Problem-Independent Machine Learning (PIML) with Residual-Corrected Substructures for Thermoelastic Topology Optimization

Learning reusable local operators can accelerate thermoelastic topology optimization, yet accurate stiffness prediction alone does not ensure accurate thermal-force transfer between fields. A hybrid Problem-Independent Machine Learning (PIML) framework combines reference-anchored thermal shape-function learning with mechanical residual-enriched static condensation. A fixed-trace error analysis exposes the mechanism: stiffness errors are quadratic about interior equilibrium, whereas thermal-load projection can retain first-order errors. This distinction motivates a field-specific strategy that learns the compact thermal response and corrects the larger mechanical response from current-material equilibrium. Shared Ritz factors supply stiffness, coupling and local state/adjoint products without mechanical training or explicitly forming the full mechanical basis. Across eight three-dimensional optimization benchmarks exceeding one million fine elements each, thermal designs have compliance gaps below 0.3% relative to full finite element method (FEM) reference designs; coupled designs have mixed-objective gaps below 0.027% relative to exact linear-boundary substructure references. Complete coupled optimizations are 4.75–5.05× faster than exact Q1 substructuring in total online time. In separate warmed benchmarks covering states, sensitivities and update proposals, the coupled hybrid gives a 186× speedup over matched Full FEM and reduces peak working-set memory by 94.4%. On a 32 GB laptop, a coupled plate with 30.752 million analysis cells is optimized in 60.54 min using 14.17 GiB peak resident memory. The framework extends reusable local learning from separate-field stiffness approximation to accurate, memory-efficient coupled design.