A framework for structural shape optimization based on automatic differentiation, the adjoint method and accelerated linear algebra

TL;DR

This paper introduces an efficient computational framework combining automatic differentiation, the adjoint method, and accelerated linear algebra to enhance gradient-based shape optimization in structural engineering, supporting complex geometries and hardware acceleration.

Contribution

The work presents a novel framework utilizing AD, the adjoint method, and XLA via JAX for faster, more accurate shape optimization, with practical applications to architectural form finding.

Findings

Framework improves gradient evaluation efficiency and accuracy.

Supports GPU acceleration for large-scale problems.

Successfully applied to complex structural shape optimization tasks.

Abstract

Shape optimization is of great significance in structural engineering, as an efficient geometry leads to better performance of structures. However, the application of gradient-based shape optimization for structural and architectural design is limited, which is partly due to the difficulty and the complexity in gradient evaluation. In this work, an efficient framework based on automatic differentiation (AD), the adjoint method and accelerated linear algebra (XLA) is proposed to promote the implementation of gradient-based shape optimization. The framework is realized by the implementation of the high-performance computing (HPC) library JAX. We leverage AD for gradient evaluation in the sensitivity analysis stage. Compared to numerical differentiation, AD is more accurate; compared to analytical and symbolic differentiation, AD is more efficient and easier to apply. In addition, the adjoint method is used to reduce the complexity of computation of the sensitivity. The XLA feature is exploited by an efficient programming architecture that we proposed, which can boost gradient evaluation. The proposed framework also supports hardware acceleration such as GPUs. The framework is applied to the form finding of arches and different free-form gridshells: gridshell inspired by Mannheim Multihalle, four-point supported gridshell, and canopy-like structures. Two geometric descriptive methods are used: non-parametric and parametric description via B\'ezier surface. Non-constrained and constrained shape optimization problems are considered, where the former is solved by gradient descent and the latter is solved by sequential quadratic programming (SQP). Through these examples, the proposed framework is shown to be able to provide structural engineers with a more efficient tool for shape optimization, enabling better design for the built environment.