Reactive SINDy: Discovering governing reactions from concentration data

Hoffmann, Moritz; Fröhner, Christoph; Noé, Frank

doi:10.1101/442095

Cited by 8 publications

(8 citation statements)

References 38 publications

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“…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]. These extensions and its simple formulation in terms of a generalized linear model in (1.1) have resulted in SINDy being adopted in the fields of fluid mechanics [34,37], nonlinear optics [31], plasma physics [32], chemical reactions [33,36,39], numerical methods [41] and structural modelling [42].…”

Section: Introductionmentioning

confidence: 99%

SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics

2020

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Accurately modelling the nonlinear dynamics of a system from measurement data is a challenging yet vital topic. The sparse identification of nonlinear dynamics (SINDy) algorithm is one approach to discover dynamical systems models from data. Although extensions have been developed to identify implicit dynamics, or dynamics described by rational functions, these extensions are extremely sensitive to noise. In this work, we develop SINDy-PI (parallel, implicit), a robust variant of the SINDy algorithm to identify implicit dynamics and rational nonlinearities. The SINDy-PI framework includes multiple optimization algorithms and a principled approach to model selection. We demonstrate the ability of this algorithm to learn implicit ordinary and partial differential equations and conservation laws from limited and noisy data. In particular, we show that the proposed approach is several orders of magnitude more noise robust than previous approaches, and may be used to identify a class of ODE and PDE dynamics that were previously unattainable with SINDy, including for the double pendulum dynamics and simplified model for the Belousov–Zhabotinsky (BZ) reaction.

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Section: Introductionmentioning

confidence: 99%

SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics

2020

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“…We now demonstrate the identification of a parsimonious nonlinear model for EC using the sparse identification of nonlinear dynamics (SINDy) [ 79 ] approach; results are summarized in figure 4 . SINDy has been widely applied for model identification in a variety of applications, including chemical reaction dynamics [ 88 ], nonlinear optics [ 89 ], fluid dynamics [ 80 – 82 , 90 , 91 ] and turbulence modelling [ 92 , 93 ], plasma convection [ 94 ], numerical algorithms [ 95 ], and structural modelling [ 96 ], among others [ 97 – 99 ]. Of particular note are its uses in identifying Lorenz-like dynamics from a thermosyphon simulation by Loiseau [ 82 ] and to identify a model for a nonlinear magnetohydrodynamic plasma system by Kaptanoglu et al [ 100 ].…”

Section: Sparse Nonlinear Reduced-order Modelsmentioning

confidence: 99%

Sparse nonlinear models of chaotic electroconvection

2021

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Convection is a fundamental fluid transport phenomenon, where the large-scale motion of a fluid is driven, for example, by a thermal gradient or an electric potential. Modelling convection has given rise to the development of chaos theory and the reduced-order modelling of multiphysics systems; however, these models have been limited to relatively simple thermal convection phenomena. In this work, we develop a reduced-order model for chaotic electroconvection at high electric Rayleigh number. The chaos in this system is related to the standard Lorenz model obtained from Rayleigh–Benard convection, although our system is driven by a more complex three-way coupling between the fluid, the charge density, and the electric field. Coherent structures are extracted from temporally and spatially resolved charge density fields via proper orthogonal decomposition (POD). A nonlinear model is then developed for the chaotic time evolution of these coherent structures using the sparse identification of nonlinear dynamics (SINDy) algorithm, constrained to preserve the symmetries observed in the original system. The resulting model exhibits the dominant chaotic dynamics of the original high-dimensional system, capturing the essential nonlinear interactions with a simple reduced-order model.

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“…In this method, many SINDy variants have been proposed, for example, exhibiting multiscale physical phenomenon by discovering nonlinear multiscale systems (Champion, Brunton, and Kutz 2019), and characterizing hybrid (switching) behaviors by using Hybrid-SINDy (Mangan et al 2019). In addition, SINDy has been widely applied to discover nonlinear equations for biological network systems (Mangan et al 2016), fluid flows (Loiseau and Brunton 2018), model predictive control (Kaiser, Kutz, and Brunton 2018), convection in a plasma (Dam et al 2017) and chemical reaction dynamics (Hoffmann, Frohner, and Noé 2019).…”

Section: Related Workmentioning

confidence: 99%

Robust Low-Rank Discovery of Data-Driven Partial Differential Equations

Sun

Zhao

et al. 2020

AAAI

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Partial differential equations (PDEs) are essential foundations to model dynamic processes in natural sciences. Discovering the underlying PDEs of complex data collected from real world is key to understanding the dynamic processes of natural laws or behaviors. However, both the collected data and their partial derivatives are often corrupted by noise, especially from sparse outlying entries, due to measurement/process noise in the real-world applications. Our work is motivated by the observation that the underlying data modeled by PDEs are in fact often low rank. We thus develop a robust low-rank discovery framework to recover both the low-rank data and the sparse outlying entries by integrating double low-rank and sparse recoveries with a (group) sparse regression method, which is implemented as a minimization problem using mixed nuclear norms with ℓ1 and ℓ0 norms. We propose a low-rank sequential (grouped) threshold ridge regression algorithm to solve the minimization problem. Results from several experiments on seven canonical models (i.e., four PDEs and three parametric PDEs) verify that our framework outperforms the state-of-art sparse and group sparse regression methods. Code is available at https://github.com/junli2019/Robust-Discovery-of-PDEs

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Reactive SINDy: Discovering governing reactions from concentration data

Cited by 8 publications

References 38 publications

SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics

SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics

Sparse nonlinear models of chaotic electroconvection

Robust Low-Rank Discovery of Data-Driven Partial Differential Equations

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