5 papers
Energy-Equidistributed Moving Sampling Physics-informed Neural Networks for Solving Conservative Partial Differential Equations
Qinjiao Gao, Longzhe Xu, Dongjiang Wang +1
This paper presents a novel Energy-Equidistributed adaptive sampling framework for multi-dimensional conservative PDEs, introducing both location-based and velocity-based formulati…
A preconditioned difference of convex functions algorithm with extrapolation and line search
Ran Zhang, Hongpeng Sun
This paper proposes a novel proximal difference-of-convex (DC) algorithm enhanced with extrapolation and aggressive non-monotone line search for solving non-convex optimization pro…
Adaptive Movement Sampling Physics-Informed Residual Network (AM-PIRN) for Solving Nonlinear Option Pricing models
Qinjiao Gao, Zuowei Wang, Ran Zhang +1
In this paper, we propose the Adaptive Movement Sampling Physics-Informed Residual Network (AM-PIRN) to address challenges in solving nonlinear option pricing PDE models, where sol…
Orthogonal greedy algorithm for linear operator learning with shallow neural network
Ye Lin, Jiwei Jia, Young Ju Lee +1
Greedy algorithms, particularly the orthogonal greedy algorithm (OGA), have proven effective in training shallow neural networks for fitting functions and solving partial different…
Helicity-conservative Physics-informed Neural Network Model for Navier-Stokes Equations
Jiwei Jia, Young Ju Lee, Ziqian Li +2
We design the helicity-conservative physics-informed neural network model for the Navier-Stokes equation in the ideal case. The key is to provide an appropriate PDE model as loss f…