Machine Learning of Partial Differential Equations from Noise Data
arXiv:2010.06507
Abstract
Machine learning of partial differential equations from data is a potential breakthrough to solve the lack of physical equations in complex dynamic systems, but because numerical differentiation is ill-posed to noise data, noise has become the biggest obstacle in the application of partial differential equation identification method. To overcome this problem, we propose Frequency Domain Identification method based on Fourier transforms, which effectively eliminates the influence of noise by using the low frequency component of frequency domain data to identify partial differential equations in frequency domain. We also propose a new sparse identification criterion, which can accurately identify the terms in the equation from low signal-to-noise ratio data. Through identifying a variety of canonical equations spanning a number of scientific domains, the proposed method is proved to have high accuracy and robustness for equation structure and parameters identification for low signal-to-noise ratio data. The method provides a promising technique to discover potential partial differential equations from noisy experimental data.
References in corpus (8)
- Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
- Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations
- Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations
- Machine Learning of Linear Differential Equations using Gaussian Processes
- PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network
- Discovery of Algebraic Reynolds-Stress Models Using Sparse Symbolic Regression
- Identification of physical processes via combined data-driven and data-assimilation methods
- Poincaré Maps for Multiscale Physics Discovery and Nonlinear Floquet Theory