4 papers
Convergence Analysis of PINNs for Fractional Diffusion Equations in Bounded Domains
Elie Abdo, Lihui Chai, Ruimeng Hu +1
We establish the convergence of physics-informed neural networks (PINNs) for time-dependent fractional diffusion equations posed on bounded domains. The presence of fractional Lapl…
Frozen Gaussian Grid-point Correction For Semi-classical Schrödinger Equation
Lihui Chai, Zili Deng
We propose an efficient reconstruction algorithm named the frozen Gaussian grid-point correction (FGGC) for computing the Schrödinger equation in the semi-classical regime using th…
SG-DeepONet: Source-generalized deep operator learning for full waveform inversion
Zekai Guo, Lihui Chai, Ye Li
Full waveform inversion (FWI) aims to reconstruct subsurface velocity models from observed seismic wavefields and has recently benefited from advances in deep learning (DL). The pe…
Error estimates of physics-informed neural networks for approximating Boltzmann equation
Elie Abdo, Lihui Chai, Ruimeng Hu +1
Motivated by the recent successful application of physics-informed neural networks (PINNs) to solve Boltzmann-type equations [S. Jin, Z. Ma, and K. Wu, J. Sci. Comput., 94 (2023),…