How the Classical Baseline Shapes Machine-Learning Speed Claims in Topology Optimization

Topology optimization (TO) remains computationally intensive due to repeated finite element analysis (FEA) evaluations required at each iteration. While neural network-based surrogates offer potential acceleration, existing approaches often suffer from gradient inconsistency between predicted objectives and sensitivities, leading to optimization instability. This work presents KATOsuper, an objective-agnostic framework that couples neural-reparameterized topology optimization with a Sensitivity-Consistent Fourier Neural Operator (SC-FNO). The framework employs the forward_split architecture, which derives deployed sensitivities via automatic differentiation through the predicted objective field and thereby preserves consistency between the predicted objective and the gradient used for optimization. The case studies include three 2D benchmark problems and three 3D structures considering compliance or stress minimization. A physics-informed multi-channel input encoding with Fourier position embedding enables resolution-invariant learning, supporting zero-shot extrapolation beyond the training resolution, with useful performance at moderate scaling factors and topology-preserving exploration at up to 64x without retraining. The framework extends to 3D through KATO3D, featuring novel KANConv3D blocks with learnable B-spline activations. KATOsuper demonstrates 15--110x deployment-time speedup over MATLAB baselines while maintaining competitive optimality, with the clearest gains observed in complex 3D and stress-optimization cases. The insight that sensitivity direction matters more than magnitude enables robust optimization even with approximate physics evaluation, extensible to other differentiable physics-driven design objectives.

Large-scale topology optimization (TO) remains computationally demanding, especially for stress-constrained problems. To address this challenge, we propose the simultaneous neural topology optimization (SNTO) framework where we represent state, adjoint, and design variables with custom neural networks (NNs) whose parameters are jointly optimized within a single optimization loop that leverages continuous adjoint analysis and automatic differentiation. This optimization minimizes a multi-component loss function that combines the design objective, an aggregation of the local stress constraints, and the potential energy functionals. Our NNs have a unique architecture that accelerates convergence while enabling the networks to capture sharp gradients and boundaries which are critical to stress-constrained TO. To achieve scalability to millions of degrees of freedom (DoF), we develop a hardware-aware training scheme in which the design domain is partitioned into subdomains that are distributed across multiple GPUs. To control peak GPU memory usage, we further slice each subdomain into smaller regions whose loss gradients are evaluated sequentially and accumulated to update the NN parameters. Unlike domain decomposition approaches, our partitioning naturally ensures field continuity across the subdomains and does not require the introduction of additional terms into the loss function. For validation, we first evaluate the proposed framework on various 2D stress-constrained benchmarks and compare our results to a conventional finite element-based approach, showing that SNTO produces super-resolution designs with sharper boundaries, smaller gray areas, and lower volume fractions. We then consider large-scale 3D problems with up to eight million collocation points and distribute the training over up to eight GPUs.

We present a framework in which a large language model (LLM) acts as an online adaptive controller for SIMP topology optimization, replacing conventional fixed-schedule continuation with real-time, state-conditioned parameter decisions. At every $k$-th iteration, the LLM receives a structured observation$-$current compliance, grayness index, stagnation counter, checkerboard measure, volume fraction, and budget consumption$-$and outputs numerical values for the penalization exponent $p$, projection sharpness $β$, filter radius $r_{\min}$, and move limit $δ$ via a Direct Numeric Control interface. A hard grayness gate prevents premature binarization, and a meta-optimization loop uses a second LLM pass to tune the agent's call frequency and gate threshold across runs. We benchmark the agent against four baselines$-$fixed (no-continuation), standard three-field continuation, an expert heuristic, and a schedule-only ablation$-$on three 2-D problems (cantilever, MBB beam, L-bracket) at $120\!\times\!60$ resolution and two 3-D problems (cantilever, MBB beam) at $40\!\times\!20\!\times\!10$ resolution, all run for 300 iterations. A standardized 40-iteration sharpening tail is applied from the best valid snapshot so that compliance differences reflect only the exploration phase. The LLM agent achieves the lowest final compliance on every benchmark: $-5.7\%$ to $-18.1\%$ relative to the fixed baseline, with all solutions fully binary. The schedule-only ablation underperforms the fixed baseline on two of three problems, confirming that the LLM's real-time intervention$-$not the schedule geometry$-$drives the gain. Code and reproduction scripts will be released upon publication.