发表机构
The University of British Columbia（不列颠哥伦比亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
KATOsuper提出灵敏度一致傅里叶神经算子与forward_split架构，实现目标无关的神经拓扑优化，在保持最优性的同时获得15-110倍加速，并支持三维扩展与零样本分辨率外推。
AI 中文摘要
拓扑优化（TO）由于每次迭代都需要重复进行有限元分析（FEA）评估，计算强度仍然很高。虽然基于神经网络的代理模型有望加速优化，但现有方法常常面临预测目标与灵敏度之间梯度不一致的问题，导致优化不稳定。本工作提出了KATOsuper，一个目标无关的框架，将神经重参数化拓扑优化与灵敏度一致傅里叶神经算子（SC-FNO）相结合。该框架采用forward_split架构，通过对预测目标场进行自动微分来推导部署所用的灵敏度，从而保持预测目标与优化所用梯度之间的一致性。案例研究包括三个二维基准问题和三个三维结构，考虑柔度或应力最小化。采用带有傅里叶位置嵌入的物理信息多通道输入编码，实现分辨率不变学习，支持超出训练分辨率的零样本外推，在中等缩放因子下具有有用性能，在高达64倍分辨率下无需重新训练即可保持拓扑保持的探索。该框架通过KATO3D扩展到三维，其特点是新颖的KANConv3D块，具有可学习的B样条激活函数。KATOsuper在部署时相比MATLAB基线实现了15至110倍的加速，同时保持有竞争力的最优性，在复杂三维和应力优化案例中增益最为明显。灵敏度方向比幅度更重要的洞察使得即使采用近似物理评估也能实现稳健优化，并可扩展到其他可微分的物理驱动设计目标。
英文摘要
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.
Comments32 pages, 24 figures, 7 tables
