Optimal Control of a Coastal Ecosystem Through Neural Ordinary Differential Equations

Cecília Coelho, Fernanda Costa, Luís Ferrás
Proceedings of the 1st ECAI Workshop on "Machine Learning Meets Differential Equations: From Theory to Applications", PMLR 255:1-9, 2024.

Abstract

Optimal control problems (OCPs) are essentials in various domains such as science, engineering, and industry, requiring the optimisation of control variables for dynamic systems, along with the corresponding state variables, that minimise a given performance index. Traditional methods for solving OCPs often rely on numerical techniques and can be computationally expensive when the discretisation grid or time horizon changes. In this work, we introduce a novel approach that leverages Neural Ordinary Differential Equations (Neural ODEs) to model the dynamics of control variables in OCPs. By embedding Neural ODEs within the optimisation problem, we effectively address the limitations of traditional methods, eliminating the need to re-solve the OCP under different discretisation schemes. We apply this method to a coastal ecosystem OCP, demonstrating its efficacy in solving the problem over a 50-year horizon and extending predictions up to 70 years without re-solve the optimisation problem.

Cite this Paper

BibTeX
@InProceedings{pmlr-v255-coelho24a, title = {Optimal Control of a Coastal Ecosystem Through Neural Ordinary Differential Equations}, author = {Coelho, Cec\'{i}lia and Costa, Fernanda and Ferr\'{a}s, Lu\'{i}s}, booktitle = {Proceedings of the 1st ECAI Workshop on "Machine Learning Meets Differential Equations: From Theory to Applications"}, pages = {1--9}, 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/coelho24a/coelho24a.pdf}, url = {https://proceedings.mlr.press/v255/coelho24a.html}, abstract = {Optimal control problems (OCPs) are essentials in various domains such as science, engineering, and industry, requiring the optimisation of control variables for dynamic systems, along with the corresponding state variables, that minimise a given performance index. Traditional methods for solving OCPs often rely on numerical techniques and can be computationally expensive when the discretisation grid or time horizon changes. In this work, we introduce a novel approach that leverages Neural Ordinary Differential Equations (Neural ODEs) to model the dynamics of control variables in OCPs. By embedding Neural ODEs within the optimisation problem, we effectively address the limitations of traditional methods, eliminating the need to re-solve the OCP under different discretisation schemes. We apply this method to a coastal ecosystem OCP, demonstrating its efficacy in solving the problem over a 50-year horizon and extending predictions up to 70 years without re-solve the optimisation problem.} }
Endnote
%0 Conference Paper %T Optimal Control of a Coastal Ecosystem Through Neural Ordinary Differential Equations %A Cecília Coelho %A Fernanda Costa %A Luís Ferrás %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-coelho24a %I PMLR %P 1--9 %U https://proceedings.mlr.press/v255/coelho24a.html %V 255 %X Optimal control problems (OCPs) are essentials in various domains such as science, engineering, and industry, requiring the optimisation of control variables for dynamic systems, along with the corresponding state variables, that minimise a given performance index. Traditional methods for solving OCPs often rely on numerical techniques and can be computationally expensive when the discretisation grid or time horizon changes. In this work, we introduce a novel approach that leverages Neural Ordinary Differential Equations (Neural ODEs) to model the dynamics of control variables in OCPs. By embedding Neural ODEs within the optimisation problem, we effectively address the limitations of traditional methods, eliminating the need to re-solve the OCP under different discretisation schemes. We apply this method to a coastal ecosystem OCP, demonstrating its efficacy in solving the problem over a 50-year horizon and extending predictions up to 70 years without re-solve the optimisation problem.
APA
Coelho, C., Costa, F. & Ferrás, L.. (2024). Optimal Control of a Coastal Ecosystem Through Neural Ordinary Differential Equations. Proceedings of the 1st ECAI Workshop on "Machine Learning Meets Differential Equations: From Theory to Applications", in Proceedings of Machine Learning Research 255:1-9 Available from https://proceedings.mlr.press/v255/coelho24a.html.

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