Sparse Regression and Adaptive Feature Generation for the Discovery of Dynamical Systems

Kulkarni, Chinmay S.; Gupta, Abhinav; Lermusiaux, Pierre F. J.

doi:10.1007/978-3-030-61725-7_25

Cited by 8 publications

(3 citation statements)

References 21 publications

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“…In practice, the value of λ may need to be adjusted in different systems and can be determined considering the expected sparsity level of Ξ ab . Besides, the sparse promoting process for the thresholded Least absolute Shrinkage and Selection Operator (thresholded LASSO) [39] can also be used to promote the non-zero coefficients in the proposed algorithm without the need of selecting λ.…”

Section: Remarksmentioning

confidence: 99%

An Online Data-Driven Method to Locate Forced Oscillation Sources From Power Plants Based on Sparse Identification of Nonlinear Dynamics (SINDy)

Cai

Wang

Joós

et al. 2023

IEEE Trans. Power Syst.

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Forced oscillations may jeopardize the secure operation of power systems. To mitigate forced oscillations, locating the sources is critical. In this paper, leveraging on Sparse Identification of Nonlinear Dynamics (SINDy), an online purely data-driven method to locate the forced oscillation is developed. Validations in all simulated cases (in the WECC 179-bus system) and actual oscillation events (in ISO New England system) in the IEEE Task Force test cases library are carried out, which demonstrate that the proposed algorithm, requiring no model information, can accurately locate sources in most cases, even under resonance condition and when the natural modes are poorly damped. The little tuning requirement and low computational cost make the proposed method viable for online application.

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Section: Remarksmentioning

confidence: 99%

An Online Data-Driven Method to Locate Forced Oscillation Sources From Power Plants Based on Sparse Identification of Nonlinear Dynamics (SINDy)

Cai

Wang

Joós

et al. 2023

IEEE Trans. Power Syst.

View full text Add to dashboard Cite

show abstract

“…Such a requirement on the training data can be a luxury in a lot of scenarios. The requirement of very frequent snapshot data of the system is also true for methods which achieve model discovery using sparse-regression and provide interpretable learned models [8,18,19]. All of the above issues are addressed by using neural ordinary differential equations (nODEs; [20]) and some researchers recently used nODEs for closure modelling.…”

Section: Introductionmentioning

confidence: 99%

Neural closure models for dynamical systems

Gupta

Lermusiaux

2021

Proc. R. Soc. A.

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Complex dynamical systems are used for predictions in many domains. Because of computational costs, models are truncated, coarsened or aggregated. As the neglected and unresolved terms become important, the utility of model predictions diminishes. We develop a novel, versatile and rigorous methodology to learn non-Markovian closure parametrizations for known-physics/low-fidelity models using data from high-fidelity simulations. The new neural closure models augment low-fidelity models with neural delay differential equations (nDDEs), motivated by the Mori–Zwanzig formulation and the inherent delays in complex dynamical systems. We demonstrate that neural closures efficiently account for truncated modes in reduced-order-models, capture the effects of subgrid-scale processes in coarse models and augment the simplification of complex biological and physical–biogeochemical models. We find that using non-Markovian over Markovian closures improves long-term prediction accuracy and requires smaller networks. We derive adjoint equations and network architectures needed to efficiently implement the new discrete and distributed nDDEs, for any time-integration schemes and allowing non-uniformly spaced temporal training data. The performance of discrete over distributed delays in closure models is explained using information theory, and we find an optimal amount of past information for a specified architecture. Finally, we analyse computational complexity and explain the limited additional cost due to neural closure models.

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“…Such requirement on the training data might be a luxury in a lot of scenarios. The requirement of very frequent snapshot data of the system is also true for methods which achieve model discovery using sparse-regression and provide interpretable learned models [12,42]. These issues are addressed by using neural ordinary differential equations (nODEs; [16]) and some researchers recently used nODEs for closure modeling.…”

Section: Introductionmentioning

confidence: 99%

Neural Closure Models for Dynamical Systems

Gupta,

Lermusiaux

2020

Preprint

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Complex dynamical systems are used for predictions in many applications. Because of computational costs, models are however often truncated, coarsened, or aggregated. As the neglected and unresolved terms along with their interactions with the resolved ones become important, the usefulness of model predictions diminishes. We develop a novel, versatile, and rigorous methodology to learn non-Markovian closure parameterizations for low-fidelity models using data from high-fidelity simulations. The new neural closure models augment low-fidelity models with neural delay differential equations (nDDEs), motivated by the Mori-Zwanzig formulation and the inherent delays in natural dynamical systems. We demonstrate that neural closures efficiently account for truncated modes in reduced-order-models, capture the effects of subgridscale processes in coarse models, and augment the simplification of complex biochemical models. We show that using non-Markovian over Markovian closures improves long-term accuracy and requires smaller networks. We provide adjoint equation derivations and network architectures needed to efficiently implement the new discrete and distributed nDDEs. The performance of discrete over distributed delays in closure models is explained using information theory, and we observe an optimal amount of past information for a specified architecture. Finally, we analyze computational complexity and explain the limited additional cost due to neural closure models.

show abstract

Sparse Regression and Adaptive Feature Generation for the Discovery of Dynamical Systems

Cited by 8 publications

References 21 publications

An Online Data-Driven Method to Locate Forced Oscillation Sources From Power Plants Based on Sparse Identification of Nonlinear Dynamics (SINDy)

An Online Data-Driven Method to Locate Forced Oscillation Sources From Power Plants Based on Sparse Identification of Nonlinear Dynamics (SINDy)

Neural closure models for dynamical systems

Neural Closure Models for Dynamical Systems

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