Session: 20-17-01: Rising Stars of Mechanical Engineering

Paper Number: 172394

Geometry-Infused Reduced-Order ModelingTowards Control Co-Design of Complex Dynamical Systems 

This poster addresses the challenges in designing the next-generation engineering systems — think high-speed aircraft and autonomous vehicles — which require a control co-design approach that considers dynamical and control performance at an early design stage.  In this case, the co-design suffers from a computational bottleneck, denoted as the Impossible Trinity of Modeling.  This means, for a dynamical model, satisfying any two sacrifices the third: high fidelity, computational efficiency, and design parametrization.

We present our recent efforts in resolving the bottleneck via the Geometry-Informed Reduced-Order Modeling.  In simple terms, we use known physical laws and the inherent topology of the system dynamics to build data-driven models that turn the Impossible Trinity to a possible one.  This methodology potentially opens up the path towards integrated multi-disciplinary optimization of complex dynamical systems.

We will present two concrete examples showing different roles of geometry in the modeling of dynamical systems.

The first example is a physics-infused reduced-order modeling (PIROM) framework for efficient and accurate prediction of transient thermal behavior in multi-layered hypersonic thermal protection systems (TPS). The PIROM architecture integrates a reduced-physics backbone, based on the lumped-capacitance model (LCM), with data-driven correction dynamics formulated via a coarse-graining approach rooted in the Mori-Zwanzig formalism. While the LCM captures the dominant heat transfer mechanisms, the correction terms compensate for residual dynamics arising from higher-order non-linear interactions and heterogeneities across material layers. The proposed PIROM is benchmarked against two non-intrusive reduced-order models (ROMs): Operator Inference (OpInf) and Neural Ordinary Differential Equations (NODE). The PIROM consistently achieves errors below 1% for a wide range of extrapolative settings involving time- and space-dependent boundary conditions and temperature-varying material property perturbations. In contrast, OpInf exhibits moderate degradation, and NODE suffers substantial loss in accuracy due to its lack of embedded physics. Despite higher training costs, PIROM delivers online evaluations of two orders of magnitude faster than the full-order model. These results demonstrate that PIROM effectively reconciles the trade-offs between accuracy, generalizability, and efficiency, providing a robust framework for thermal modeling of TPS under diverse operating conditions.

The second example focuses on the topology of a complex system.  We consider a Graph Neural Network (GNN) non-Markovian modeling framework to identify coarse-grained dynamical systems on graphs. Our main idea is to systematically determine the GNN architecture by inspecting how the leading term of the Mori-Zwanzig memory term depends on the coarse-grained interaction coefficients that encode the graph topology. Based on this analysis, we found that the appropriate GNN architecture that will account for $K$-hop dynamical interactions has to employ a Message Passing (MP) mechanism with at least 2K steps.  We also deduce that the memory length required for an accurate closure model decreases as a function of the interaction strength under the assumption that the interaction strength exhibits a power law that decays as a function of the hop distance. Supporting numerical demonstrations on two examples, a heterogeneous Kuramoto oscillator model and a power system, suggest that the proposed GNN architecture can predict the coarse-grained dynamics under fixed and time-varying graph topologies.

Presenting Author: Daning Huang Pennsylvania State University

Presenting Author Biography: Daning Huang is an Assistant Professor of Aerospace Engineering, and leads the Aerospace multi-Physical and Unconventional Systems (APUS) laboratory. He earned his Ph.D. in Aerospace Engineering from University of Michigan in 2019. His research and teaching focus on the multi-disciplinary analysis, optimization, and control of dynamical systems via high-performance computing, machine learning, and mathematical analysis. Ongoing projects span a range of complex engineering and scientific systems, including high-speed vehicles, morphing aircraft, rotary-wing vehicles, power grids, climate systems, etc., with financial supports from NSF, DoD, and national labs. He is a recipient of the NSF CAREER Award in 2024. He is also a co-author of textbook on Structural Dynamics (Cambridge University Press, 2023).

Authors:

Daning Huang Pennsylvania State University