Data-driven sparse identification of governing PDEs via knockoff filters and multi-criteria trade-offs
arXiv:2605.26631v1 Announce Type: cross Abstract: We propose KO-PDE-IDENT, a data-driven framework for identifying parsimonious partial differential equations (PDEs) with false discovery rate (FDR) control. PDE discovery from noisy observations is often hindered by extreme multicollinearity among candidate terms, which causes typical sparse-regression methods to select spurious terms. To address this problem, KO-PDE-IDENT initially mines a support set of potential candidate terms via model-X knockoff filters with finite-sample FDR control, then refines and ranks the surviving PDE alternatives.
The continuous advancements in AI and machine learning techniques, specifically in physics-informed neural networks and sparse regression, enable more sophisticated data-driven scientific discovery.
This development offers a more robust and data-efficient method for discovering fundamental physical laws from noisy observational data, potentially accelerating scientific breakthroughs across various domains.
The ability to identify governing partial differential equations with controlled false discovery rates from complex and noisy datasets improves the reliability and interpretability of data-driven scientific models.
- · Scientific research institutions
- · Physics-based AI applications
- · Engineering design sectors
- · Autonomous systems development
- · Traditional empirical modelers
- · Trial-and-error scientific discovery processes
Improved accuracy and efficiency in modeling complex physical systems and identifying their underlying principles.
Faster development of new materials, more precise climate models, and better control for advanced engineering systems.
Potential for a paradigm shift in scientific methodology, where data-driven approaches become central to formulating theoretical physics and engineering principles.
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