EMILY: Extracting sparse Model from ImpLicit dYnamics

Ayan Banerjee, Sandeep Gupta
Proceedings of the 1st ECAI Workshop on "Machine Learning Meets Differential Equations: From Theory to Applications", PMLR 255:1-11, 2024.

Abstract

Sparse model recovery requires us to extract model coefficients of ordinary differential equations (ODE) with few nonlinear terms from data. This problem has been effectively solved in recent literature for the case when all state variables of the ODE are measured. In practical deployments, measurements of all the state variables of the underlying ODE model of a process are not available, resulting in implicit (unmeasured) dynamics. In this paper, we propose EMILY, that can extract the underlying ODE of a dynamical process even if much of the dynamics is implicit. We show the utility of EMILY on four baseline examples and compare with the state-of-the-art techniques such as SINDY-MPC. Results show that unlike SINDY-MPC, EMILY can recover model coefficients accurately under implicit dynamics.

Cite this Paper

BibTeX
@InProceedings{pmlr-v255-banerjee24a, title = {EMILY: Extracting sparse Model from ImpLicit dYnamics}, author = {Banerjee, Ayan and Gupta, Sandeep}, booktitle = {Proceedings of the 1st ECAI Workshop on "Machine Learning Meets Differential Equations: From Theory to Applications"}, pages = {1--11}, year = {2024}, editor = {Coelho, Cecı́lia and Zimmering, Bernd and Costa, M. Fernanda P. and Ferrás, Luı́s L. and Niggemann, Oliver}, volume = {255}, series = {Proceedings of Machine Learning Research}, month = {20 Oct}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v255/main/assets/banerjee24a/banerjee24a.pdf}, url = {https://proceedings.mlr.press/v255/banerjee24a.html}, abstract = {Sparse model recovery requires us to extract model coefficients of ordinary differential equations (ODE) with few nonlinear terms from data. This problem has been effectively solved in recent literature for the case when all state variables of the ODE are measured. In practical deployments, measurements of all the state variables of the underlying ODE model of a process are not available, resulting in implicit (unmeasured) dynamics. In this paper, we propose EMILY, that can extract the underlying ODE of a dynamical process even if much of the dynamics is implicit. We show the utility of EMILY on four baseline examples and compare with the state-of-the-art techniques such as SINDY-MPC. Results show that unlike SINDY-MPC, EMILY can recover model coefficients accurately under implicit dynamics.} }
Endnote
%0 Conference Paper %T EMILY: Extracting sparse Model from ImpLicit dYnamics %A Ayan Banerjee %A Sandeep Gupta %B Proceedings of the 1st ECAI Workshop on "Machine Learning Meets Differential Equations: From Theory to Applications" %C Proceedings of Machine Learning Research %D 2024 %E Cecı́lia Coelho %E Bernd Zimmering %E M. Fernanda P. Costa %E Luı́s L. Ferrás %E Oliver Niggemann %F pmlr-v255-banerjee24a %I PMLR %P 1--11 %U https://proceedings.mlr.press/v255/banerjee24a.html %V 255 %X Sparse model recovery requires us to extract model coefficients of ordinary differential equations (ODE) with few nonlinear terms from data. This problem has been effectively solved in recent literature for the case when all state variables of the ODE are measured. In practical deployments, measurements of all the state variables of the underlying ODE model of a process are not available, resulting in implicit (unmeasured) dynamics. In this paper, we propose EMILY, that can extract the underlying ODE of a dynamical process even if much of the dynamics is implicit. We show the utility of EMILY on four baseline examples and compare with the state-of-the-art techniques such as SINDY-MPC. Results show that unlike SINDY-MPC, EMILY can recover model coefficients accurately under implicit dynamics.
APA
Banerjee, A. & Gupta, S.. (2024). EMILY: Extracting sparse Model from ImpLicit dYnamics. Proceedings of the 1st ECAI Workshop on "Machine Learning Meets Differential Equations: From Theory to Applications", in Proceedings of Machine Learning Research 255:1-11 Available from https://proceedings.mlr.press/v255/banerjee24a.html.

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