Search Results for author: Da Long

Found 5 papers, 3 papers with code

Invertible Fourier Neural Operators for Tackling Both Forward and Inverse Problems

no code implementations18 Feb 2024 Da Long, Shandian Zhe

In this paper, we propose an invertible Fourier Neural Operator (iFNO) that tackles both the forward and inverse problems.

Operator learning

Solving High Frequency and Multi-Scale PDEs with Gaussian Processes

1 code implementation8 Nov 2023 Shikai Fang, Madison Cooley, Da Long, Shibo Li, Robert Kirby, Shandian Zhe

Machine learning based solvers have garnered much attention in physical simulation and scientific computing, with a prominent example, physics-informed neural networks (PINNs).

Computational Efficiency Gaussian Processes

Equation Discovery with Bayesian Spike-and-Slab Priors and Efficient Kernels

1 code implementation9 Oct 2023 Da Long, Wei W. Xing, Aditi S. Krishnapriyan, Robert M. Kirby, Shandian Zhe, Michael W. Mahoney

To overcome the computational challenge of kernel regression, we place the function values on a mesh and induce a Kronecker product construction, and we use tensor algebra to enable efficient computation and optimization.

regression Uncertainty Quantification

A Kernel Approach for PDE Discovery and Operator Learning

no code implementations14 Oct 2022 Da Long, Nicole Mrvaljevic, Shandian Zhe, Bamdad Hosseini

This article presents a three-step framework for learning and solving partial differential equations (PDEs) using kernel methods.

Operator learning

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