ThermIC: Physics-Informed Graph Reinforcement Learning for Thermal–Mechanical Co-Optimization in 3D-IC Placement

In 3D integrated circuits, a placement decision that looks acceptable from a 2D wirelength view can still create a local thermal or stress problem after stacking. This issue becomes more visible as the number of tiers and the density of vertical interconnects increase. We propose ThermIC, a placement framework that brings thermal and mechanical risk estimates into the placement loop rather than treating them only as post-layout checks. The novelty of ThermIC does not lie in treating graph neural networks, reinforcement learning, uncertainty-aware learning, or physics-informed regularization as individually new techniques. Instead, ThermIC contributes a placement-time coupling mechanism in which physically typed graph propagation, dense multi-constraint risk prediction, and action-level reinforcement learning feedback are jointly organized for stacked 3D-IC placement. ThermIC uses a heterogeneous graph encoder to carry thermal, stress, timing, and congestion information through the netlist; a constraint head to estimate local hotspot, stress-risk, timing-violation, and congestion probabilities; and a sequential placement policy trained with physics-informed penalties. We evaluate the method on ThermIC-Bench, a simulated corpus with more than 30,000 finite-element samples from 18 heterogeneous 3D-IC designs with 4–8 tiers. Because the present study does not include proprietary industrial circuits, silicon measurements, or a tape-out case, the experimental results are interpreted as simulation-based benchmark evidence rather than final industrial qualification. ThermIC connects the heat-kernel branch to the discretized heat-conduction equation and the stress-filter branch to linear thermo-elastic equilibrium, providing a mechanism-level basis for physical interpretability. The analysis distinguishes offline simulation/training cost from online deployment cost and reports complexity, runtime, and memory scaling for practical large-scale use. Under joint DRC, thermo-mechanical stress, and thermally coupled timing checks, ThermIC obtains an 82.1% physical verification pass rate. The peak-temperature error is 3.1 °C, the hotspot localization IoU is 0.89, and the number of placement-closure iterations is reduced by 3.7× relative to the heuristic baseline. Together, these benchmark results indicate that early, differentiable multi-physics feedback can make 3D placement less dependent on late correction cycles.