mlsanityData to 7 Oct 2026

Discover governing differential equations from evolving systems

arXiv 2301.07863 ↗First posted 19 Jan 2023physics.comp-ph cs.LG cs.SCcited by 5

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Abstract (arXiv)

Discovering the governing equations of evolving systems from available observations is essential and challenging. In this paper, we consider a new scenario: discovering governing equations from streaming data. Current methods struggle to discover governing differential equations with considering measurements as a whole, leading to failure to handle this task. We propose an online modeling method capable of handling samples one by one sequentially by modeling streaming data instead of processing the entire dataset. The proposed method performs well in discovering ordinary differential equations (ODEs) and partial differential equations (PDEs) from streaming data. Evolving systems are changing over time, which invariably changes with system status. Thus, finding the exact change points is critical. The measurement generated from a changed system is distributed dissimilarly to before; hence, the difference can be identified by the proposed method. Our proposal is competitive in identifying the change points and discovering governing differential equations in three hybrid systems and two switching linear systems.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 15 of its 67 references that are in the map. First posted on arXiv 19 Jan 2023.

Builds on

15 of 67 references.

References · 15

  1. 2017Deep learning for universal linear embeddings of nonlinear dynamicscited by 491
  2. 2017PDE-Net: Learning PDEs from Datacited by 304
  3. 2017Network Inference via the Time-Varying Graphical Lassocited by 55
  4. 2021Any equation is a forest: Symbolic genetic algorithm for discovering open-form partial differential equations (SGA-PDE)cited by 38
  5. 2022Reduced order modeling of parametrized systems through autoencoders and SINDy approach: continuation of periodic solutionscited by 29
  6. 2020SINDy-BVP: Sparse Identification of Nonlinear Dynamics for Boundary Value Problemscited by 22
  7. 2021Robust discovery of partial differential equations in complex situationscited by 21
  8. 2022Online Weak-form Sparse Identification of Partial Differential Equationscited by 13
  9. 2013Estimating Time-varying Brain Connectivity Networks from Functional MRI Time Seriescited by 11
  10. 2020Sparse Identification of Slow Timescale Dynamicscited by 10
  11. 2020Uncovering differential equations from data with hidden variablescited by 8
  12. 2019Time-varying Autoregression with Low Rank Tensorscited by 6
3 more
  1. 2020Principal component trajectories for modeling spectrally-continuous dynamics as forced linear systemscited by 5
  2. 2022An Online Data-Driven Method to Locate Forced Oscillation Sources from Power Plants Based on Sparse Identification of Nonlinear Dynamics (SINDy)cited by 5
  3. 2016Resolving coiled shapes reveals new reorientation behaviors in C. eleganscited by 2

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Cited by year

Citing papers per year: 2024: 2; 2025: 3.

5 papers.

  1. 2024Weak-Form Inference for Hybrid Dynamical Systems in Ecologycited by 7
  2. 2025Mitigating Data Scarcity in Time Series Analysis: A Foundation Model with Series-Symbol Data Generationcited 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. 2024Automating the Discovery of Partial Differential Equations in Dynamical Systemscited by 0