Joint discovery of governing partial differential equations from multi-source datasets by competitive optimization
Mirrored from arXiv — Machine Learning for archival readability. Support the source by reading on the original site.
Computer Science > Machine Learning
Title:Joint discovery of governing partial differential equations from multi-source datasets by competitive optimization
Abstract: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.
| Subjects: | Machine Learning (cs.LG); Computational Physics (physics.comp-ph) |
| Cite as: | arXiv:2606.30699 [cs.LG] |
| (or arXiv:2606.30699v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2606.30699
arXiv-issued DOI via DataCite (pending registration)
|
Access Paper:
- View PDF
Current browse context:
References & Citations
Bookmark
Bibliographic and Citation Tools
Code, Data and Media Associated with this Article
Demos
Recommenders and Search Tools
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
More from arXiv — Machine Learning
-
Representation as a Bottleneck for Mechanistic Interpretability: The Manifestation Unit Protocol
Jul 2
-
SNAP-FM: Sparse Nonlinear Accelerated Projection for Physics-Constrained Generative Modeling
Jul 2
-
SemiScope: Disentangling Classifier Tuning and Joint Optimization in Semi-Supervised Security Classification
Jul 2
-
A Filtered Mixture-of-Generators for Fully Synthetic Survival Training
Jul 2
Discussion (0)
Sign in to join the discussion. Free account, 30 seconds — email code or GitHub.
Sign in →No comments yet. Sign in and be the first to say something.