Partitioned Surrogates and Thompson Sampling for Multidisciplinary Bayesian Optimization

TL;DR

This paper introduces MDO-TS, a Bayesian optimization method for multidisciplinary design that uses Gaussian process surrogates for each discipline and employs Thompson sampling with random Fourier features to efficiently explore complex, coupled systems.

Contribution

It proposes a novel Bayesian optimization approach for MDO that leverages Thompson sampling and Gaussian process surrogates for each discipline, reducing the need for full system evaluations.

Findings

Thompson sampling effectively balances exploration and exploitation in MDO.

The method reduces the number of expensive multidisciplinary evaluations.

Application to fluid-structure interaction demonstrates practical utility.

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.