Multi-scale Deep Neural Networks for Solving High Dimensional PDEs
In this paper, we propose the idea of radial scaling in frequency domain and activation functions with compact support to produce a multi-scale DNN (MscaleDNN), which will have the multi-scale capability in approximating high frequency and high dimensional functions and speeding up the solution of high dimensional PDEs. Numerical results on high dimensional function fitting and solutions of high dimensional PDEs, using loss functions with either Ritz energy or least squared PDE residuals, have validated the increased power of multi-scale resolution and high frequency capturing of the proposed MscaleDNN.
Code (0)
등록된 구현이 없습니다.
Tasks
Vocal Bursts Intensity PredictionSimilar Papers 제목 키워드 기반
Solving High-Dimensional PDEs with Latent Spectral Models
Deep models have achieved impressive progress in solving partial differential equations (PDEs). A burgeoning paradigm is learning neural operators to approximate the input-output mappings of PDEs. While previous deep mod…
Vocal Bursts Intensity PredictionTackling the Curse of Dimensionality with Physics-Informed Neural Networks
The curse-of-dimensionality taxes computational resources heavily with exponentially increasing computational cost as the dimension increases. This poses great challenges in solving high-dimensional PDEs, as Richard E. B…
GPUMulti-Scale Separable Fourier Neural Networks for Solving High-Frequency PDEs
Solving high-frequency partial differential equations (PDEs) with neural networks is notoriously difficult due to the spectral bias of conventional architectures. We propose the Multi-Scale Separable Fourier Neural Netwo…
Reinforcement Learning Closures for Underresolved Partial Differential Equations using Synthetic Data
Partial Differential Equations (PDEs) describe phenomena ranging from turbulence and epidemics to quantum mechanics and financial markets. Despite recent advances in computational science, solving such PDEs for real-worl…
Neural-PDE: A RNN based neural network for solving time dependent PDEs
Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired…
BIG-bench Machine Learning