Fig. 1 The physical layout of the 2D and 3D TO problems that we will test ID methods on, adapted from Refs. [ 4 , 5 ]. Note that the bar refers to the value of the mass function at a given point. More about this image found in The physical layout of the 2D and 3D TO problems that we will test ID metho...

Fig. 2 The physical layout of the topology optimization problem of a cantilever beam: (left) design domain of a cantilever beam with design parameters of force location ( h ) and direction ( α ) on the free side of the beam, (right) topology-optimized beam More about this image found in The physical layout of the topology optimization problem of a cantilever be...

Fig. 3 Median normalized optimization trajectories for the tested initialization techniques More about this image found in Median normalized optimization trajectories for the tested initialization t...

Fig. 4 The normalized initial optimality gap of the either PMSEM or POFMM optimized of KNN, RF, and DeCNN models for 2D heat conduction problem. The lines in the middle of each box plot represent the median, and the dashed line represents the optimal value achieved under uniform initialization (th... More about this image found in The normalized initial optimality gap of the either PMSEM or POFMM optimize...

Fig. 5 Median normalized optimization trajectories for the tested initialization techniques More about this image found in Median normalized optimization trajectories for the tested initialization t...

Fig. 6 The normalized initial optimality gap of the PMSEM and POFMM optimized of KNN, RF, and DeCNN models for 3D heat conduction problem. The lines in the middle of each box plot represent the median, and the dashed line represents the optimal value achieved under uniform initialization (the cont... More about this image found in The normalized initial optimality gap of the PMSEM and POFMM optimized of K...

Fig. 7 (Left) Median normalized optimization trajectories for the tested initialization techniques and (right) a detailed view of initial ID models’ warm start trajectories More about this image found in (Left) Median normalized optimization trajectories for the tested initializ...