Meta-neural Topology Optimization: Knowledge Infusion with Meta-learning

TL;DR

A meta-learning strategy is proposed, termed meta-neural TO, that finds effective initial designs through a systematic transfer of knowledge between related tasks, building on the mesh-agnostic representation provided by neural reparameterization.

Abstract

Engineers learn from every design they create, building intuition that helps them quickly identify promising solutions for new problems. Topology optimization (TO) - a well-established computational method for designing structures with optimized performance - lacks this ability to learn from experience. Existing approaches treat design tasks in isolation, starting from a "blank canvas" design for each new problem, often requiring many computationally expensive steps to converge. We propose a meta-learning strategy, termed meta-neural TO, that finds effective initial designs through a systematic transfer of knowledge between related tasks, building on the mesh-agnostic representation provided by neural reparameterization. We compare our approach against established TO methods, demonstrating efficient optimization across diverse test cases without compromising design quality. Further, we demonstrate powerful cross-resolution transfer capabilities, where initializations learned on lower-resolution discretizations lead to superior convergence in 74.1% of tasks on a higher-resolution test set, reducing the average number of iterations by 33.6% compared to standard neural TO. Remarkably, we discover that meta-learning naturally gravitates toward the strain energy patterns found in uniform density designs as effective starting points, aligning with engineering intuition.

Figures (9)

• Figure 1: Meta-neural topology optimization framework.a. Meta-learning identifies an initialization that adapts to new design tasks in fewer iterations. b. Example design trajectories demonstrating accelerated convergence using meta-learned versus standard initialization in neural topology optimization. c. Neural topology optimization pipeline: neural network maps input coordinates $\mathbf{x}$ and strain energy $\mathbf{E}(\mathbf{x})$ to density fields $\boldsymbol{\rho}(\mathbf{x})$, which are filtered and evaluated with FE analysis.
• Figure 2: Performance profiles for meta-neural TO and baseline methods. The top row compares the number of iterations for in-distribution (left), out-of-distribution (middle), and cross-resolution (right) experiments. The bottom row (d-f) compares the thresholded design compliances for the corresponding experiments.
• Figure 3: Comparison of neural-TO and meta-neural TO on representative in-distribution tasks. Convergence plots showcase the tasks with the best, worst, and typical improvements in continuous design compliance from using meta-learned initializations and corresponding final designs.
• Figure 4: Relationship between meta-learned initial designs and filtered strain energy density fields. Initial designs generated by meta-neural TO (middle and bottom rows) closely mirror the filtered strain energy density fields of uniform density designs, suggesting meta-learning naturally discovers the physical relevance of strain energy patterns.
• Figure 5: Performance profiles comparing compliance of continuous (not thresholded) designs obtained with meta-neural TO against the baseline methods. The plots (a-c) compare the continuous design compliances for the corresponding in-distribution (a), out-of-distribution (b), and cross-resolution (c) experiments.