Skip the Equations: Learning Behavior of Personalized Dynamical Systems Directly From Data

Krzysztof Kacprzyk, Julianna Piskorz, Mihaela Van Der Schaar
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:28619-28643, 2025.

Abstract

While black-box approaches are commonly used for data-driven modeling of dynamical systems, they often obscure a system’s underlying behavior and properties, limiting adoption in areas such as medicine and pharmacology. A two-step process of discovering ordinary differential equations (ODEs) and their subsequent mathematical analysis can yield insights into the system’s dynamics. However, this analysis may be infeasible for complex equations, and refining the ODE to meet certain behavioral requirements can be challenging. Direct semantic modeling has recently been proposed to address these issues by predicting the system’s behavior, such as the trajectory’s shape, directly from data, bypassing post-hoc mathematical analysis. In this work, we extend the original instantiation, limited to one-dimensional trajectories and inputs, to accommodate multi-dimensional trajectories with additional personalization, allowing evolution to depend on auxiliary static features (e.g., patient covariates). In a series of experiments, we show how our approach enables practitioners to integrate prior knowledge, understand the dynamics, ensure desired behaviors, and revise the model when necessary.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-kacprzyk25a, title = {Skip the Equations: Learning Behavior of Personalized Dynamical Systems Directly From Data}, author = {Kacprzyk, Krzysztof and Piskorz, Julianna and Van Der Schaar, Mihaela}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {28619--28643}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/kacprzyk25a/kacprzyk25a.pdf}, url = {https://proceedings.mlr.press/v267/kacprzyk25a.html}, abstract = {While black-box approaches are commonly used for data-driven modeling of dynamical systems, they often obscure a system’s underlying behavior and properties, limiting adoption in areas such as medicine and pharmacology. A two-step process of discovering ordinary differential equations (ODEs) and their subsequent mathematical analysis can yield insights into the system’s dynamics. However, this analysis may be infeasible for complex equations, and refining the ODE to meet certain behavioral requirements can be challenging. Direct semantic modeling has recently been proposed to address these issues by predicting the system’s behavior, such as the trajectory’s shape, directly from data, bypassing post-hoc mathematical analysis. In this work, we extend the original instantiation, limited to one-dimensional trajectories and inputs, to accommodate multi-dimensional trajectories with additional personalization, allowing evolution to depend on auxiliary static features (e.g., patient covariates). In a series of experiments, we show how our approach enables practitioners to integrate prior knowledge, understand the dynamics, ensure desired behaviors, and revise the model when necessary.} }
Endnote
%0 Conference Paper %T Skip the Equations: Learning Behavior of Personalized Dynamical Systems Directly From Data %A Krzysztof Kacprzyk %A Julianna Piskorz %A Mihaela Van Der Schaar %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-kacprzyk25a %I PMLR %P 28619--28643 %U https://proceedings.mlr.press/v267/kacprzyk25a.html %V 267 %X While black-box approaches are commonly used for data-driven modeling of dynamical systems, they often obscure a system’s underlying behavior and properties, limiting adoption in areas such as medicine and pharmacology. A two-step process of discovering ordinary differential equations (ODEs) and their subsequent mathematical analysis can yield insights into the system’s dynamics. However, this analysis may be infeasible for complex equations, and refining the ODE to meet certain behavioral requirements can be challenging. Direct semantic modeling has recently been proposed to address these issues by predicting the system’s behavior, such as the trajectory’s shape, directly from data, bypassing post-hoc mathematical analysis. In this work, we extend the original instantiation, limited to one-dimensional trajectories and inputs, to accommodate multi-dimensional trajectories with additional personalization, allowing evolution to depend on auxiliary static features (e.g., patient covariates). In a series of experiments, we show how our approach enables practitioners to integrate prior knowledge, understand the dynamics, ensure desired behaviors, and revise the model when necessary.
APA
Kacprzyk, K., Piskorz, J. & Van Der Schaar, M.. (2025). Skip the Equations: Learning Behavior of Personalized Dynamical Systems Directly From Data. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:28619-28643 Available from https://proceedings.mlr.press/v267/kacprzyk25a.html.

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