Agentic Symbolic Search: Characterizing PDEs Beyond Hand-crafted Expressions, Meshes, and Neural Networks
arXiv:2606.20467v1 Announce Type: new Abstract: Mathematicians understand a PDE solution through mathematical structures rather than tables of computed values. Historically, this has been the product of mathematical analysis, carried out by hand for each problem individually. Neither numerical simulation nor neural networks produce those structures directly. We propose Agentic Symbolic Search (ASYS), a prior-guided framework in which an agent translates PDE theory, public problem constraints, and accumulated search experience into testable differentiable symbolic programs. The mathematical for
The increasing sophistication of AI models and the demand for more interpretable and robust scientific discovery methods provide the impetus for agentic approaches to complex mathematical problems.
This development could fundamentally alter how scientific knowledge, particularly in areas governed by partial differential equations, is discovered, understood, and applied, moving beyond brute force computation to symbolic insight.
The explicit search for mathematical structures and symbolic programs to characterize PDEs, rather than relying solely on numerical or neural network approximations, represents a significant methodological paradigm shift in scientific AI.
- · AI researchers in scientific discovery
- · Applied mathematicians
- · Industries relying on physical simulations (e.g., aerospace, materials science)
- · Traditional numerical simulation methods
- · AI approaches lacking interpretability
ASYS, by creating testable differentiable symbolic programs, offers a new pathway to derive fundamental scientific laws from data.
This could lead to accelerated discovery of new materials, more efficient engineering designs, and breakthroughs in fields currently limited by complex simulations.
Long-term, the ability for AI to directly generate structured mathematical understanding might lead to novel theoretical physics and engineering principles currently beyond human intuition.
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Read at arXiv cs.LG