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KATOsuper addresses the computational bottleneck in topology optimization by integrating a Sensitivity-Consistent Fourier Neural Operator to resolve gradient inconsistencies common in surrogate-based methods. This approach achieves significant speedups over traditional finite element analysis while maintaining robustness through resolution-invariant learning and automatic differentiation of predicted objectives. The framework demonstrates that preserving sensitivity direction is critical for stable optimization, enabling efficient design exploration even with approximate physics evaluations.
KATOsuper: Surrogate-accelerated neural topology optimization with sensitivity-consistent Fourier neural operators
arXiv:2609.27216v1 Announce Type: cross 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.
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.
Computational Engineering, Finance, and Science (cs.CE); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Numerical Analysis (math.NA)
arXiv:2609.27216 [cs.CE]
(or arXiv:2609.27216v1 [cs.CE] for this version)
https://doi.org/10.48550/arXiv.2609.27216 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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