DeepOHeat-v2: Self-Improving Operator Learning for Fast and Trustworthy Thermal Optimization in 3D-IC Design

2026-08-17

AI Summary

This work proposes DeepOHeat-v2 to address training failures in operator learning for 3D-IC thermal optimization caused by material discontinuities and ill-conditioning. The method employs a discrete energy-based physics loss and a matrix-preconditioned optimizer to overcome interface discontinuities and numerical instability, while introducing an incremental self-improvement framework with hotspot trust gating to enhance generalization. Experimental results demonstrate that DeepOHeat-v2 achieves a peak temperature error of 0.55 K and reduces design temperature discrepancy to 0.11 K. By matching traditional solver accuracy while delivering a 56× speedup, this approach effectively overcomes thermal simulation bottlenecks in high-contrast multi-chip stacking scenarios, offering a robust and efficient solution for advanced 3D-IC thermal analysis.

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.

Problem

• 3D-IC thermal optimization
• operator learning
• high-contrast geometry
• discontinuous conductivity
• ill-conditioning

Innovation

• Operator Learning
• Self-Improving Framework
• Discretized Energy Loss
• Matrix Preconditioning
• 3D-IC Thermal Optimization