🤖 AI Summary
This work addresses the challenges of gradient computation and geometric parameter coupling in traditional multi-objective acoustic structural optimization. It presents the first integration of automatic differentiation with the boundary element method (BEM), leveraging JAX to construct an end-to-end differentiable acoustic simulation solver. This framework enables efficient gradient-based shape optimization and inverse problem solving while maintaining accuracy comparable to conventional BEM approaches. By significantly accelerating optimization over complex geometries, the proposed method establishes a new paradigm for acoustic design, offering both computational efficiency and high fidelity in solving intricate multi-objective problems.
📝 Abstract
Engineering structures are increasingly designed using numerical optimisation. However, traditional optimisation methods can be challenging with multiple objectives and many parameters. In machine learning, stable training of artificial neural networks with millions or billions of parameters is achieved using automatic differentiation frameworks such as JAX and Pytorch. Because these frameworks provide accelerated numerical linear algebra with automatic gradient tracking, they also enable differentiable implementations of numerical methods to be built. This facilitates faster gradient-based optimisation of geometry and materials, as well as solution of inverse problems. We demonstrate JAX-BEM, a differentiable Boundary Element Method (BEM) solver, showing that it matches the error of existing BEM codes for a benchmark problem and enables gradient-based geometry optimisation. Although the demonstrated examples are for acoustic simulations, the concept could be readily extended to electromagnetic waves.