Joint discovery of governing partial differential equations from multi-source datasets by competitive optimization
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Abstract (arXiv)
Discovering governing equations directly from observational data is a key step towards interpretable scientific machine learning. Current data-driven approaches typically operate on a single dataset, inherently limiting their performance when faced with restricted observations. In practice, multiple datasets are often available for the same physical system, distinguished only by distinct initial conditions or boundary configurations. Here, we present a competitive optimization framework designed to discover shared partial differential equations (PDEs) from multi-source datasets, termed MCO-PDE. The framework first trains independent neural surrogates for each data source, and then employs a soft-competitive weighting mechanism to dynamically assess dataset credibility and aggregate a consensus global coefficient. Integrated with a genetic algorithm for structural search, this approach simultaneously identifies the functional forms and parameters of the governing laws. We demonstrate that fusing as few as 50 observations per dataset across seven cases recovers canonical equations with high accuracy. The framework inherently handles two- and three-dimensional domains characterized by irregular boundaries and heterogeneous coefficients, and successfully extracts physically meaningful laws from real-world wave-tank experiments. Overall, this work establishes a promising route for automated scientific discovery via heterogeneous data fusion.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 21 of its 33 references that are in the map. First posted on arXiv 29 Jun 2026.
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21 of 33 references.
References · 21
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9 more
- 2022WeakIdent: Weak formulation for Identifying Differential Equations using Narrow-fit and Trimmingcited by 18
- 2022Discovery of partial differential equations from highly noisy and sparse data with physics-informed information criterioncited by 16
- 2023Weak-PDE-LEARN: A Weak Form Based Approach to Discovering PDEs From Noisy, Limited Datacited by 16
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- 2024LLM4ED: Large Language Models for Automatic Equation Discoverycited by 13
- 2025Generative Discovery of Partial Differential Equations by Learning from Math Handbookscited by 12
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