Learning partial differential equations via data discovery and sparse optimization

By Hayden Schaeffer. 2017

531 citations recorded by the source corpus.

Subfields: Computational Mechanics, Modeling and Simulation, Statistical and Nonlinear Physics

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Citations in the corpus

PDE-Net: Learning PDEs from Data (2017, methodology): “Recently, Brunton et al. (2016), Schaeffer (2017), Rudy et al. (2017) and Wu & Zhang (2017) propose an alternative approach using sparse regression.”
Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control (2021, methodology): “First, we introduce SINDy to identify ordinary differential equations, followed by its generalization to identify partial differential equations [17, 26].”
Data Driven Governing Equations Approximation Using Deep Neural Networks (2018, background): “Many studies have been conducted to effectively deal with noises in data ([7, 40]), corruptions in data ([48]), partial differential equations [38, 41], etc.”
Data-driven discovery of PDEs in complex datasets (2018, methodology): “Depending on the choice of parametrization of L̂ it is possible to discover a wide range of PDEs and encompass the methods described in [31, 5, 33, 34, 25, 29] in a single framework.”
Data-driven Discovery of Partial Differential Equations for Multiple-Physics Electromagnetic Problem (2019, methodology): “Later, sparse regression method was raised by Brunton et al. (2016) [3], Schaeffer (2017) [4], and Rudy et al. (2017) [5].”
Identifying Causal Structure in Large-Scale Kinetic Systems (2018, unknown): “These approaches can also be extended and applied to finding PDEs [Rudy et al., 2017, Schaeffer, 2017].”
SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics (2020, methodology): “In a short time, the SINDy algorithm has been extended to include inputs and control [48], to identify partial differential equations [29, 30], to incorporate physically relevant constraints [34], to include tensor bases [45], and to incorporate integral terms for denoising [49, 50].”
Universal Differential Equations for Scientific Machine Learning (2020, background): “Symbolic reconstruction of equations has utilized symbolic regressions which require a prechosen basis [73, 74], or evolutionary meth-ods to grow a basis [75, 76].”
Data-driven discovery of coordinates and governing equations (2019, unknown): “There are also a number of theoretical extensions to the SINDy framework, including for identifying partial differential equations (10, 37), and models with rational function nonlinearities (38).”
Solving Irregular and Data-enriched Differential Equations using Deep Neural Networks (2019, background): “These types of approaches are emerging with increasing interest [54, 55, 56, 57, 58], and it is easy to see how such approaches naturally lend themselves to the DNN frameworks.”
Constrained sparse Galerkin regression (2016, methodology): “However, the extensions of SINDy to identify partial differential equations (Rudy et al. 2017; Schaeffer 2017) and biological regulatory networks (Mangan et al. 2016) highlight the flexibility of this simple regression framework.”
WEAK SINDY FOR PARTIAL DIFFERENTIAL EQUATIONS (2020, methodology): “Sparse regression approaches for learning PDEs from data have seen a tremendous spike in activity in the years since 2016, stemming from the pioneering works [34] and [32].”