Non-Intrusive Learning of Physics-Informed Spatio-Temporal Surrogate Models for Fluid Flow Prediction*

Multi-physics simulations are often performed to capture the fine spatio-temporal scales governing the evolution of fluid flows. These simulations are often high-fidelity in nature, and can be computationally very expensive for data generation, thereby creating a computational bottleneck for practical engineering design problems. Data-driven spatio-temporal surrogate modeling has been a popular solution to tackle this computational bottleneck because these machine learning models can be orders of magnitude faster than the actual simulations. However, one key limitation of purely data-driven approaches is their lack of generalization to out-of-distribution inputs. In this paper, we propose a physics-informed spatio-temporal surrogate modeling framework constrained by the physics of the underlying nonlinear dynamical system representing the fluid flow process. The framework leverages state-of-the-art advancements in the field of Koopman autoencoders to learn the underlying fluid flow dynamics in a non-intrusive way, coupled with a spatio-temporal surrogate model which forecasts the flowfields in a specified time window for unknown operating conditions. We evaluate our framework on a prototypical fluid flow problem of interest: two-dimensional incompressible flow around a cylinder.