Summary
Designing optimal shapes and structures can take a long time because it requires many detailed physics calculations at each step. The authors introduce KATOsuper, a method that uses a special type of neural network to predict both the design quality and its sensitivity consistently, helping the design process run much faster without losing accuracy. Their approach works on both 2D and 3D problems, can handle different resolutions without retraining, and achieves significant speed improvements, especially for complex designs. This method also shows that having the right direction for changes in design matters more than exact amounts, allowing robust optimization even when physics calculations are approximate.
What this means in practice
- •For mechanical design engineers: Speed up structural shape optimization workflows by replacing repeated physics calculations with fast neural network surrogates that maintain reliable gradient information.
- •For additive manufacturing teams: Generate optimized 3D part geometries faster to improve design iterations in lightweight and stress-critical components for 3D printing.
Abstract
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.