Topology optimization (TO) requires repeated finite element analysis (FEA) at every iteration, making it computationally expensive. Neural‑network surrogates can speed up the prediction, but most existing methods suffer from gradient inconsistency between the predicted objective and its sensitivities, causing instability in the optimization loop. KATOsuper introduces an objective‑agnostic framework that couples neural‑reparameterized topology optimization with a Sensitivity‑Consistent Fourier Neural Operator (SC‑FNO).
The core of the framework is the forward_split architecture: SC‑FNO first predicts the objective field (e.g., displacement or stress), then automatic differentiation is applied to the predicted field to obtain sensitivities that are mathematically consistent with the predicted objective. This eliminates the gradient bias typical of surrogate‑based TO.
$$ C = \mathbf{u}^\top \mathbf{K} \mathbf{u} $$
where $C$ denotes compliance (to be minimized), $\mathbf{u}$ the displacement vector, and $\mathbf{K}$ the stiffness matrix. SC‑FNO uses a multi‑channel input encoding enriched with Fourier position embedding, enabling resolution‑invariant learning. The model can extrapolate zero‑shot to higher resolutions—experiments show faithful topology preservation up to a 64× up‑scaling without retraining.
For three‑dimensional problems, the framework extends to KATO3D, featuring novel KANConv3D blocks and learnable B‑spline activations, which boost expressive power. Compared with MATLAB baselines, KATOsuper achieves a 15‑110× speed‑up at deployment time while delivering competitive optimality for both compliance and stress‑minimization tasks. The most pronounced gains appear in complex 3D and stress‑driven cases.
A key insight is that the direction of the sensitivity matters more than its magnitude. Even with approximate physics evaluations, as long as the gradient direction aligns with the true physics, the optimization remains robust. This principle can be extended to other differentiable physics‑driven design objectives.
Review: KATOsuper’s consistency‑preserving surrogate and resolution‑agnostic learning deliver dramatic acceleration without sacrificing solution quality, paving the way for scalable, reliable topology optimization in high‑dimensional design spaces.