Decompose-and-Superpose: A Superposition-Informed Neural Network for Steady-State Temperature Field Prediction

The finite element method (FEM) is the standard tool for steady-state temperature field simulation, but every change of a design parameter – thermal conductivity, convective heat transfer coefficient, or domain size – requires a new mesh and a new matrix solve, which is prohibitive in parametric thermal design and in real-time thermal management. This paper proposes a superposition-informed neural network (SINN) for fast steady-state temperature field prediction. Starting from the linear operator structure of the steady-state heat conduction equation with Robin boundary conditions, the control parameters are split into operator parameters, which alter the operator itself (thermal conductivity, convective heat transfer coefficient, geometric dimensions), and load parameters, which act linearly on the solution once the operator is fixed (heat source strength, ambient reference temperature, imposed boundary values). The temperature field is accordingly decomposed into one source-driven base subfield and several boundary-response subfields; neural networks learn only the non-superposable mapping from operator parameters to these subfields, and the field under an arbitrary load is reconstructed analytically from them without further network evaluation. On a two-dimensional steady-state heat conduction dataset covering 9 boundary condition combinations and 52 rectangular geometries, the method attains an RMSE of 1.94 mK and is 229–980 times faster than COMSOL FEM at inference. Because the field under an arbitrary load is assembled from the learned subfields rather than re-predicted, load conditions absent from the training data are reconstructed at the same accuracy, without retraining and without any further network evaluation. Because the operator/load split relies only on the linear structure of the governing equation, the framework extends to other steady-state linear diffusion problems; the conditions for this transfer are analyzed in Section 6. The source code is provided as supplementary material.