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[2503.05993] SODAs: Sparse Optimization for the Discovery of Differential and Algebraic Equations
Summary
The paper introduces SODAs, a method for discovering differential-algebraic equations (DAEs) using sparse optimization, enhancing model development for dynamical systems.
Why It Matters
Understanding and modeling dynamical systems is crucial in various scientific fields. SODAs addresses limitations in existing methods by allowing for the identification of DAEs without prior variable elimination, making it applicable to a broader range of systems. This advancement can lead to more accurate models in biology, mechanics, and electrical engineering, ultimately improving predictions and system designs.
Key Takeaways
- SODAs enables the discovery of DAEs without prior identification of algebraic variables.
- The method improves numerical stability in high-correlation scenarios.
- SODAs produces interpretable models that reflect the physical system's structure.
- Demonstrated effectiveness on biological, mechanical, and electrical systems.
- Robustness to noise in both simulated and real-time data is highlighted.
Mathematics > Dynamical Systems arXiv:2503.05993 (math) [Submitted on 8 Mar 2025 (v1), last revised 26 Feb 2026 (this version, v2)] Title:SODAs: Sparse Optimization for the Discovery of Differential and Algebraic Equations Authors:Manu Jayadharan, Christina Catlett, Arthur N. Montanari, Niall M. Mangan View a PDF of the paper titled SODAs: Sparse Optimization for the Discovery of Differential and Algebraic Equations, by Manu Jayadharan and 3 other authors View PDF HTML (experimental) Abstract:Differential-algebraic equations (DAEs) integrate ordinary differential equations (ODEs) with algebraic constraints, providing a fundamental framework for developing models of dynamical systems characterized by timescale separation, conservation laws, and physical constraints. While sparse optimization has revolutionized model development by allowing data-driven discovery of parsimonious models from a library of possible equations, existing approaches for dynamical systems assume DAEs can be reduced to ODEs by eliminating variables before model discovery. This assumption limits the applicability of such methods for DAE systems with unknown constraints and time scales. We introduce Sparse Optimization for Differential-Algebraic Systems (SODAs), a data-driven method for the identification of DAEs in their explicit form. By discovering the algebraic and dynamic components sequentially without prior identification of the algebraic variables, this approach leads to a sequence of convex opt...