Non-intrusive Learning of Physics-Informed Spatio-temporal Surrogate for Accelerating Design
For engineers designing systems with expensive multi-physics simulations, this work offers a surrogate that balances accuracy and speed with improved generalization, though it is an incremental improvement over existing Koopman-based methods.
The paper proposes a physics-informed spatio-temporal surrogate modeling framework that uses Koopman autoencoders to learn dynamics non-intrusively, achieving accurate predictions for unknown operating conditions while reducing computational cost. On a 2D cylinder flow problem, the model generalizes beyond training data, unlike purely data-driven approaches.
Most practical engineering design problems involve nonlinear spatio-temporal dynamical systems. Multi-physics simulations are often performed to capture the fine spatio-temporal scales which govern the evolution of these systems. However, these simulations are often high-fidelity in nature, and can be computationally very expensive. Hence, generating data from these expensive simulations becomes a bottleneck in an end-to-end engineering design process. Spatio-temporal surrogate modeling of these dynamical systems has been a popular data-driven solution to tackle this computational bottleneck. This is because accurate machine learning models emulating the dynamical systems can be orders of magnitude faster than the actual simulations. However, one key limitation of purely data-driven approaches is their lack of generalizability to inputs outside the training distribution. In this paper, we propose a physics-informed spatio-temporal surrogate modeling (PISTM) framework constrained by the physics of the underlying dynamical system. The framework leverages state-of-the-art advancements in the field of Koopman autoencoders to learn the underlying spatio-temporal dynamics in a non-intrusive manner, coupled with a spatio-temporal surrogate model which predicts the behavior of the Koopman operator 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.