Automated reverse engineering of nonlinear dynamical systems

By Josh C. Bongard, Hod Lipson. 2007

819 citations recorded by the source corpus.

Subfields: Molecular Biology, Plant Science

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Citations in the corpus

Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations (2018, background): “, 2011; Daniels and Nemenman, 2015a,b), and symbolic regression (Bongard and Lipson, 2007; Schmidt and Lipson, 2009).”
Data-driven discovery of partial differential equations (2016, background): “In this series of developments, seminal contributions leveraging symbolic regression and an evolutionary algorithm (13, 14) were capable of directly determining nonlinear dynamical system from data.”
Discovering governing equations from data by sparse identification of nonlinear dynamical systems (2015, background): “A seminal breakthrough by Bongard and Lipson (3) and Schmidt and Lipson (4) has resulted in a new approach to determine the underlying structure of a nonlinear dynamical system from data.”
Hidden physics models: Machine learning of nonlinear partial differential equations (2017, background): “The literature on data-driven discovery of dynamical systems [3] is vast and encompasses equation-free modeling [4], artificial neural networks [5], nonlinear regression [6], empirical dynamic modeling [7,8], modeling emergent behavior [9], automated inference of dynamics [10–12], normal form identi”
PDE-Net: Learning PDEs from Data (2017, background): “One of earlier attempts on data-driven discovery of hidden physical laws is by Bongard & Lipson (2007) and Schmidt & Lipson (2009).”
Constrained sparse Galerkin regression (2016, background): “Bongard & Lipson (2007) and Schmidt & Lipson (2009) introduced nonlinear system identification based on genetic programming, which has been used in numerous practical applications in aerospace engineering, the petroleum industry and in finance.”
Data-driven discovery of coordinates and governing equations (2019, neutral): “A breakthrough approach used symbolic regression to learn the form of dynamical systems and governing laws from data (1, 3).”
Machine Learning of Space-Fractional Differential Equations (2018, methodology): “Earlier, in [2] in a dynamical system context, the equations were evaluated using “probing” tests while the overfitting was addressed using a separate “snipping” process.”
Inferring Biological Networks by Sparse Identification of Nonlinear Dynamics (2016, methodology): “been used to discover dynamical systems and conservation laws from data [52], [53].”
Data Driven Governing Equations Approximation Using Deep Neural Networks (2018, methodology): “Earlier eﬀorts include methods using symbolic regression ([5, 43]), equation-free modeling [24], heterogeneous multi-scale method (HMM) ([15]), artiﬁcial neural networks ([19]), nonlinear regression ([50]), empirical dynamic modeling ([46, 53]), nonlinear Laplacian spectral analysis ([18]),…”
Physics-Informed Neural Networks for Multiphysics Data Assimilation with Application to Subsurface Transport (2019, background): “For example, Schmidt and Lipson [20] applied symbolic regression to learn conservation laws, and Brunton et al. [21] used sparse regression to discover equations of nonlinear dynamics directly from data.”
Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control (2021, background): “…exist, including equation-free modeling [1], normal form identiﬁcation [2–4], nonlinear Laplacian spectral analysis [5], Koop-man analysis [6, 7] and dynamic mode decomposition (DMD) [8–10], symbolic regression [11–15], sparse regression [16, 17], Gaussian processes [18], and deep learning [19–24].”
Integrating Physics-Based Modeling with Machine Learning: A Survey (2020, background): “Recently, general and robust data-driven discovery of potentially unknown governing equations has been pioneered by [30, 227], where they apply symbolic regression to differences between computed derivatives and analytic derivatives to determine underlying dynamical systems.”
SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics (2020, methodology): “…Koopman theory [6–9], nonlinear autoregressive models [10, 11], neural networks [12–20], Gaussian process regression [21, 22], nonlinear Laplacian spectral analysis [23], diffusion maps [24], genetic programming [25–27], and sparse regression [28, 29], to highlight some of the recent developments.”
PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network (2018, background): “Earlier attempts on data-driven discovery of hidden physical laws include [4, 5].”
Identifying Causal Structure in Large-Scale Kinetic Systems (2018, methodology): “A similar idea for polynomials is proposed by Tran and Ward [2017] and for stochastic differential equations by Boninsegna et al. [2018]. These approaches can also be extended and applied to finding PDEs [Rudy et al., 2017, Schaeffer, 2017]. On a critical note, it has been suggested that approaches ”