2 papers
math.NA2025
An Efficient Deep Learning Approach for Approximating Parameter-to-Solution Maps of PDEs
Guanhang Lei, Zhen Lei, Lei Shi +1
In this paper, we consider approximating the parameter-to-solution maps of parametric partial differential equations (PPDEs) using deep neural networks (DNNs). We propose an effici…
math.NA2025
Long-time Integration of Nonlinear Wave Equations with Neural Operators
Guanhang Lei, Zhen Lei, Lei Shi
Neural operators have shown promise in solving many types of Partial Differential Equations (PDEs). They are significantly faster compared to traditional numerical solvers once the…