AI summaryⓘ
The authors address the problem of predicting heat in complex multi-layered computer chips, which is usually slow because it requires solving difficult equations. Their first method, DeepOHeat-v1, worked well only for simpler cases with smooth materials. To fix issues in more complex chips with sharp material differences, they developed DeepOHeat-v2, which uses a different math approach and special optimization tricks to make predictions much more accurate. They also created a system that learns and improves itself by double-checking tricky cases with the original slow solver and updating only when better results are found. This new approach is nearly as accurate as the slow method but runs 56 times faster according to their tests.
multi-die 3D integrated circuitsthermal optimizationoperator-learning surrogatesheat equationdiscontinuous conductivitiesdiscretized physics lossloss-Hessian conditioningpreconditioned optimizerself-improving frameworksurrogate modeling
Authors
Xinling Yu, Yixing Li, Ziyue Liu, Xin Ai, Zhiyu Zeng, Hai Li, Zheng Zhang
Abstract
Thermal-aware optimization of multi-die 3D integrated circuits evaluates many designs, each a costly heat-equation solve. Operator-learning surrogates replace this solve with a fast forward pass, ideally trained from physics alone, without labeled data. DeepOHeat-v1 made such surrogates fast and trustworthy, but only on low-contrast geometries. High-contrast multi-die stacks break it in two ways: discontinuous conductivities make the continuous physics loss ill-defined at material interfaces, and ill-conditioning ($κ_2(A_h) \approx 6 \times 10^4$) puts the discretized strong-form loss beyond first-order optimization. We propose DeepOHeat-v2 to overcome both. First, we train on a discretized physics loss that handles the discontinuities natively; its energy form reduces the prediction-space loss-Hessian conditioning from $κ^2$ to $κ$, and a matrix-preconditioned optimizer cuts the mean peak temperature error from over 30 K to 0.55 K. Second, because optimization leaves the training distribution, we propose a self-improving framework: a hotspot trust gate sends flagged placements to a reference solver, and the surrogate incrementally retrains on the refined solutions, keeping an update only when it improves held-out validation error. On a multi-die benchmark, the surrogate-true peak gap on the returned design falls from 1.12 K to 0.11 K, matching a solve-at-every-step optimizer while running $56\times$ faster.