Non-intrusive Learning of Physics-Informed Spatio-temporal Surrogate for Accelerating Design

2026-04-15

AI Summary

High-fidelity multiphysics simulations are computationally expensive, while purely data-driven surrogate models often suffer from limited generalization capabilities. To address this challenge, this work proposes a non-intrusive physics-informed spatiotemporal surrogate modeling framework (PISTM) that leverages a Koopman autoencoder to learn the intrinsic spatiotemporal dynamics of the system. By embedding physical constraints without modifying the original simulation code, PISTM significantly enhances out-of-distribution generalization to unseen operating conditions. Integrating principles from physics-informed neural networks and spatiotemporal dynamical systems modeling, the method is validated on the two-dimensional incompressible flow past a cylinder, demonstrating its ability to accurately and efficiently replace high-fidelity simulations and substantially accelerate engineering design workflows.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

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.

Problem

• spatio-temporal surrogate modeling
• computational bottleneck
• generalizability
• physics-informed learning
• nonlinear dynamical systems

Innovation

• physics-informed
• spatio-temporal surrogate
• Koopman autoencoder
• non-intrusive learning
• dynamical systems