mlsanityData to 7 Oct 2026

Learning Sparse Nonlinear Dynamics via Mixed-Integer Optimization

arXiv 2206.00176 ↗First posted 1 Jun 2022cs.LG cs.SY eess.SYcited by 29

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Abstract (arXiv)

Discovering governing equations of complex dynamical systems directly from data is a central problem in scientific machine learning. In recent years, the sparse identification of nonlinear dynamics (SINDy) framework, powered by heuristic sparse regression methods, has become a dominant tool for learning parsimonious models. We propose an exact formulation of the SINDy problem using mixed-integer optimization (MIO) to solve the sparsity constrained regression problem to provable optimality in seconds. On a large number of canonical ordinary and partial differential equations, we illustrate the dramatic improvement of our approach in accurate model discovery while being more sample efficient, robust to noise, and flexible in accommodating physical constraints.

Key facts. Cited by 29 papers in the map (data through 7 Oct 2026). Builds on 25 of its 72 references that are in the map. First posted on arXiv 1 Jun 2022.

Builds on

25 of 72 references.

References · 25

  1. 2017Deep learning for universal linear embeddings of nonlinear dynamicscited by 491
  2. 2017Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equationscited by 362
  3. 2020Weak SINDy For Partial Differential Equationscited by 154
  4. 2017Sparse identification of nonlinear dynamics for model predictive control in the low-data limitcited by 139
  5. 2021Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and controlcited by 134
  6. 2017Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systemscited by 125
  7. 2020SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamicscited by 125
  8. 2015Best Subset Selection via a Modern Optimization Lenscited by 99
  9. 2018Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systemscited by 88
  10. 2021PySINDy: A comprehensive Python package for robust sparse system identificationcited by 88
  11. 2017Sparse learning of stochastic dynamic equationscited by 76
  12. 2017Time-lagged autoencoders: Deep learning of slow collective variables for molecular kineticscited by 64
13 more
  1. 2019A unified sparse optimization framework to learn parsimonious physics-informed models from datacited by 49
  2. 2020Sparse Regression at Scale: Branch-and-Bound rooted in First-Order Optimizationcited by 45
  3. 2017Sparse High-Dimensional Regression: Exact Scalable Algorithms and Phase Transitionscited by 43
  4. 2018A Unified Framework for Sparse Relaxed Regularized Regression: SR3cited by 36
  5. 2019Sparse Regression: Scalable algorithms and empirical performancecited by 27
  6. 2020Numerical differentiation of noisy data: A unifying multi-objective optimization frameworkcited by 19
  7. 2021A toolkit for data-driven discovery of governing equations in high-noise regimescited by 15
  8. 2021Cardinality Minimization, Constraints, and Regularization: A Surveycited by 12
  9. 2020Sparse Methods for Automatic Relevance Determinationcited by 8
  10. 2019Stability selection enables robust learning of partial differential equations from limited noisy datacited by 7
  11. 2020The Backbone Method for Ultra-High Dimensional Sparse Machine Learningcited by 7
  12. 2019Scalable Holistic Linear Regressioncited by 6
  13. 2020Robust subset selectioncited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 10; 2024: 3; 2025: 7; 2026: 8.

29 papers.

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  1. 2023Direct Estimation of Parameters in ODE Models Using WENDy: Weak-form Estimation of Nonlinear Dynamicscited by 20
  2. 2023Weak-Form Latent Space Dynamics Identificationcited by 20
  3. 2023Benchmarking sparse system identification with low-dimensional chaoscited by 19
  4. 2023Evolving Scientific Discovery by Unifying Data and Background Knowledge with AI Hilbertcited by 18
  5. 2022Asymptotic consistency of the WSINDy algorithm in the limit of continuum datacited by 14
  6. 2023Coarse-Graining Hamiltonian Systems Using WSINDycited by 11
  7. 2023OKRidge: Scalable Optimal k-Sparse Ridge Regressioncited by 7
  8. 2024Learning Governing Equations of Unobserved States in Dynamical Systemscited by 7
  9. 2023Adaptive Uncertainty-Guided Model Selection for Data-Driven PDE Discoverycited by 6
  10. 2024Statistical Mechanics of Dynamical System Identificationcited by 5
  11. 2024Correlating Time Series with Interpretable Convolutional Kernelscited by 3
  12. 2025Mesh-free sparse identification of nonlinear dynamicscited by 3
17 more
  1. 2025No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEscited by 2
  2. 2025Interpretable Time Series Autoregression for Periodicity Quantificationcited by 2
  3. 2025Data-driven Discovery of Digital Twins in Biomedical Researchcited by 2
  4. 2023A Physics-informed Machine Learning-based Control Method for Nonlinear Dynamic Systems with Highly Noisy Measurementscited by 1
  5. 2025Scalable First-order Method for Certifying Optimal k-Sparse GLMscited by 1
  6. 2026Learning a Stochastic Differential Equation Model of Tropical Cyclone Intensification from Reanalysis and Observational Datacited by 1
  7. 2026Dynamics-aware identification of governing equations from sparse and noisy datacited by 1
  8. 2023Improved identification accuracy in equation learning via comprehensive boldsymbolR2-elimination and Bayesian model selectioncited by 0
  9. 2023BackboneLearn: A Library for Scaling Mixed-Integer Optimization-Based Machine Learningcited by 0
  10. 2025Bridging the Gap Between Scientific Laws Derived by AI Systems and Canonical Knowledge via Abductive Inference with AI-Noethercited by 0
  11. 2025A joint optimization approach to identifying sparse dynamics using least squares kernel collocationcited by 0
  12. 2026When to Retrain after Drift: A Data-Only Test of Post-Drift Data Size Sufficiencycited by 0
  13. 2026Uncertainty-Aware Sparse Identification of Dynamical Systems via Bayesian Model Averagingcited by 0
  14. 2026From Sequential Nodes to GPU Batches: Parallel Branch and Bound for Optimal k-Sparse GLMscited by 0
  15. 2026Modeling Dynamic Mixtures of Time-Delay Systems from Streaming Time Seriescited by 0
  16. 2026AdaKoop: Efficient Modeling of Nonlinear Dynamics from Nonstationary Data Streams with Koopman Operator Regressioncited by 0
  17. 2026On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancementcited by 0