199 citations · 225 across the 10 of their papers we have counts for
11 papers
Carleman Estimates for Wave Equations on the Half-Line: AI-Assisted Weights and Applications
Chenyang An, Yu Wang, Qihao Ye +2
We develop an AI-assisted search-and-certification workflow for constructing Carleman weights for wave equations on semi-infinite domains. Starting from a weighted cross-term ident…
Two-scale neural networks for optimal control of linear convection-dominated equations
Sijing Liu, Marcus Sarkis, Yi Zhang +1
We propose a two-scale neural network method for optimal control problems governed by convection-dominated convection-diffusion-reaction equations. Building on two-scale architectu…
Two-scale Neural Networks for Singularly Perturbed Dynamical Systems with Multiple Parameters
Qiao Zhuang, Taorui Wang, Rita Wanjiku +2
We extend our two-scale neural-network method for scalar singularly perturbed problems with one small parameter to dynamical systems with multiple small parameters. To accommodate…
State-dependent temperature control in Langevin diffusions using numerical exploratory Hamiltonian-Jacobi-Bellman equations
Taorui Wang, Xun Li, Gu Wang +1
Choosing how much noise to add in Langevin dynamics is essential for making these algorithms effective in challenging optimization problems. One promising approach is to determine…
Tackling the Curse of Dimensionality in Fractional and Tempered Fractional PDEs with Physics-Informed Neural Networks
Zheyuan Hu, Kenji Kawaguchi, Zhongqiang Zhang +1
Fractional and tempered fractional partial differential equations (PDEs) are effective models of long-range interactions, anomalous diffusion, and non-local effects. Traditional nu…
Score-fPINN: Fractional Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck-Levy Equations
Zheyuan Hu, Zhongqiang Zhang, George Em Karniadakis +1
We introduce an innovative approach for solving high-dimensional Fokker-Planck-Lévy (FPL) equations in modeling non-Brownian processes across disciplines such as physics, finance,…
Transformers as Neural Operators for Solutions of Differential Equations with Finite Regularity
Benjamin Shih, Ahmad Peyvan, Zhongqiang Zhang +1
Neural operator learning models have emerged as very effective surrogates in data-driven methods for partial differential equations (PDEs) across different applications from comput…
Tensor neural networks for high-dimensional Fokker-Planck equations
Taorui Wang, Zheyuan Hu, Kenji Kawaguchi +2
We solve high-dimensional steady-state Fokker-Planck equations on the whole space by applying tensor neural networks. The tensor networks are a linear combination of tensor product…
Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck Equations
Zheyuan Hu, Zhongqiang Zhang, George Em Karniadakis +1
The Fokker-Planck (FP) equation is a foundational PDE in stochastic processes. However, curse of dimensionality (CoD) poses challenge when dealing with high-dimensional FP PDEs. Al…
Two-scale Neural Networks for Partial Differential Equations with Small Parameters
Qiao Zhuang, Chris Ziyi Yao, Zhongqiang Zhang +1
We propose a two-scale neural network method for solving partial differential equations (PDEs) with small parameters using physics-informed neural networks (PINNs). We directly inc…
Variational Physics-Informed Neural Networks For Solving Partial Differential Equations
E. Kharazmi, Z. Zhang, G. E. Karniadakis
Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random se…