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Towards true discovery of the differential equations

arXiv 2308.04901 ↗First posted 9 Aug 2023cs.LGcited by 0

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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.

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References · 14

  1. 2018Neural Ordinary Differential Equationscited by 3,779
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  3. 2019DeepXDE: A deep learning library for solving differential equationscited by 619
  4. 2020Universal Differential Equations for Scientific Machine Learningcited by 353
  5. 2018PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Networkcited by 210
  6. 2020Weak SINDy For Partial Differential Equationscited by 155
  7. 2021Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and controlcited by 137
  8. 2021A survey of Bayesian Network structure learningcited by 87
  9. 2020DLGA-PDE: Discovery of PDEs with incomplete candidate library via combination of deep learning and genetic algorithmcited by 46
  10. 2021Any equation is a forest: Symbolic genetic algorithm for discovering open-form partial differential equations (SGA-PDE)cited by 41
  11. 2019Data-driven discovery of free-form governing differential equationscited by 16
  12. 2021Parsimony-Enhanced Sparse Bayesian Learning for Robust Discovery of Partial Differential Equationscited by 3
2 more
  1. 2021Multi-objective discovery of PDE systems using evolutionary approachcited by 2
  2. 2022Automated differential equation solver based on the parametric approximation optimizationcited by 1

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