mlsanityData to 7 Oct 2026

Discovering Sparse Interpretable Dynamics from Partial Observations

arXiv 2107.10879 ↗First posted 22 Jul 2021cs.LG physics.comp-ph physics.data-ancited by 25

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Abstract (arXiv)

Identifying the governing equations of a nonlinear dynamical system is key to both understanding the physical features of the system and constructing an accurate model of the dynamics that generalizes well beyond the available data. We propose a machine learning framework for discovering these governing equations using only partial observations, combining an encoder for state reconstruction with a sparse symbolic model. Our tests show that this method can successfully reconstruct the full system state and identify the underlying dynamics for a variety of ODE and PDE systems.

Key facts. Cited by 25 papers in the map (data through 7 Oct 2026). Builds on 22 of its 47 references that are in the map. First posted on arXiv 22 Jul 2021.

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22 of 47 references.

References · 22

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10 more
  1. 2019Integration of Neural Network-Based Symbolic Regression in Deep Learning for Scientific Discoverycited by 93
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 3; 2023: 1; 2024: 6; 2025: 8; 2026: 7.

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  1. 2022Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoderscited by 58
  2. 2023Deep Generative Symbolic Regressioncited by 27
  3. 2022Deep Learning and Symbolic Regression for Discovering Parametric Equationscited by 22
  4. 2024Marrying Causal Representation Learning with Dynamical Systems for Sciencecited by 22
  5. 2022Discovering Conservation Laws using Optimal Transport and Manifold Learningcited by 12
  6. 2024Data-Driven Stochastic Closure Modeling via Conditional Diffusion Model and Neural Operatorcited by 12
  7. 2025Interpretable Machine Learning in Physics: A Reviewcited by 11
  8. 2024Scalable Mechanistic Neural Networks for Differential Equations and Machine Learningcited by 5
  9. 2025On the definition and importance of interpretability in scientific machine learningcited by 5
  10. 2024Learning Macroscopic Dynamics from Partial Microscopic Observationscited by 3
  11. 2026Data-driven discovery of governing differential equations across physical systemscited by 3
  12. 2025Characterizing control between interacting subsystems with deep Jacobian estimationcited by 2
13 more
  1. 2025Data-driven Discovery of Digital Twins in Biomedical Researchcited by 2
  2. 2024Decomposing heterogeneous dynamical systems with graph neural networkscited by 1
  3. 2025SODAs: Sparse Optimization for the Discovery of Differential and Algebraic Equationscited by 1
  4. 2025CTSR: Cartesian tensor-based sparse regression for data-driven discovery of high-dimensional invariant governing equationscited by 1
  5. 2025Variational Rank Reduction Autoencoders for Generative Thermal Designcited by 1
  6. 2026Discovering Latent Response Laws in Forced Physical Systemscited by 1
  7. 2024Automating the Discovery of Partial Differential Equations in Dynamical Systemscited by 0
  8. 2025Self-induced stochastic resonance: A physics-informed machine learning approachcited by 0
  9. 2026Knowledge-Informed Kernel State Reconstruction from Heterogeneous Partial Observationscited by 0
  10. 2026Harnessing AI for Inverse Partial Differential Equation Problems: Past, Present, and Prospectscited by 0
  11. 2026Data Enrichment for Symbolic Regression Using Diffusion Modelscited by 0
  12. 2026Hypothesize, Evaluate, Refine: A Scientific Agent for PDE Discovery with Unknown Spatial Coefficient Fieldscited by 0
  13. 2026Retracing Hodgkin and Huxley: State Recovery Does Not Certify Mechanismcited by 0