Stochastic and Non-local Closure Modeling for Nonlinear Dynamical Systems via Latent Score-based Generative Models
arXiv:2506.20771v2 Announce Type: replace Abstract: We propose a latent score-based generative AI framework for learning stochastic, non-local closure models and constitutive laws in nonlinear dynamical systems of computational mechanics. This work addresses a key challenge of modeling complex multiscale dynamical systems without a clear scale separation, for which numerically resolving all scales is prohibitively expensive, e.g., for engineering turbulent flows. While classical closure modeling methods leverage domain knowledge to approximate subgrid-scale phenomena, their deterministic and l
The proliferation of advanced AI frameworks such as score-based generative models enables new approaches to complex computational problems in fluid dynamics and materials science, where traditional methods are computationally prohibitive.
This development offers a potential breakthrough in accurately modeling multiscale dynamical systems, which is critical for engineering, scientific research, and industrial applications that rely on understanding complex physical phenomena.
The ability to generate stochastic, non-local closure models via AI could lead to more efficient and accurate simulations of systems like turbulent flows, reducing the need for costly empirical testing and high-fidelity numerical resolutions.
- · Computational fluid dynamics researchers
- · Aerospace engineering
- · Climate modeling
- · Materials science
- · High-performance computing infrastructure reliant on traditional simulation meth
- · Developers of less efficient, deterministic closure models
Improved predictive capabilities for complex engineering systems, leading to optimized designs and operational efficiencies.
Reduced R&D cycles and costs for industries dependent on physical simulations, accelerating innovation in fields like renewable energy and transportation.
The AI framework itself could generalize to other scientific domains facing similar multiscale challenges, fostering new interdisciplinary research.
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Read at arXiv cs.LG