arXiv:2508.09156v3 Announce Type: replace Abstract: We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems. Starting from a model trained on low-fidelity or observational data, we apply a differentiable post-training procedure that minimizes weak-form residuals of governing partial differential equations (PDEs), promoting physical consistency and adherence to boundary conditions without distorting the underlying learned distribution. To infer unknown physical inputs, such as source terms, material
This research addresses a critical limitation of current AI models in scientific domains: their lack of inherent physical consistency, which is increasingly vital as AI is applied to complex systems like PDEs.
A strategic reader should care because integrating physics into AI models enhances their reliability and utility for scientific discovery, engineering, and inverse problems, leading to more robust and trustworthy applications.
AI models can now be fine-tuned to intrinsically respect physical laws and boundary conditions, moving beyond purely data-driven approaches to physically-informed AI solutions.
- · Scientific research institutions
- · Engineering firms (e.g., aerospace, materials)
- · AI model developers
- · Industries relying on predictive simulations
- · Purely data-driven simulation providers (if they don't adapt)
- · Traditional physical modeling approaches (if they don't integrate AI)
- · AI models that generate physically inconsistent results
More accurate and reliable AI-driven simulations and predictions across scientific and engineering disciplines.
Accelerated drug discovery, material science, and climate modeling by embedding physical laws directly into generative AI.
The development of 'scientific AI agents' that can autonomously design experiments, analyze data, and propose solutions while adhering to fundamental physical principles.
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Read at arXiv cs.LG