Neural reparameterization improves structural optimization

TL;DR

The paper investigates how the choice of parameterization governs solution quality in topology optimization. It introduces a neural-network reparameterization, outputting densities from a CNN and trained end-to-end with implicit differentiation through the physics solver. On 116 structural-optimization tasks, the CNN-based approach matches or exceeds the performance of strong baselines, with particularly large gains on high-resolution problems and qualitatively simpler, more multi-scale designs. This work highlights the power of neural priors in computational engineering and suggests broad applicability to physics-constrained optimization.

Abstract

Structural optimization is a popular method for designing objects such as bridge trusses, airplane wings, and optical devices. Unfortunately, the quality of solutions depends heavily on how the problem is parameterized. In this paper, we propose using the implicit bias over functions induced by neural networks to improve the parameterization of structural optimization. Rather than directly optimizing densities on a grid, we instead optimize the parameters of a neural network which outputs those densities. This reparameterization leads to different and often better solutions. On a selection of 116 structural optimization tasks, our approach produces the best design 50% more often than the best baseline method.

Figures (5)

• Figure 1: A multi-story building task. Figure (a) is a structure optimized in CNN weight space. Figures (b) and (c) are structures optimized in pixel space.
• Figure 2: Schema of our approach to reparameterizing a structural optimization problem with a neural network. Each of these steps -- the CNN parameterization, the constraint step, and the physics simulation -- is differentiable. We implement the forward pass as a TensorFlow graph and compute gradients via automatic differentiation.
• Figure 3: Comparing baselines on the MBB beam example, on a $60 \times 20$ grid. Whereas Pixel-LBFGS and CNN-LBFGS use the same optimizer, we found that MMA and OC are much stronger baselines, so we decided to report all three. We use the implementation of MMA from NLopt nlopt. We re-implemented OC, but verified the results agree exactly on the tasks reported in 88lines.
• Figure 4: Empirical distribution of the relative error across design tasks. The $x$-axes measure design error relative to the best overall design. The $y$-axes measure the probability that the method's solution has an error below the $x$-axis threshold.
• Figure 5: Qualitative examples of structural optimization via reparameterization. The scores below each structure measure relative difference between the design and the best overall design in that row. The "best of ensemble" CNN-parameterized solutions were best or near-best (score $\leq$ 0.005) in 99 out of 116 tasks including these five, vs. 66 out of 116 tasks for MMA. The CNN solutions are qualitatively different from the baselines and often involve simpler and more effective structures.