# Data-driven PDE discovery with evolutionary approach

arXiv: https://arxiv.org/abs/1903.08011 · HTML: https://mlsanity.com/paper/1903.08011/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Mar 2019.

## Built on by (most cited first, 7 of 7)

- [Discovery of partial differential equations from highly noisy and sparse data with physics-informed information criterion](https://mlsanity.com/paper/2208.03322/) (2022)
- [Quantum Quantile Mechanics: Solving Stochastic Differential Equations for Generating Time-Series](https://mlsanity.com/paper/2108.03190/) (2021)
- [Symbolic Regression for PDEs using Pruned Differentiable Programs](https://mlsanity.com/paper/2303.07009/) (2023)
- [Deep-Learning Discovers Macroscopic Governing Equations for Viscous Gravity Currents from Microscopic Simulation Data](https://mlsanity.com/paper/2106.00009/) (2021)
- [Parsimony-Enhanced Sparse Bayesian Learning for Robust Discovery of Partial Differential Equations](https://mlsanity.com/paper/2107.07040/) (2021)
- [Bayesian Learning of Coupled Biogeochemical-Physical Models](https://mlsanity.com/paper/2211.06714/) (2022)
- [Uncovering Closed-form Governing Equations of Nonlinear Dynamics from Videos](https://mlsanity.com/paper/2106.04776/) (2021)

## Abstract (arXiv)

The data-driven models allow one to define the model structure in cases when a priori information is not sufficient to build other types of models. The possible way to obtain physical interpretation is the data-driven differential equation discovery techniques. The existing methods of PDE (partial derivative equations) discovery are bound with the sparse regression. However, sparse regression is restricting the resulting model form, since the terms for PDE are defined before regression. The evolutionary approach described in the article has a symbolic regression as the background instead and thus has fewer restrictions on the PDE form. The evolutionary method of PDE discovery (EPDE) is described and tested on several canonical PDEs. The question of robustness is examined on a noised data example.