arXiv:2505.22391v2 Announce Type: replace Abstract: Modeling physical systems in a generative manner offers several advantages, including the ability to handle partial observations, generate diverse solutions, and address both forward and inverse problems. Recently, diffusion models have gained increasing attention in the modeling of physical systems, particularly those governed by partial differential equations (PDEs). However, diffusion models only access noisy data $\boldsymbol{x}_t$ at intermediate steps, making it infeasible to directly enforce constraints on the clean sample $\boldsymbol
The increasing maturity and widespread application of diffusion models highlight current limitations, necessitating innovation to integrate hard physical constraints for reliability and accuracy.
Improving diffusion models with physics-informed methods will lead to more robust and scientifically consistent AI, crucial for critical applications in engineering, medicine, and climate modeling.
The ability to directly enforce physical constraints on generative AI output means generated solutions are more likely to be physically realistic and trustworthy, broadening their applicability in scientific and industrial domains.
- · Engineering sectors
- · Scientific research institutions
- · Generative AI developers
- · Climate modeling
- · AI models lacking physical consistency
- · Trial-and-error physical simulations
More accurate and reliable AI-generated models for complex physical systems.
Accelerated design and optimization cycles in industries like aerospace and energy, driven by trustworthy AI simulations.
Reduced need for expensive physical prototypes and experiments, leading to faster innovation and lower development costs across a range of fields.
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