Topology Optimization through Differentiable Finite Element Solver

TL;DR

This paper introduces a novel topology optimization framework using a fully differentiable finite element solver implemented in Julia, enabling efficient gradient-based design updates for 2D density-based problems.

Contribution

It presents a differentiable physics solver integrated with a learnable generator, allowing end-to-end gradient computation for topology optimization, which is a significant advancement over traditional methods.

Findings

Successfully applied to MBB beam design.

Achieved comparable results with the efficient 88-line code.

Extended to design a compliant force inverter mechanism.

Abstract

In this paper, a topology optimization framework utilizing automatic differentiation is presented as an efficient way for solving 2D density-based topology optimization problem by calculating gradients through the fully differentiable finite element solver. The optimization framework with the differentiable physics solver is proposed and tested on several classical topology optimization examples. The differentiable solver is implemented in Julia programming language and can be automatically differentiated in reverse mode to provide the pullback functions of every single operation. The entire end-to-end gradient information can be then backed up by utilizing chain rule. This framework incorporates a generator built from convolutional layers with a set of learnable parameters to propose new designs for every iteration. Since the whole process is differentiable, the parameters of the generator can be updated using any optimization algorithm given the gradient information from automatic differentiation. The proposed optimization framework is demonstrated on designing a half MBB beam and compared to the results with the ones from the efficient 88-line code. By only changing the objective function and the boundary conditions, it can run an optimization for designing a compliant mechanism, e.g. a force inverter where the output displacement is in the opposite direction of the input.