arXiv:2602.02788v2 Announce Type: replace Abstract: We aim to develop physics foundation models for science and engineering that provide real-time solutions to Partial Differential Equations (PDEs) which preserve structure and accuracy under adaptation to unseen geometries. To this end, we introduce General-Geometry Neural Whitney Forms (Geo-NeW): a data-driven finite element method. We jointly learn a differential operator and compatible reduced finite element spaces defined on the underlying geometry. The resulting model is solved to generate predictions, while exactly preserving physical co
The continuous drive to improve AI's ability to model complex physical systems and the increasing computational power make this research timely, demonstrating progress towards more robust and generalizable AI in scientific computing.
This development can significantly accelerate scientific discovery and engineering design by enabling real-time, accurate, and physically consistent simulations, particularly for complex geometries where traditional methods struggle.
The ability of AI models to generalize across different geometries while preserving physical laws becomes more robust, potentially reducing the need for extensive re-training or manual adaptation for new problems.
- · Scientific research institutions
- · Engineering design firms
- · High-performance computing sector
- · AI-driven simulation software companies
- · Traditional CFD/FEA software reliant on manual meshing/adaptation
- · Industries with long, expensive simulation cycles
Artificial intelligence will become more capable of directly solving complex partial differential equations (PDEs) with high accuracy and physical fidelity.
This capability will lead to faster iteration cycles in R&D for fields like aerospace, materials science, and drug discovery due to rapid, reliable simulations.
The democratization of advanced simulation tools, accessible through AI, could empower smaller teams to compete with larger enterprises traditionally possessing vast computational resources and specialized expertise.
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Read at arXiv cs.LG