Cost-aware evaluation of uncertainty-guided neural operators for topology optimization

Abstract

Neural-operator predictions can replace some finite-element (FE) calculations in topology optimization, but its prediction errors can negatively affect the final design. This study tested whether model uncertainty helps to make a decision when FE calculations are needed. Seven policies were compared using Fourier neural operators to predict displacement on two 80 by 80 meshes, an L-bracket and a plate with a hole. Held-out displacement errors were 5.2% and 2.5%, respectively. Each setting was tested from 50 initial designs. Every final design was checked independently by FE analysis against a predefined unit-load stress limit. On the L-bracket, the method without FE corrections produced a mean peak stress 12.9 times the limit. Uncertainty gating with a fixed surrogate did not make all 50 designs feasible for all L-bracket tested settings. Retraining the surrogate during optimization achieved this target at a mean of 39.90 solves per design. Random timing reached the same target at an average of 43.76 solves across twelve independent schedules. On the plate with a hole, disagreement between ensemble predictions achieved the target at 27.26 solves, compared with 34.02 for random timing. At comparable budgets, it produced 50 feasible designs against 41 for the random control. Relative to full FE optimization, the cost of generating training labels was offset after approximately 100 L-bracket deployments and 87 plate deployments. These results showed that the benefit of uncertainty-guided timing differs between problems. Independent verification and a random-timing comparison are needed to assess that benefit.