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[2602.15603] Symbolic recovery of PDEs from measurement data
Summary
This paper explores the symbolic recovery of partial differential equations (PDEs) from measurement data, highlighting a neural network approach that enhances interpretability and reconstructibility of physical laws.
Why It Matters
Understanding and accurately reconstructing PDEs is crucial in various scientific fields. This research addresses the challenges posed by noisy measurements and provides a method that improves the interpretability of the underlying physical laws, which can significantly impact scientific modeling and data analysis.
Key Takeaways
- The paper presents a method for recovering PDEs using neural networks based on rational functions.
- It demonstrates that symbolic networks can uniquely reconstruct physical laws from noiseless measurements.
- Regularization techniques improve interpretability and sparsity in the reconstructed models.
- Empirical validation supports the theoretical findings, showcasing practical applications.
- The research contributes to enhancing the understanding of complex systems in natural sciences.
Computer Science > Machine Learning arXiv:2602.15603 (cs) [Submitted on 17 Feb 2026] Title:Symbolic recovery of PDEs from measurement data Authors:Erion Morina, Philipp Scholl, Martin Holler View a PDF of the paper titled Symbolic recovery of PDEs from measurement data, by Erion Morina and 2 other authors View PDF HTML (experimental) Abstract:Models based on partial differential equations (PDEs) are powerful for describing a wide range of complex relationships in the natural sciences. Accurately identifying the PDE model, which represents the underlying physical law, is essential for a proper understanding of the problem. This reconstruction typically relies on indirect and noisy measurements of the system's state and, without specifically tailored methods, rarely yields symbolic expressions, thereby hindering interpretability. In this work, we address this issue by considering existing neural network architectures based on rational functions for the symbolic representation of physical laws. These networks leverage the approximation power of rational functions while also benefiting from their flexibility in representing arithmetic operations. Our main contribution is an identifiability result, showing that, in the limit of noiseless, complete measurements, such symbolic networks can uniquely reconstruct the simplest physical law within the PDE model. Specifically, reconstructed laws remain expressible within the symbolic network architecture, with regularization-minimizing...