Amortized Equation Discovery in Hybrid Dynamical Systems

Yongtuo Liu, Sara Magliacane, Miltiadis Kofinas, Stratis Gavves
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:31645-31668, 2024.

Abstract

Hybrid dynamical systems are prevalent in science and engineering to express complex systems with continuous and discrete states. To learn laws of systems, all previous methods for equation discovery in hybrid systems follow a two-stage paradigm, i.e. they first group time series into small cluster fragments and then discover equations in each fragment separately through methods in non-hybrid systems. Although effective, performance is then limited because these methods ignore the commonalities in the shared dynamics of fragments that are driven by the same equations. Besides, the two-stage paradigm breaks the interdependence between categorizing and representing dynamics that jointly form hybrid systems. In this paper, we reformulate the problem and propose an end-to-end learning framework, i.e. Amortized Equation Discovery (AMORE), to jointly categorize modes and discover equations characterizing motion dynamics of each mode by all segments of the mode. Experiments on four hybrid and six non-hybrid systems demonstrate the superior performance of our method against previous methods on equation discovery, segmentation, and forecasting.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-liu24at, title = {Amortized Equation Discovery in Hybrid Dynamical Systems}, author = {Liu, Yongtuo and Magliacane, Sara and Kofinas, Miltiadis and Gavves, Stratis}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {31645--31668}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/liu24at/liu24at.pdf}, url = {https://proceedings.mlr.press/v235/liu24at.html}, abstract = {Hybrid dynamical systems are prevalent in science and engineering to express complex systems with continuous and discrete states. To learn laws of systems, all previous methods for equation discovery in hybrid systems follow a two-stage paradigm, i.e. they first group time series into small cluster fragments and then discover equations in each fragment separately through methods in non-hybrid systems. Although effective, performance is then limited because these methods ignore the commonalities in the shared dynamics of fragments that are driven by the same equations. Besides, the two-stage paradigm breaks the interdependence between categorizing and representing dynamics that jointly form hybrid systems. In this paper, we reformulate the problem and propose an end-to-end learning framework, i.e. Amortized Equation Discovery (AMORE), to jointly categorize modes and discover equations characterizing motion dynamics of each mode by all segments of the mode. Experiments on four hybrid and six non-hybrid systems demonstrate the superior performance of our method against previous methods on equation discovery, segmentation, and forecasting.} }
Endnote
%0 Conference Paper %T Amortized Equation Discovery in Hybrid Dynamical Systems %A Yongtuo Liu %A Sara Magliacane %A Miltiadis Kofinas %A Stratis Gavves %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-liu24at %I PMLR %P 31645--31668 %U https://proceedings.mlr.press/v235/liu24at.html %V 235 %X Hybrid dynamical systems are prevalent in science and engineering to express complex systems with continuous and discrete states. To learn laws of systems, all previous methods for equation discovery in hybrid systems follow a two-stage paradigm, i.e. they first group time series into small cluster fragments and then discover equations in each fragment separately through methods in non-hybrid systems. Although effective, performance is then limited because these methods ignore the commonalities in the shared dynamics of fragments that are driven by the same equations. Besides, the two-stage paradigm breaks the interdependence between categorizing and representing dynamics that jointly form hybrid systems. In this paper, we reformulate the problem and propose an end-to-end learning framework, i.e. Amortized Equation Discovery (AMORE), to jointly categorize modes and discover equations characterizing motion dynamics of each mode by all segments of the mode. Experiments on four hybrid and six non-hybrid systems demonstrate the superior performance of our method against previous methods on equation discovery, segmentation, and forecasting.
APA
Liu, Y., Magliacane, S., Kofinas, M. & Gavves, S.. (2024). Amortized Equation Discovery in Hybrid Dynamical Systems. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:31645-31668 Available from https://proceedings.mlr.press/v235/liu24at.html.

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