S3THERM: A SOURCE-SHEET NEURAL OPERATOR FOR 3D STEADY HEAT CONDUCTION

Repeated thermal analysis requires predicting three-dimensional steady tempera- ture fields for changing volumetric heat sources. A neural predictor must capture how a source’s shape and position affect the full field and how the responses to multiple sources combine. For fixed geometry, material properties, and Robin boundary conditions, temperature rise is linear in the heat source. This makes a thin source layer a useful response unit: it retains an in-plane heat pattern and a representative vertical position, while responses to different layers can be com- bined. We introduce S3Therm, which uses one shared neural operator to predict the three-dimensional response to each layer and sums these responses to predict the field of the full source. The operator is trained from the governing equation and boundary conditions without paired temperature fields. Energy-balance rescaling and symmetry averaging refine the combined prediction. On ten held-out source configurations evaluated at matched COMSOL coordinates across seven planes, S3Therm achieves a three-seed mean per-layout RMSE of 0.397 K, compared with 1.529 K for supervised FactFormer.