Physics-Informed Generative Solver: Bridging Data-Driven Priors and Conservation Laws for Stable Spatiotemporal Field Reconstruction
arXiv:2605.22338v1 Announce Type: new Abstract: Reconstructing continuous physical fields from sparse measurements is a central inverse problem, but data-driven generative models can produce states that violate governing dynamics. We introduce a physics-informed generative solver that separates stable prior learning from inference-time enforcement of conservation laws. Martingale-Regularized Score Matching regularizes score pretraining with a Score Fokker-Planck constraint, yielding a dynamically stable prior. Physics-Informed Implicit Score Sampling then guides denoising trajectories by gradi
The proliferation of generative models necessitates robust methods to ensure their outputs adhere to physical laws, particularly in scientific and engineering applications.
This breakthrough addresses a fundamental limitation of data-driven generative AI by integrating physical conservation laws, making AI models more reliable and applicable to complex real-world systems.
Generative AI can now achieve greater stability and physical accuracy in reconstructing spatiotemporal fields, moving beyond purely data-driven, potentially non-physical outputs.
- · Scientific research institutions
- · Engineering industries
- · AI model developers
- · Simulation and modeling software companies
- · AI models without physics-informed constraints (in critical applications)
- · Traditional, purely data-driven inverse problem solvers
Improved accuracy and reliability of AI-generated simulations and reconstructions in fields like climate modeling, fluid dynamics, and materials science.
Accelerated discovery and design processes due to more trustworthy AI predictions and reduced need for manual validation of physical consistency.
New frontiers in AI applications where physical constraints are paramount, potentially leading to paradigm shifts in scientific methodology and industrial design.
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Read at arXiv cs.LG