mlsanityData to 7 Oct 2026

Sparse learning of stochastic dynamic equations

arXiv 1712.02432 ↗First posted 6 Dec 2017stat.ML cond-mat.stat-mechcited by 76

Not on the map. Why?

Abstract (arXiv)

With the rapid increase of available data for complex systems, there is great interest in the extraction of physically relevant information from massive datasets. Recently, a framework called Sparse Identification of Nonlinear Dynamics (SINDy) has been introduced to identify the governing equations of dynamical systems from simulation data. In this study, we extend SINDy to stochastic dynamical systems, which are frequently used to model biophysical processes. We prove the asymptotic correctness of stochastics SINDy in the infinite data limit, both in the original and projected variables. We discuss algorithms to solve the sparse regression problem arising from the practical implementation of SINDy, and show that cross validation is an essential tool to determine the right level of sparsity. We demonstrate the proposed methodology on two test systems, namely, the diffusion in a one-dimensional potential, and the projected dynamics of a two-dimensional diffusion process.

Key facts. Cited by 76 papers in the map (data through 7 Oct 2026). First posted on arXiv 6 Dec 2017.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 13; 2022: 14; 2023: 21; 2024: 9; 2025: 10; 2026: 9.

76 papers.

Sort:

  1. 2021PySINDy: A comprehensive Python package for robust sparse system identificationcited by 88
  2. 2022Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoderscited by 58
  3. 2021Deeptime: a Python library for machine learning dynamical models from time series datacited by 36
  4. 2021Learning Mean-Field Equations from Particle Data Using WSINDycited by 29
  5. 2022Learning Sparse Nonlinear Dynamics via Mixed-Integer Optimizationcited by 29
  6. 2021Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modelingcited by 27
  7. 2021PDE-READ: Human-readable Partial Differential Equation Discovery using Deep Learningcited by 24
  8. 2022Bayesian autoencoders for data-driven discovery of coordinates, governing equations and fundamental constantscited by 24
  9. 2023Learning Stochastic Dynamical System via Flow Map Operatorcited by 24
  10. 2021Robust discovery of partial differential equations in complex situationscited by 21
  11. 2023Benchmarking sparse system identification with low-dimensional chaoscited by 19
  12. 2022Discovery of partial differential equations from highly noisy and sparse data with physics-informed information criterioncited by 16
38 more
  1. 2021A toolkit for data-driven discovery of governing equations in high-noise regimescited by 15
  2. 2023Convergence of uncertainty estimates in Ensemble and Bayesian sparse model discoverycited by 15
  3. 2022Online Weak-form Sparse Identification of Partial Differential Equationscited by 13
  4. 2023Learning About Structural Errors in Models of Complex Dynamical Systemscited by 13
  5. 2024ADAM-SINDy: An Efficient Optimization Framework for Parameterized Nonlinear Dynamical System Identificationcited by 10
  6. 2022Accurate Machine Learned Quantum-Mechanical Force Fields for Biomolecular Simulationscited by 9
  7. 2021Extracting stochastic dynamical systems with α-stable L'evy noise from datacited by 8
  8. 2022A Causality-Based Learning Approach for Discovering the Underlying Dynamics of Complex Systems from Partial Observations with Stochastic Parameterizationcited by 8
  9. 2021Extracting Governing Laws from Sample Path Data of Non-Gaussian Stochastic Dynamical Systemscited by 7
  10. 2022D-CIPHER: Discovery of Closed-form Partial Differential Equationscited by 7
  11. 2023OKRidge: Scalable Optimal k-Sparse Ridge Regressioncited by 7
  12. 2023Detach-ROCKET: Sequential feature selection for time series classification with random convolutional kernelscited by 7
  13. 2023HyperSINDy: Deep Generative Modeling of Nonlinear Stochastic Governing Equationscited by 7
  14. 2025In-Context Learning of Stochastic Differential Equations with Foundation Inference Modelscited by 7
  15. 2023Discovering stochastic partial differential equations from limited data using variational Bayes inferencecited by 6
  16. 2023Equivariance and partial observations in Koopman operator theory for partial differential equationscited by 6
  17. 2023A Robust SINDy Approach by Combining Neural Networks and an Integral Formcited by 6
  18. 2025Data assimilation and discrepancy modeling with shallow recurrent decoderscited by 6
  19. 2021Deep Learning of Conjugate Mappingscited by 5
  20. 2022Learning Effective SDEs from Brownian Dynamics Simulations of Colloidal Particlescited by 5
  21. 2022MAntRA: A framework for model agnostic reliability analysiscited by 5
  22. 2021Control of Stochastic Quantum Dynamics by Differentiable Programmingcited by 4
  23. 2021Bayesian data-driven discovery of partial differential equations with variable coefficientscited by 4
  24. 2022Model-Based Reinforcement Learning with SINDycited by 4
  25. 2023Symbolic Regression on Sparse and Noisy Data with Gaussian Processescited by 4
  26. 2024Modeling Latent Non-Linear Dynamical System over Time Seriescited by 4
  27. 2022Machine Learning in Heterogeneous Porous Materialscited by 3
  28. 2023Discovering interpretable Lagrangian of dynamical systems from datacited by 3
  29. 2023Tasks Makyth Models: Machine Learning Assisted Surrogates for Tipping Pointscited by 3
  30. 2023Measurement-driven neural-network training for integrated magnetic tunnel junction arrayscited by 3
  31. 2024Learning dynamical systems from data: Gradient-based dictionary optimizationcited by 3
  32. 2026Symbolic--KAN: Kolmogorov-Arnold Networks with Discrete Symbolic Structure for Interpretable Learningcited by 3
  33. 2023Reservoir Computing with Error Correction: Long-term Behaviors of Stochastic Dynamical Systemscited by 2
  34. 2023Data-Driven Model Selections of Second-Order Particle Dynamics via Integrating Gaussian Processes with Low-Dimensional Interacting Structurescited by 2
  35. 2024GN-SINDy: Greedy Sampling Neural Network in Sparse Identification of Nonlinear Partial Differential Equationscited by 2
  36. 2024Minimum Reduced-Order Models via Causal Inferencecited by 2
  37. 2026Data-driven sparse identification of governing PDEs via knockoff filters and multi-criteria trade-offscited by 2
  38. 2021Uncovering Closed-form Governing Equations of Nonlinear Dynamics from Videoscited by 1

50 most cited of 76 All 76 (JSON)