# Machine Learning of Partial Differential Equations from Noise Data

arXiv: https://arxiv.org/abs/2010.06507 · HTML: https://mlsanity.com/paper/2010.06507/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Sep 2020.

## Built on by (most cited first, 4 of 4)

- [DySMHO: Data-Driven Discovery of Governing Equations for Dynamical Systems via Moving Horizon Optimization](https://mlsanity.com/paper/2108.00069/) (2021)
- [Adaptive Uncertainty-Guided Model Selection for Data-Driven PDE Discovery](https://mlsanity.com/paper/2308.10283/) (2023)
- [Parsimony-Enhanced Sparse Bayesian Learning for Robust Discovery of Partial Differential Equations](https://mlsanity.com/paper/2107.07040/) (2021)
- [Symbolic Graph Networks for Robust PDE Discovery from Noisy Sparse Data](https://mlsanity.com/paper/2603.22380/) (2026)

## Abstract (arXiv)

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.