4 papers
Multiscale Neural Networks for Approximating Green's Functions
Wenrui Hao, Rui Peng Li, Yuanzhe Xi +2
Neural networks (NNs) have been widely used to solve partial differential equations (PDEs) in the applications of physics, biology, and engineering. One effective approach for solv…
Physics-Informed Neural Networks for the Korteweg-de Vries Equation for Internal Solitary Wave Problem: Forward Simulation and Inverse Parameter Estimation
Ming Kang, Hang Li, Qiwen Tan +5
Physics-informed neural networks (PINNs) have emerged as a transformative framework for addressing operator learning and inverse problems involving the Korteweg-de Vries (KdV) equa…
Spectral-Refiner: Accurate Fine-Tuning of Spatiotemporal Fourier Neural Operator for Turbulent Flows
Shuhao Cao, Francesco Brarda, Ruipeng Li +1
Recent advancements in operator-type neural networks have shown promising results in approximating the solutions of spatiotemporal Partial Differential Equations (PDEs). However, t…
LE-PDE++: Mamba for accelerating PDEs Simulations
Aoming Liang, Zhaoyang Mu, Qi liu +3
Partial Differential Equations are foundational in modeling science and natural systems such as fluid dynamics and weather forecasting. The Latent Evolution of PDEs method is desig…