ArticleScience advances2017
Data-driven discovery of partial differential equations.
Article in Science advances, 2017. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 155 papers.
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Who cites it
155 citing papers in PubMed.
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- Exploring memory effects: Sparse identification in vector-borne diseases.Proceedings of the National Academy of Sciences of the United States of America · 2026Article
- Nonlinear Correlation of POD and DMD Modal Coefficients in Reduced-Order Modeling of Flow Around a Cylinder in a Microchannel.Micromachines · 2026Article
- Discovering multiscale deep formulas in complex systems via neural-guided lambda calculus.Nature communications · 2026Article
- Journey toward a Global Understanding of Recombination in Halide Perovskites for Photovoltaic Applications.ACS energy letters · 2026Review
- Moving from table to graph in physics-informed spatio-temporal symbolic regression.Scientific reports · 2026Article
- Reduced-order modeling of nonlinear multiscale industrial systems via sparse regression in latent representations.Scientific reports · 2026Article
- Encoding Cumulation to Learn Perturbative Nonlinear Oscillatory Dynamics.Advanced science (Weinheim, Baden-Wurttemberg, Germany) · 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
- Identification of a personalized eGFR threshold improves the prediction of kidney failure risk after transplantation.Communications medicine · 2026Article
- Gaps and ways forward in atmospheric blocking and extreme weather research.Nature communications · 2026Review
- A novel spatiotemporal decomposition and identification of sparse equations for human brain deformation.Scientific reports · 2026Article
- Article
- Dynamic Temporal Modeling of Abdominal Aortic Aneurysm Morphology with Z-SINDy.medRxiv : the preprint server for health sciences · 2026Article
95 more citing papers are in PubMed but not listed here.
Corrections and comments
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Authors and funding
4 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with the dynamics. The method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Moreover, the method is capable of disambiguating between potentially nonunique dynamical terms by using multiple time series taken with different initial data. Thus, for a traveling wave, the method can distinguish between a linear wave equation and the Korteweg-de Vries equation, for instance. The method provides a promising new technique for discovering governing equations and physical laws in parameterized spatiotemporal systems, where first-principles derivations are intractable.
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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.