Session: 12-10-02: Advancements of Data-Driven and Differentiable Computing in Solid Mechanics

Paper Number: 150594

150594 - Topology Optimization via Physics-Informed Gaussian Processes 

Topology optimization (TO) is a mathematical approach for optimizing the performance of structures by designing material distribution within a predefined domain under specific constraints. Recently, the pace of developments in TO has been further fueled by the emergence of advanced manufacturing techniques such as additive manufacturing, which enable the fabrication of intricate and complex structures designed by TO. However, TO approaches are typically computationally expensive since they are nested, involving iterative design updates where each step requires solving a system of partial differential equations (PDEs) to simulate the structure’s response. Another common thread in existing TO methods is that these methods rely heavily on meshing the structure, as numerical solvers need to discretize the design domain. To arrive at mesh-independent designs, spatial filters must be used in the optimization loop. While these choices increase numerical stability and speed, they rely on manual tuning, especially in applications that involve solid-fluid interaction or large deformations.

In contrast to these existing methods, we introduce a simultaneous and mesh-free TO approach that unifies the design and analysis steps into a single optimization loop. Our method is grounded on Gaussian processes (GPs) which incorporate deep neural networks as their mean functions. In our proposed class of machine learning (ML)-based methods for TO, we design the loss function, architecture, and training mechanism of a PIML model that simultaneously optimizes the performance metric (e.g., dissipated power) while satisfying both the design constraints (e.g., solid volume fraction) and the governing equations of the system. The fundamental idea behind our approach differs from most existing works that combine ML with conventional TO methods because we aim to find the optimal design along with solving the state equations that govern the problem simultaneously via ML. That is, training our ML model amounts to solving a constrained optimization problem. Our method is inherently mesh-independent and significantly aids in (1) satisfying equality constraints in the domain and boundaries of the design problem, (2) minimizing gray areas which are unfavorable in real-world applications, and (3) simplifying the inverse design by reducing the sensitivity of neural networks to factors such as random initialization, architecture type, and choice of optimizer.

To show the impact of our work, we evaluate the performance of our model on four cases across ten repetitions against SIMP (solid isotropic material with penalisation) based TO of COMSOL. Our findings demonstrate the robustness and efficiency of our PIML-based simultaneous TO approach, highlighting its potential to significantly advance topology optimization techniques.

Presenting Author: Amin Yousefpour University of California, Irvine

Presenting Author Biography: As a Research Assistant at the Department of Mechanical and Aerospace Engineering, University of California, Irvine, Amin applies his expertise in Scientific Machine Learning, Data Fusion under Uncertainty, and Topology Optimization to various engineering problems. He is grateful to have the support of prestigious organizations such as NASA and NSF for his current projects, which involve designing metamaterials, identifying systems, and quantifying uncertainties.

His research interests stem from a strong background in Mathematics, Control Theory, and Machine Learning where he has developed robust and data-driven techniques for dynamic identification and nonlinear control systems. He has also applied numerical methods to financial systems and nonlinear vibration and has published multiple papers in high-impact journals. Additionally, he holds a master's degree in Mechanical Engineering, Vibration and Control from the University of Tehran, where he worked as a Research and Teaching Assistant.

Authors:

Amin Yousefpour University of California, Irvine
Shirin Hosseinmardi University of California, Irvine
Carlos Mora University of California, Irvine
Ramin Bostanabad University of California, Irvine