Computer Science > Machine Learning
arXiv:2501.18563 (cs)
[Submitted on 30 Jan 2025 (v1), last revised 11 Apr 2025 (this version, v2)]
Title:No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs
View a PDF of the paper titled No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs, by Krzysztof Kacprzyk and 1 other authors
View PDFHTML (experimental)Abstract:Data-driven modeling of dynamical systems is a crucial area of machine learning. In many scenarios, a thorough understanding of the model's behavior becomes essential for practical applications. For instance, understanding the behavior of a pharmacokinetic model, constructed as part of drug development, may allow us to both verify its biological plausibility (e.g., the drug concentration curve is non-negative and decays to zero) and to design dosing guidelines. Discovery of closed-form ordinary differential equations (ODEs) can be employed to obtain such insights by finding a compact mathematical equation and then analyzing it (a two-step approach). However, its widespread use is currently hindered because the analysis process may be time-consuming, requiring substantial mathematical expertise, or even impossible if the equation is too complex. Moreover, if the found equation's behavior does not satisfy the requirements, editing it or influencing the discovery algorithms to rectify it is challenging as the link between the symbolic form of an ODE and its behavior can be elusive. This paper proposes a conceptual shift to modeling low-dimensional dynamical systems by departing from the traditional two-step modeling process. Instead of first discovering a closed-form equation and then analyzing it, our approach, direct semantic modeling, predicts the semantic representation of the dynamical system (i.e., description of its behavior) directly from data, bypassing the need for complex post-hoc analysis. This direct approach also allows the incorporation of intuitive inductive biases into the optimization algorithm and editing the model's behavior directly, ensuring that the model meets the desired specifications. Our approach not only simplifies the modeling pipeline but also enhances the transparency and flexibility of the resulting models compared to traditional closed-form ODEs.
| Comments: | To appear in the Proceedings of the Thirteenth International Conference on Learning Representations (ICLR 2025) |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2501.18563 [cs.LG] |
| (orarXiv:2501.18563v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2501.18563 arXiv-issued DOI via DataCite |
Submission history
From: Krzysztof Kacprzyk [view email][v1] Thu, 30 Jan 2025 18:36:48 UTC (1,314 KB)
[v2] Fri, 11 Apr 2025 16:59:39 UTC (1,171 KB)
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View a PDF of the paper titled No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs, by Krzysztof Kacprzyk and 1 other authors
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