# Towards true discovery of the differential equations

arXiv: https://arxiv.org/abs/2308.04901 · HTML: https://mlsanity.com/paper/2308.04901/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 23 references that are in the map.
- First posted on arXiv 9 Aug 2023.

## Builds on (most cited first, 14 of 14)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network](https://mlsanity.com/paper/1812.04426/) (2018)
- [Weak SINDy For Partial Differential Equations](https://mlsanity.com/paper/2007.02848/) (2020)
- [Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control](https://mlsanity.com/paper/2111.10992/) (2021)
- [A survey of Bayesian Network structure learning](https://mlsanity.com/paper/2109.11415/) (2021)
- [DLGA-PDE: Discovery of PDEs with incomplete candidate library via combination of deep learning and genetic algorithm](https://mlsanity.com/paper/2001.07305/) (2020)
- [Any equation is a forest: Symbolic genetic algorithm for discovering open-form partial differential equations (SGA-PDE)](https://mlsanity.com/paper/2106.11927/) (2021)
- [Data-driven discovery of free-form governing differential equations](https://mlsanity.com/paper/1910.05117/) (2019)
- [Parsimony-Enhanced Sparse Bayesian Learning for Robust Discovery of Partial Differential Equations](https://mlsanity.com/paper/2107.07040/) (2021)
- [Multi-objective discovery of PDE systems using evolutionary approach](https://mlsanity.com/paper/2103.06739/) (2021)
- [Automated differential equation solver based on the parametric approximation optimization](https://mlsanity.com/paper/2205.05383/) (2022)

## Abstract (arXiv)

Differential equation discovery, a machine learning subfield, is used to develop interpretable models, particularly in nature-related applications. By expertly incorporating the general parametric form of the equation of motion and appropriate differential terms, algorithms can autonomously uncover equations from data. This paper explores the prerequisites and tools for independent equation discovery without expert input, eliminating the need for equation form assumptions. We focus on addressing the challenge of assessing the adequacy of discovered equations when the correct equation is unknown, with the aim of providing insights for reliable equation discovery without prior knowledge of the equation form.