ArticleProceedings. Mathematical, physical, and engineering sciences2018
Robust data-driven discovery of governing physical laws with error bars.
Article in Proceedings. Mathematical, physical, and engineering sciences, 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 18 papers.
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Who cites it
18 citing papers in PubMed.
- Gaps and ways forward in atmospheric blocking and extreme weather research.Nature communications · 2026Review
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- Data-driven discovery of digital twins in biomedical research.Briefings in bioinformatics · 2026Review
- Generative discovery of partial differential equations by learning from math handbooks.Nature communications · 2025Article
- Distilling identifiable and interpretable dynamic models from biological data.PLoS computational biology · 2023Article
- Sparse regression for low-dimensional time-dynamic varying coefficient models with application to air quality data.Journal of applied statistics · 2023Article
- Actual evapotranspiration by machine learning and remote sensing without the thermal spectrum.PloS one · 2023Article
- Sparse inference and active learning of stochastic differential equations from data.Scientific reports · 2022Article
- Model-informed experimental design recommendations for distinguishing intrinsic and acquired targeted therapeutic resistance in head and neck cancer.NPJ systems biology and applications · 2022Article
- Stability selection enables robust learning of differential equations from limited noisy data.Proceedings. Mathematical, physical, and engineering sciences · 2022Article
- WEAK SINDY FOR PARTIAL DIFFERENTIAL EQUATIONS.Journal of computational physics · 2021Article
- Learning differential equation models from stochastic agent-based model simulations.Journal of the Royal Society, Interface · 2021Article
- WEAK SINDy: GALERKIN-BASED DATA-DRIVEN MODEL SELECTION.Multiscale modeling & simulation : a SIAM interdisciplinary journal · 2021Article
- Development of a hybrid model for a partially known intracellular signaling pathway through correction term estimation and neural network modeling.PLoS computational biology · 2020Article
- SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics.Proceedings. Mathematical, physical, and engineering sciences · 2020Article
- Learning Equations from Biological Data with Limited Time Samples.Bulletin of mathematical biology · 2020Article
- Learning partial differential equations for biological transport models from noisy spatio-temporal data.Proceedings. Mathematical, physical, and engineering sciences · 2020Article
- Applying Machine Learning to Improve Simulations of a Chaotic Dynamical System Using Empirical Error Correction.Journal of advances in modeling earth systems · 2019Article
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2 authors.
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Abstract
Discovering governing physical laws from noisy data is a grand challenge in many science and engineering research areas. We present a new approach to data-driven discovery of ordinary differential equations (ODEs) and partial differential equations (PDEs), in explicit or implicit form. We demonstrate our approach on a wide range of problems, including shallow water equations and Navier-Stokes equations. The key idea is to select candidate terms for the underlying equations using dimensional analysis, and to approximate the weights of the terms with error bars using our threshold sparse Bayesian regression. This new algorithm employs Bayesian inference to tune the hyperparameters automatically. Our approach is effective, robust and able to quantify uncertainties by providing an error bar for each discovered candidate equation. The effectiveness of our algorithm is demonstrated through a collection of classical ODEs and PDEs. Numerical experiments demonstrate the robustness of our algorithm with respect to noisy data and its ability to discover various candidate equations with error bars that represent the quantified uncertainties. Detailed comparisons with the sequential threshold least-squares algorithm and the lasso algorithm are studied from noisy time-series measurements and indicate that the proposed method provides more robust and accurate results. In addition, the data-driven prediction of dynamics with error bars using discovered governing physical laws is more accurate and robust than classical polynomial regressions.
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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.