Jan 31, 2023 · Abstract:We develop a novel computational framework to approximate solution operators of evolution partial differential equations (PDEs).

We develop a novel computational framework to approximate solution operators of evolution partial differential equations (PDEs).

We develop a novel computational framework to approximate solution operators of evolution partial differential equations (PDEs).

Jan 27, 2023 · We develop a novel computational framework to approximate solution operators of evolution partial differential equations (PDEs).

Mar 9, 2024 · In this class, we obtain the evolution operator explicitly. We find parametric families of symmetry operators of the Hartree-type equation.

Apr 25, 2024 · Nathan Gaby, Xiaojing Ye , Haomin Zhou: Neural Control of Parametric Solutions for High-Dimensional Evolution PDEs. SIAM J. Sci. Comput.

In this work, a comprehensive numerical study involving analysis and experiments shows why a two-layer neural network has difficulties handling high frequencies ...

Jan 18, 2024 · We propose a finite-dimensional control-based method to approximate solution operators for evolutional partial differential equations (PDEs), ...

Published or Accepted. Neural Control of Parametric Solutions for High-dimensional Evolution PDEs. N. Gaby, X. Ye, H. Zhou SIAM Journal on Scientific ...

To tackle this challenge, we propose to construct surrogates for high-dimensional PDE-governed parametric maps in the form of derivative-informed projected ...