At San Lab, we focus on developing advanced computational methods for complex nonlinear dynamical systems driven by multiscale and multiphysics processes. We are particularly interested in achieving fast, scalable, and generalizable methods for scientific machine learning, particularly in the context of turbulent flows at various spatial and temporal scales. Our efforts center on hybrid analysis and modeling approaches in LES and ROM frameworks, exploiting the integration of physics-based and data-driven modeling for emerging digital twin technologies.
Hybrid Analysis and Modeling (HAM)
In the modeling landscape, two primary approaches are considered: physics-based and data-driven. Physics-based models are rooted in first principles, providing high generalizability and trustworthiness. On the other hand, data-driven models aim to explain phenomena using statistical methods applied to archival data. These models assume data reflects both known and unknown physics, suggesting that with ample training data, they can learn underlying physics independently. Deep learning, particularly, has shown human-level performance in various tasks. Data-driven models offer advantages such as online learning, computational efficiency, and accuracy when appropriately prepared. However, they face challenges including data-hunger, limited generalizability, inherent bias, and lack of robust theory for model stability analysis, restricting their application in multi-scale and multi-physics systems. To overcome these limitations, we propose a set of HAM approaches that synergistically combine deterministic and statistical model components.
Large Eddy Simulations (LES)
Large eddy simulation (LES), a successful approach for turbulent flow simulation, aims to decompose the flow into large and small scales through spatial low-pass filtering. However, the nonlinearity of governing equations leads to a well-known closure problem. Our current focus involves developing functional, structural, and data-driven closure modeling techniques to address subgrid-scale effects in LES. Closure modeling entails incorporating truncated scales (due to limited numerical resolution and computational resources) into resolved dynamics to account for missing subgrid-scale physics. This is particularly crucial for nonlinear dynamical processes with strong interactions between small and large scales. Our research aims to improve the accuracy and fidelity of LES simulations by better capturing subgrid-scale phenomena.
Reduced Order Modeling (ROM)
Reduced order models are highly efficient, low-dimensional representations that significantly reduce the computational cost of existing models by several orders of magnitude. They offer great potential, particularly in scenarios where traditional methods involve numerous model evaluations across a wide range of parameter values. To achieve accurate and realistic results, addressing the closure problem is essential. Closure can be broadly defined as encompassing missing physics, model uncertainty, or representation limitations. Our research focuses on modeling the impact of discarded modes on the model dynamics, enabling the development of precise and reliable low-dimensional models for complex problems.
We are grateful for the support from DOE, NSF, NASA, ASHRAE, NVIDIA, and RCN.