no code implementations • 18 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.
1 code implementation • 8 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).
1 code implementation • 9 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.
no code implementations • 14 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.
1 code implementation • 24 Feb 2022 • Da Long, Zheng Wang, Aditi Krishnapriyan, Robert Kirby, Shandian Zhe, Michael Mahoney
Physical modeling is critical for many modern science and engineering applications.