Partitioned Surrogates and Thompson Sampling for Multidisciplinary Bayesian Optimization

TL;DR

This work tackles the computational burden of multidisciplinary design optimization for strongly coupled systems by introducing MDO-TS, a framework that replaces each discipline with Gaussian process surrogates and uses Thompson sampling with decoupled sampling via random Fourier features. By drawing approximate GP paths and solving a random MDO to propose design and coupling variables, MDO-TS enables efficient exploration-exploitation without solving the full MDA at every step. The method is demonstrated on a modified Sellar problem and a 2D airfoil with FSI, showing high convergence rates (e.g., 95 of 100 runs converged on the Sellar-like case) and meaningful performance gains in lift for the airfoil. The work highlights both the potential to reduce evaluations and the challenges of scaling to high-dimensional, non-scalar coupling, and it points to future extensions such as constrained optimization and multi-output GP models.

Abstract

The long runtime associated with simulating multidisciplinary systems challenges the use of Bayesian optimization for multidisciplinary design optimization (MDO). This is particularly the case if the coupled system is modeled in a partitioned manner and feedback loops, known as strong coupling, are present. This work introduces a method for Bayesian optimization in MDO called "Multidisciplinary Design Optimization using Thompson Sampling", abbreviated as MDO-TS. Instead of replacing the whole system with a surrogate, we substitute each discipline with such a Gaussian process. Since an entire multidisciplinary analysis is no longer required for enrichment, evaluations can potentially be saved. However, the objective and associated uncertainty are no longer analytically estimated. Since most adaptive sampling strategies assume the availability of these estimates, they cannot be applied without modification. Thompson sampling does not require this explicit availability. Instead, Thompson sampling balances exploration and exploitation by selecting actions based on optimizing random samples from the objective. We combine Thompson sampling with an approximate sampling strategy that uses random Fourier features. This approach produces continuous functions that can be evaluated iteratively. We study the application of this infill criterion to both an analytical problem and the shape optimization of a simple fluid-structure interaction example.

Figures (6)

• Figure 1: (a) MDO problem with two disciplines and feedback coupling. (b) Surrogate MDO problem where both disciplinary models are replaced by Gaussian processes.
• Figure 2: Control points for constructing the surrogates for the functions $f_1$ (a) and $f_2$ (b) of the toy problem. The reference solution is shown in red. The numbers indicate the order in which the points were added. The number "$0$" indicates that the respective point belongs to the initial DoE. The remaining points were added adaptively by MDO-TS.
• Figure 3: Function $f_1$ of the toy problem and three approximate random draws $\hat{f}_1^{(1)}$, $\hat{f}_1^{(2)}$ and $\hat{f}_1^{(3)}$ generated with decoupled sampling before (a) and after (b) 3 iterations of MDO-TS.
• Figure 4: The deformed mesh of the optimized airfoil.
• Figure 5: The FSI problem under consideration.