mlsanityData to 7 Oct 2026

Discovering stochastic partial differential equations from limited data using variational Bayes inference

arXiv 2306.15873 ↗First posted 28 Jun 2023stat.ML cs.LGcited by 6

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Abstract (arXiv)

We propose a novel framework for discovering Stochastic Partial Differential Equations (SPDEs) from data. The proposed approach combines the concepts of stochastic calculus, variational Bayes theory, and sparse learning. We propose the extended Kramers-Moyal expansion to express the drift and diffusion terms of an SPDE in terms of state responses and use Spike-and-Slab priors with sparse learning techniques to efficiently and accurately discover the underlying SPDEs. The proposed approach has been applied to three canonical SPDEs, (a) stochastic heat equation, (b) stochastic Allen-Cahn equation, and (c) stochastic Nagumo equation. Our results demonstrate that the proposed approach can accurately identify the underlying SPDEs with limited data. This is the first attempt at discovering SPDEs from data, and it has significant implications for various scientific applications, such as climate modeling, financial forecasting, and chemical kinetics.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 22 of its 51 references that are in the map. First posted on arXiv 28 Jun 2023.

Builds on

22 of 51 references.

References · 22

  1. 2019Hamiltonian Neural Networkscited by 702
  2. 2020Lagrangian Neural Networkscited by 388
  3. 2020Physics-informed learning of governing equations from scarce datacited by 167
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10 more
  1. 2022Bayesian-EUCLID: discovering hyperelastic material laws with uncertaintiescited by 23
  2. 2021Adaptable Hamiltonian neural networkscited by 21
  3. 2020A Data-Driven Approach for Discovering Stochastic Dynamical Systems with Non-Gaussian Levy Noisecited by 15
  4. 2021Bayesian Deep Learning for Partial Differential Equation Parameter Discovery with Sparse and Noisy Datacited by 12
  5. 2022Automated Learning of Interpretable Models with Quantified Uncertaintycited by 8
  6. 2023A Bayesian Framework for learning governing Partial Differential Equation from Datacited by 8
  7. 2022Model-agnostic stochastic model predictive controlcited by 5
  8. 2022MAntRA: A framework for model agnostic reliability analysiscited by 5
  9. 2022Probabilistic machine learning based predictive and interpretable digital twin for dynamical systemscited by 4
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 2; 2025: 1; 2026: 2.

6 papers.

  1. 2024Statistical Mechanics of Dynamical System Identificationcited by 5
  2. 2026Data-driven discovery of governing differential equations across physical systemscited by 3
  3. 2023A Bayesian framework for discovering interpretable Lagrangian of dynamical systems from datacited by 2
  4. 2024Discovering governing equation in structural dynamics from acceleration-only measurementscited by 1
  5. 2025Principled model selection for stochastic dynamicscited by 0
  6. 2026Hypothesize, Evaluate, Refine: A Scientific Agent for PDE Discovery with Unknown Spatial Coefficient Fieldscited by 0