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.

翻译：工程结构日益借助数值优化进行设计。然而，传统优化方法在多目标与多参数问题中面临挑战。机器学习领域通过JAX和PyTorch等自动微分框架，实现了数百万乃至数十亿参数人工神经网络的稳定训练。由于这些框架提供配备自动梯度追踪的加速数值线性代数运算，它们也支持构建数值方法的可微分实现，从而促进几何结构、材料特性的快速梯度优化及反问题求解。我们展示了JAX-BEM——一种可微分边界元法求解器，验证其在基准问题中与现有边界元代码的误差相当，并实现基于梯度的几何优化。尽管演示案例针对声学仿真，该概念可便捷推广至电磁波领域。