H. Jane Bae

Di Zhou, Michael P. Whitmore, Kevin P. Griffin et al.

We develop a wall model for large-eddy simulation (LES) that takes into account various pressure-gradient effects using multi-agent reinforcement learning (MARL). The model is trained using low-Reynolds-number flow over periodic hills with agents distributed on the wall along the computational grid points. The model utilizes a wall eddy-viscosity formulation as the boundary condition, which is shown to provide better predictions of the mean velocity field, rather than the typical wall-shear stress formulation. Each agent receives states based on local instantaneous flow quantities at an off-wall location, computes a reward based on the estimated wall-shear stress, and provides an action to update the wall eddy viscosity at each time step. The trained wall model is validated in wall-modeled LES (WMLES) of flow over periodic hills at higher Reynolds numbers, and the results show the effectiveness of the model on flow with pressure gradients. The analysis of the trained model indicates that the model is capable of distinguishing between the various pressure gradient regimes present in the flow.

Diederik Beckers, H. Jane Bae, Andres Goza

We introduce a refined immersed boundary (IB) methodology that is better-than-first-order accurate in practice, while preserving key properties of "continuous-forcing" IB approaches that retain a singular source term in the governing equations. Our method leverages a smoothed indicator (Heaviside) function, following ideas from multiphase flow and immersed layers formulations, to recast the IB solution as a composite of distinct interior and exterior fields. We demonstrate that, when cast through this composite-solution lens, prior continuous-forcing IB methods can be seen as neglecting terms in the governing and constraint equations that restrict the solution to first-order accuracy. We incorporate these terms to systematically improve accuracy without the need for heuristic corrections. In canonical Poisson problems, we empirically demonstrate second-order convergence, and in incompressible Navier-Stokes simulations the method achieves slightly sub-second-order performance. While our present study focuses on these cases, the framework suggests a path towards second-order accuracy or higher, with further extensions. This perspective reframes accuracy limitations typically attributed to IB schemes. Although continuous-forcing IB methods are often reported to be only first-order accurate, we show that neither smoothing nor interface interpolation inherently restricts attainable order. Moreover, we naturally incorporate this higher-order formulation into a projection-based solution process. The resulting algorithm simultaneously mitigates the spurious surface stresses produced by ill-conditioned linear systems and reduces sensitivity to geometric resolution, addressing both conditioning and accuracy concerns within a unified approach.

Sze Chai Leung, Di Zhou, H. Jane Bae

Optimal sensor placement (OSP) is critical for efficient, accurate monitoring, control, and inference in complex real-world systems. We propose a machine-learning-based feature attribution framework to identify OSP for the prediction of quantities of interest. Feature attribution quantifies input contributions to a model's output; however, it struggles with highly correlated input data often encountered in real-world applications. To address this, we propose a Correlation-Aware Attribution Framework (CAAF), which introduces a clustering step before performing feature attribution to reduce redundancy and enhance generalizability. We first illustrate the core principles of the proposed framework through a series of validation cases, then demonstrate its effectiveness in real-world dynamical systems, such as structural health monitoring, airfoil lift prediction, and wall-normal velocity estimation for turbulent channel flow. The results show that the CAAF outperforms alternative approaches that typically struggle due to the presence of nonlinear dynamics, chaotic behavior, and multi-scale interactions, and enables the effective application of feature attribution for identifying OSP in real-world environments.

Zelin Zhao, Zongyi Li, Kimia Hassibi et al.

Assessing turbulence control effects for wall friction numerically is a significant challenge since it requires expensive simulations of turbulent fluid dynamics. We instead propose an efficient deep reinforcement learning (RL) framework for modeling and control of turbulent flows. It is model-based RL for predictive control (PC), where both the policy and the observer models for turbulence control are learned jointly using Physics Informed Neural Operators (PINO), which are discretization invariant and can capture fine scales in turbulent flows accurately. Our PINO-PC outperforms prior model-free reinforcement learning methods in various challenging scenarios where the flows are of high Reynolds numbers and unseen, i.e., not provided during model training. We find that PINO-PC achieves a drag reduction of 39.0\% under a bulk-velocity Reynolds number of 15,000, outperforming previous fluid control methods by more than 32\%.

H. Jane Bae, Petros Koumoutsakos

The predictive capabilities of turbulent flow simulations, critical for aerodynamic design and weather prediction, hinge on the choice of turbulence models. The abundance of data from experiments and simulations and the advent of machine learning have provided a boost to turbulence modeling efforts. However, simulations of turbulent flows remain hindered by the inability of heuristics and supervised learning to model the near-wall dynamics. We address this challenge by introducing scientific multi-agent reinforcement learning (SciMARL) for the discovery of wall models for large-eddy simulations (LES). In SciMARL, discretization points act also as cooperating agents that learn to supply the LES closure model. The agents self-learn using limited data and generalize to extreme Reynolds numbers and previously unseen geometries. The present simulations reduce by several orders of magnitude the computational cost over fully-resolved simulations while reproducing key flow quantities. We believe that SciMARL creates unprecedented capabilities for the simulation of turbulent flows.