11 citations · 11 across the 4 of their papers we have counts for
4 papers
Expansive Natural Neural Gradient Flows for Energy Minimization
Wolfgang Dahmen, Wuchen Li, Yuankai Teng +1
This paper develops expansive gradient dynamics in deep neural network-induced mapping spaces. Specifically, we generate tools and concepts for minimizing a class of energy functio…
Weak TransNet: A Petrov-Galerkin based neural network method for solving elliptic PDEs
Zhihang Xu, Min Wang, Zhu Wang
While deep learning has achieved remarkable success in solving partial differential equations (PDEs), it still faces significant challenges, particularly when the PDE solutions hav…
Data-Driven Reduced-Order Models for Port-Hamiltonian Systems with Operator Inference
Yuwei Geng, Lili Ju, Boris Kramer +1
Hamiltonian operator inference has been developed in [Sharma, H., Wang, Z., Kramer, B., Physica D: Nonlinear Phenomena, 431, p.133122, 2022] to learn structure-preserving reduced-o…
Gradient Preserving Operator Inference: Data-Driven Reduced-Order Models for Equations with Gradient Structure
Yuwei Geng, Jasdeep Singh, Lili Ju +2
Hamiltonian Operator Inference has been introduced in [Sharma, H., Wang, Z., Kramer, B., Physica D: Nonlinear Phenomena, 431, p.133122, 2022] to learn structure-preserving reduced-…