VSTherm: A Virtual Path-Based Stochastic Solver for Full-Chip Leakage-Aware Nonlinear Thermal Simulation

The continuous advancement of semiconductor processes has led to increasingly prominent leakage power issues in integrated circuits (ICs), making leakage-aware nonlinear thermal simulation a critical challenge in modern chip design. Traditional deterministic field solvers provide high accuracy but suffer from significant computational inefficiencies when handling large-scale mesh structures. Conversely, stochastic methods offer rapid computation speeds but are inherently limited to single-point solutions, preventing them from effectively addressing nonlinear thermal problems. To address this challenge, we propose a virtual path-based stochastic solver that enables efficient leakage-aware thermal simulation. The virtual path algorithm decomposes each real path in Brownian motion into virtual paths, extending stochastic solvers from single-point solutions to regional solutions, allowing a stochastic method to achieve full-chip thermal simulation for the first time, thus enabling the handling of nonlinearity. Additionally, we further accelerate the iteration process by reusing the path trajectories from the first solution process. Extensive experimental evaluations demonstrate that our method achieves a speedup of 20.17× to 52.23× compared to the state-of-the-art solver 3D-ICE on 4 GPUs across various scenarios while maintaining comparable accuracy.