Bayesian system ID: optimal management of parameter, model, and measurement uncertainty

Galioto, Nicholas; Gorodetsky, Alex

doi:10.1007/s11071-020-05925-8

Cited by 24 publications

(66 citation statements)

References 66 publications

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“…SINDy has been widely adopted, in part, because it is highly extensible. Extensions of the SINDy algorithm include accounting for control inputs [46] and rational functions [47,48], enforcing known conservation laws and symmetries [30], promoting stability [49], improved noise robustness through the integral formulation [37,[50][51][52][53][54], generalizations for stochastic dynamics [44,55] and tensor formulations [56], and probabilistic model discovery via sparse Bayesian inference [57][58][59][60][61]. Many of these innovations have been incorporated into the open source software package PySINDy [62,63].…”

Section: Introductionmentioning

confidence: 99%

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Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control

et al. 2022

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Sparse model identification enables the discovery of nonlinear dynamical systems purely from data; however, this approach is sensitive to noise, especially in the low-data limit. In this work, we leverage the statistical approach of bootstrap aggregating (bagging) to robustify the sparse identification of the nonlinear dynamics (SINDy) algorithm. First, an ensemble of SINDy models is identified from subsets of limited and noisy data. The aggregate model statistics are then used to produce inclusion probabilities of the candidate functions, which enables uncertainty quantification and probabilistic forecasts. We apply this ensemble-SINDy (E-SINDy) algorithm to several synthetic and real-world datasets and demonstrate substantial improvements to the accuracy and robustness of model discovery from extremely noisy and limited data. For example, E-SINDy uncovers partial differential equations models from data with more than twice as much measurement noise as has been previously reported. Similarly, E-SINDy learns the Lotka Volterra dynamics from remarkably limited data of yearly lynx and hare pelts collected from 1900 to 1920. E-SINDy is computationally efficient, with similar scaling as standard SINDy. Finally, we show that ensemble statistics from E-SINDy can be exploited for active learning and improved model predictive control.

show abstract

Section: Introductionmentioning

confidence: 99%

“…When dealing with noise-compromised data, it is also critical to provide uncertainty estimates of the discovered models. In this direction, recent innovations of SINDy use sparse Bayesian inference for probabilistic model discovery [57][58][59][60]. Such methods employ Markov Chain Monte Carlo, which is extremely computationally intensive.…”

Section: Introductionmentioning

confidence: 99%

Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control

et al. 2022

View full text Add to dashboard Cite

show abstract

“…SINDy has been widely adopted, in part, because it is highly extensible. Extensions of the SINDy algorithm include accounting for control inputs [43] and rational functions [44,45], enforcing known conservation laws and symmetries [27], promoting stability [46], improved noise robustness through the integral formulation [34,[47][48][49][50][51], generalizations for stochastic dynamics [41,52] and tensor formulations [53], and probabilistic model discovery via sparse Bayesian inference [54][55][56][57][58]. Many of these innovations have been incorporated into the open source software package PySINDy [59,60].…”

Section: Introductionmentioning

confidence: 99%

“…When dealing with noise compromised data, it is also critical to provide uncertainty estimates of the discovered models. In this direction, recent innovations of SINDy use sparse Bayesian inference for probabilistic model discovery [54][55][56][57]. Such methods employ Markov Chain Monte Carlo, which is extremely computationally intensive.…”

Section: Introductionmentioning

confidence: 99%

Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control

Fasel,

Kutz,

Brunton

et al. 2021

Preprint

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Sparse model identification enables the discovery of nonlinear dynamical systems purely from data; however, this approach is sensitive to noise, especially in the low-data limit. In this work, we leverage the statistical approach of bootstrap aggregating (bagging) to robustify the sparse identification of nonlinear dynamics (SINDy) algorithm. First, an ensemble of SINDy models is identified from subsets of limited and noisy data. The aggregate model statistics are then used to produce inclusion probabilities of the candidate functions, which enables uncertainty quantification and probabilistic forecasts. We apply this ensemble-SINDy (E-SINDy) algorithm to several synthetic and real-world data sets and demonstrate substantial improvements to the accuracy and robustness of model discovery from extremely noisy and limited data. For example, E-SINDy uncovers partial differential equations models from data with more than twice as much measurement noise as has been previously reported. Similarly, E-SINDy learns the Lotka Volterra dynamics from remarkably limited data of yearly lynx and hare pelts collected from 1900-1920. E-SINDy is computationally efficient, with similar scaling as standard SINDy. Finally, we show that ensemble statistics from E-SINDy can be exploited for active learning and improved model predictive control.

show abstract

“…Learning methods that do not require time derivatives have also been developed, in conjunction with, for example, dynamic mode decomposition (DMD) [26], Koopman operator theory [13,14], hidden Markov models [6], and more recently, deep neural network (DNN) [20]. The work of [20] also established a newer framework, which, instead of directly approximating the underlying governing equations like in most other methods, seeks to approximate the flow map of the unknown system.…”

mentioning

confidence: 99%

Data-driven learning of non-autonomous systems

Qin

Chen

Jakeman

et al. 2020

Preprint

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We present a numerical framework for recovering unknown non-autonomous dynamical systems with time-dependent inputs. To circumvent the difficulty presented by the nonautonomous nature of the system, our method transforms the solution state into piecewise integration of the system over a discrete set of time instances. The time-dependent inputs are then locally parameterized by using a proper model, for example, polynomial regression, in the pieces determined by the time instances. This transforms the original system into a piecewise parametric system that is locally time invariant. We then design a deep neural network structure to learn the local models. Once the network model is constructed, it can be iteratively used over time to conduct global system prediction. We provide theoretical analysis of our algorithm and present a number of numerical examples to demonstrate the effectiveness of the method.

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Bayesian system ID: optimal management of parameter, model, and measurement uncertainty

Cited by 24 publications

References 66 publications

Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control

Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control

Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control

Data-driven learning of non-autonomous systems

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