mlsanityData to 14 Oct 2026

Discover physical concepts and equations with machine learning

arXiv 2412.12161 ↗First posted 11 Dec 2024cs.LG cond-mat.dis-nn cs.AIcited by 1

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Abstract (arXiv)

Machine learning can uncover physical concepts or physical equations when prior knowledge from the other is available. However, these two aspects are often intertwined and cannot be discovered independently. We extend SciNet, which is a neural network architecture that simulates the human physical reasoning process for physics discovery, by proposing a model that combines Variational Autoencoders (VAE) with Neural Ordinary Differential Equations (Neural ODEs). This allows us to simultaneously discover physical concepts and governing equations from simulated experimental data across various physical systems. We apply the model to several examples inspired by the history of physics, including Copernicus' heliocentrism, Newton's law of gravity, Schr"odinger's wave mechanics, and Pauli's spin-magnetic formulation. The results demonstrate that the correct physical theories can emerge in the neural network.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 26 of its 74 references that are in the map. First posted on arXiv 11 Dec 2024.

Builds on

26 of 74 references.

References · 26

  1. 2014Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translationcited by 4,057
  2. 2018Neural Ordinary Differential Equationscited by 3,779
  3. 2015Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classificationcited by 3,611
  4. 2021Modern Koopman Theory for Dynamical Systemscited by 276
  5. 2020How to train your neural ODE: the world of Jacobian and kinetic regularizationcited by 228
  6. 2018Discovering physical concepts with neural networkscited by 117
  7. 2020Learning Differential Equations that are Easy to Solvecited by 81
  8. 2020AI Poincar'e: Machine Learning Conservation Laws from Trajectoriescited by 77
  9. 2022Rediscovering orbital mechanics with machine learningcited by 71
  10. 2022On scientific understanding with artificial intelligencecited by 70
  11. 2020STEER: Simple Temporal Regularization For Neural ODEscited by 58
  12. 2021Heavy Ball Neural Ordinary Differential Equationscited by 42
14 more
  1. 2020"Hey, that's not an ODE": Faster ODE Adjoints via Seminormscited by 35
  2. 2021Noether Networks: Meta-Learning Useful Conserved Quantitiescited by 26
  3. 2023A Unified Framework to Enforce, Discover, and Promote Symmetry in Machine Learningcited by 22
  4. 2022AI Poincar'e 2.0: Machine Learning Conservation Laws from Differential Equationscited by 20
  5. 2023Evolving Scientific Discovery by Unifying Data and Background Knowledge with AI Hilbertcited by 18
  6. 2022Latent Neural ODEs with Sparse Bayesian Multiple Shootingcited by 17
  7. 2020Operationally meaningful representations of physical systems in neural networkscited by 16
  8. 2021Forecasting the outcome of spintronic experiments with Neural Ordinary Differential Equationscited by 13
  9. 2023Explainable Representation Learning of Small Quantum Statescited by 10
  10. 2023Metalearning generalizable dynamics from trajectoriescited by 9
  11. 2023Learning minimal representations of stochastic processes with variational autoencoderscited by 7
  12. 2022Neural modal ordinary differential equations: Integrating physics-based modeling with neural ordinary differential equations for modeling high-dimensional monitored structurescited by 5
  13. 2024Application of Neural Ordinary Differential Equations for Tokamak Plasma Dynamics Analysiscited by 5
  14. 2022Optical Neural Ordinary Differential Equationscited by 1

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Cited by year

Citing papers per year: 2025: 1.

1 paper.

  1. 2025AI-Newton: A Concept-Driven Physical Law Discovery System without Prior Physical Knowledgecited by 5

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  5. 2026From Phenomenological Fitting to Endogenous Deduction: A Paradigm Leap via Meta-Principle Physics Architecture
  6. 2026Prediction Is Not Physics: Learning and Evaluating Conserved Quantities in Neural Simulators
  7. 2025Universal Physics Simulation: A Foundational Diffusion Approach
  8. 2025Aligning Perception, Reasoning, Modeling and Interaction: A Survey on Physical AI