Conceitos essenciais
Scientific machine learning combines physics-based modeling with data-driven techniques to address closure problems in multiscale systems.
Resumo
This review explores scientific machine learning approaches for closure models, emphasizing the importance of physical laws adherence and discussing challenges and advancements. Soft and hard constraints, spatial and temporal discretization, neural ODEs, autoregressive methods, and reinforcement learning are covered.
The content delves into various reduced model forms, objective function choices (a priori vs. a posteriori learning), physics-constrained learning, discretization aspects, and the application of neural networks in turbulence closure modeling.
Key highlights include soft constraint applications like physics-informed neural networks, hard constraint methods ensuring symmetry preservation in closures, and the impact of spatial/temporal discretization on neural ODEs and autoregressive models.
The review also touches on online learning strategies, field inversion techniques for turbulence models using experimental data, and the significance of preserving physical laws in data-driven models for computational physics applications.
Estatísticas
Equation (1) describes full model form F(u; µ) = 0.
The Smagorinsky model is represented by equation (17).
Fully discrete approaches are common in autoregressive methods like equation (33).
Citações
"Constraints can be embedded as 'soft' or 'hard' to ensure physical laws adherence."
"Neural ODEs offer continuous-time solutions but may lack generalizability across different grids."
"Reinforcement learning presents an alternative to supervised methods for closure modeling."