ArticleJournal of computational physics2021
WEAK SINDY FOR PARTIAL DIFFERENTIAL EQUATIONS.
Article in Journal of computational physics, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 34 papers.
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34 citing papers in PubMed.
- Beyond empirical models: Discovering constitutive laws in solids with graph-based equation discovery.Science advances · 2026Article
- Explainable AI: learning from the learners.Nature communications · 2026Review
- Discovering a low-dimensional temperature control architecture across animals.Scientific reports · 2026Article
- Sparse identification of nonlinear dynamics and Koopman operators with Shallow Recurrent Decoder Networks.Proceedings of the National Academy of Sciences of the United States of America · 2026Article
- Enhancing generalizability of model discovery across parameter space with multi-experiment equation learning for biological systems.PLoS computational biology · 2026Article
- A Practical Identifiability Criterion Leveraging Weak-Form Parameter Estimation.Bulletin of mathematical biology · 2026Article
- Article
- Learning structured population models from data with WSINDy.PLoS computational biology · 2025Article
- SINDy-RL for interpretable and efficient model-based reinforcement learning.Nature communications · 2025Article
- Generative discovery of partial differential equations by learning from math handbooks.Nature communications · 2025Article
- Data-driven identification of biological systems using multi-scale analysis.PLoS computational biology · 2025Article
- WEAK FORM LEARNING FOR MEAN-FIELD PARTIAL DIFFERENTIAL EQUATIONS: AN APPLICATION TO INSECT MOVEMENT.ArXiv · 2025Article
- Inference of weak-form partial differential equations describing migration and proliferation mechanisms in wound healing experiments on cancer cells.PLoS computational biology · 2025Article
- Implicit Runge-Kutta based sparse identification of governing equations in biologically motivated systems.Scientific reports · 2025Article
- Article
- Hypergraph reconstruction from dynamics.Nature communications · 2025Article
- Data-driven model discovery and model selection for noisy biological systems.PLoS computational biology · 2025Article
- Weak-form inference for hybrid dynamical systems in ecology.Journal of the Royal Society, Interface · 2024Article
- Physics-informed genetic programming for discovery of partial differential equations from scarce and noisy data.Journal of computational physics · 2024Article
- Coarse-graining Hamiltonian systems using WSINDy.Scientific reports · 2024Article
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2 authors.
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Abstract
Sparse Identification of Nonlinear Dynamics (SINDy) is a method of system discovery that has been shown to successfully recover governing dynamical systems from data [6, 39]. Recently, several groups have independently discovered that the weak formulation provides orders of magnitude better robustness to noise. Here we extend our Weak SINDy (WSINDy) framework introduced in [28] to the setting of partial differential equations (PDEs). The elimination of pointwise derivative approximations via the weak form enables effective machine-precision recovery of model coefficients from noise-free data (i.e. below the tolerance of the simulation scheme) as well as robust identification of PDEs in the large noise regime (with signal-to-noise ratio approaching one in many well-known cases). This is accomplished by discretizing a convolutional weak form of the PDE and exploiting separability of test functions for efficient model identification using the Fast Fourier Transform. The resulting WSINDy algorithm for PDEs has a worst-case computational complexity of
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