Multi-Order Loss Functions For Accelerating Unsteady Flow Simulations with Physics-Based AI

Studies show that artificial intelligence (AI) with embedded physics solvers has improved the accuracy of predictions on various physics problems, especially those associated with fluid dynamics. The crucial element in optimizing weight training for estimating flow fields within the AI network lies in the choice of the loss function. In addressing regression-type problems, particularly those involving the temporal evolution of flow fields, the mean square error (MSE) loss function is commonly employed at the current and single time step. However, an issue arises in existing methodologies that utilize MSE-based loss functions with single-time step information for predicting unsteady flow. Most of these approaches overlook the significance of incorporating the temporal history of the flow, a factor that cannot be disregarded in the context of numerical solvers. Hence, in this work, a physics-based AI (PbAI) method with higher-order loss functions is applied to unsteady scenarios, in particular to two distinct turbulent flows where a multitude of fine structures is present, namely, forced and decaying turbulence. Direct numerical simulations on uniform Cartesian grids are conducted to simulate these scenarios, generating two distinct datasets for training and inference. Each dataset comprises 32 randomly initialized conditions spanning 4, 848 time steps for each turbulent flow type. Five distinct models are devised, incorporating features such as rollouts from coarse numerical solvers and temporal considerations in the loss function calculation. The constructed PbAI models demonstrate consistent improvements in predictive performance over the entire temporal domain. These findings are further corroborated through vorticity correlation analyses. The empirical result demonstrates that the accuracy of the baseline case improves by up to 48% and 30% for forced and decaying turbulence, respectively. These results significantly underscore the importance of the temporal histories of flow in the loss function in enhancing predictive capabilities for complex and unsteady turbulent flows.