Neural ODEs for RANS Verification

Calibration of model coefficients is critical to ensuring the accuracy RANS model simulations of turbulent flow. Typically, these models are calibrated using data that is taken in a state which is presumed to be a self-similar state. However, the available data is typically not from a self-similar regime, as we have previously shown using reduced-order models. These models capture the essential behavior of the RANS model as a dynamical system. Recent developments in Neural Ordinary Differential Equations (Neural ODEs) allow for the dynamical system to be rewritten and parameterized by neural networks to represent model coefficients. The model coefficients can be learned better to calibrate these quantities against experimental or high-fidelity simulation data. This approach allows the calibration to consider the entire trajectory of the data, not just the self-similar fixed point. In addition to coefficient calibration, the method can also be used for model validation, by comparing the trajectories of the experimental data and the model over a range of flow regimes.