the retention of both high- and low-frequency components. While UFNO improves predictive accuracy…
Constitutive modeling based on continuum mechanics theory has been a classical approach for modeling the mechanical responses of materials. However, when constitutive laws are unknown or when defects and/or high degrees of heterogeneity are…
Solving inverse problems governed by partial differential equations (PDEs) is central to science and engineering, yet remains challenging when measurements are sparse, noisy, or when the underlying coefficients are high-dimensional or…
Neural operators (NOs) provide a new paradigm for efficiently solving partial differential equations (PDEs), but their training depends on costly high-fidelity data from numerical solvers, limiting applications in complex systems. We…
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…
The computational efficiency of many neural operators, widely used for learning solutions of PDEs, relies on the fast Fourier transform (FFT) for performing spectral computations. As the FFT is limited to equispaced (rectangular) grids,…
Neural operator learning directly constructs the mapping relationship from the equation parameter space to the solution space, enabling efficient direct inference in practical applications without the need for repeated solution of partial…
This study investigates the application of machine learning, specifically Fourier Neural Operator (FNO) and Convolutional Neural Network (CNN), to learn time-advancement operators for parametric partial differential equations (PDEs). Our…
Spectral neural operators, particularly Fourier Neural Operators (FNO), are a powerful framework for learning solution operators of partial differential equations (PDEs) due to their efficient global mixing in the frequency domain. However,…
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'…
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…
Solving partial differential equations remains a central challenge in scientific machine learning. Neural operators offer a promising route by learning mappings between function spaces and enabling resolution-independent inference, yet they…
Physics-Informed Neural Operators provide efficient, high-fidelity simulations for systems governed by partial differential equations (PDEs). However, most existing studies focus only on multi-scale, multi-physics systems within a single…
Many real-world problems, like modelling environment dynamics, physical processes, time series etc., involve solving Partial Differential Equations (PDEs) parameterised by problem-specific conditions. Recently, a deep learning architecture…
Spatio-temporal process models are often used for modeling dynamic physical and biological phenomena that evolve across space and time. These phenomena may exhibit environmental heterogeneity and complex interactions that are difficult to…
Deep neural operators are recognized as an effective tool for learning solution operators of complex partial differential equations (PDEs). As compared to laborious analytical and computational tools, a single neural operator can predict…
Numerical simulation of multiphase flow in porous media is essential for many geoscience applications. Machine learning models trained with numerical simulation data can provide a faster alternative to traditional simulators. Here we…
We introduce the Laplace neural operator (LNO), which leverages the Laplace transform to decompose the input space. Unlike the Fourier Neural Operator (FNO), LNO can handle non-periodic signals, account for transient responses, and exhibit…
This paper proposes a physics-informed neural operator (PINO) framework for solving inverse scattering problems, enabling rapid and accurate reconstructions under diverse measurement conditions. In the proposed approach, the dielectric…