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Spherical deep learning has been widely applied to a broad range of real-world problems. Existing approaches often face challenges in balancing strong spherical geometric inductive biases with the need to model real-world heterogeneity. To…
Fourier Neural Operators (FNOs) have proven to be an efficient and effective method for resolution-independent operator learning in a broad variety of application areas across scientific machine learning. A key reason for their success is…
Scientific machine learning has seen significant progress with the emergence of operator learning. However, existing methods encounter difficulties when applied to problems on unstructured grids and irregular domains. Spatial graph neural…
Neural operators have emerged as powerful tools for learning mappings between function spaces, enabling efficient solutions to partial differential equations across varying inputs and domains. Despite the success, existing methods often…
Neural operators improve conventional neural networks by expanding their capabilities of functional mappings between different function spaces to solve partial differential equations (PDEs). One of the most notable methods is the Fourier…
Neural operators are a popular technique in scientific machine learning to learn a mathematical model of the behavior of unknown physical systems from data. Neural operators are especially useful to learn solution operators associated with…
A plentitude of applications in scientific computing requires the approximation of mappings between Banach spaces. Recently introduced Fourier Neural Operator (FNO) and Deep Operator Network (DeepONet) can provide this functionality. For…
We propose Super-resolution Neural Operator (SRNO), a deep operator learning framework that can resolve high-resolution (HR) images at arbitrary scales from the low-resolution (LR) counterparts. Treating the LR-HR image pairs as continuous…
Partial differential equations (PDEs) govern a wide variety of dynamical processes in science and engineering, yet obtaining their numerical solutions often requires high-resolution discretizations and repeated evaluations of complex…
Long-term stability stands as a crucial requirement in data-driven medium-range global weather forecasting. Spectral bias is recognized as the primary contributor to instabilities, as data-driven methods difficult to learn small-scale…
This paper introduces the Kernel Neural Operator (KNO), a provably convergent operator-learning architecture that utilizes compositions of deep kernel-based integral operators for function-space approximation of operators (maps from…
This work introduces a paradigm for constructing parametric neural operators that are derived from finite-dimensional representations of Green's operators for linear partial differential equations (PDEs). We refer to such neural operators…
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…
In the study of subsurface seismic imaging, solving the acoustic wave equation is a pivotal component in existing models. The advancement of deep learning enables solving partial differential equations, including wave equations, by applying…
Partial differential equations (PDEs) govern complex systems, yet neural operators often struggle to efficiently capture the long-range, nonlocal interactions inherent in their solution maps. We introduce Spectral Filtering Operator (SFO),…
Neural operators have emerged as powerful data-driven surrogates for learning solution operators of parametric partial differential equations (PDEs). However, widely used Fourier Neural Operators (FNOs) rely on global Fourier…
GreenLearning networks (GL) directly learn Green's function in physical space, making them an interpretable model for capturing unknown solution operators of partial differential equations (PDEs). For many PDEs, the corresponding Green's…
We introduce Neural Green's Function, a neural solution operator for linear partial differential equations (PDEs) whose differential operators admit eigendecompositions. Inspired by Green's functions, the solution operators of linear PDEs…
We consider solving partial differential equations (PDEs) with Fourier neural operators (FNOs), which operate in the frequency domain. Since the laws of physics do not depend on the coordinate system used to describe them, it is desirable…
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…