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

arXiv: https://arxiv.org/abs/2608.16080 · HTML: https://mlsanity.com/paper/2608.16080/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 44 references that are in the map.
- First posted on arXiv 17 Aug 2026.

## Builds on (most cited first, 21 of 21)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems](https://mlsanity.com/paper/1710.00211/) (2017)
- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
- [PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domain](https://mlsanity.com/paper/2004.13145/) (2020)
- [Variational Physics-Informed Neural Networks For Solving Partial Differential Equations](https://mlsanity.com/paper/1912.00873/) (2019)
- [Equinox: neural networks in JAX via callable PyTrees and filtered transformations](https://mlsanity.com/paper/2111.00254/) (2021)
- [Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation](https://mlsanity.com/paper/2405.07200/) (2024)
- [Challenges in Training PINNs: A Loss Landscape Perspective](https://mlsanity.com/paper/2402.01868/) (2024)
- [CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Method](https://mlsanity.com/paper/2110.15832/) (2021)
- [An operator preconditioning perspective on training in physics-informed machine learning](https://mlsanity.com/paper/2310.05801/) (2023)
- [A Discontinuity Capturing Shallow Neural Network for Elliptic Interface Problems](https://mlsanity.com/paper/2106.05587/) (2021)
- [Muon2: Boosting Muon via Adaptive Second-Moment Preconditioning](https://mlsanity.com/paper/2604.09967/) (2026)
- [DeepOHeat: Operator Learning-based Ultra-fast Thermal Simulation in 3D-IC Design](https://mlsanity.com/paper/2302.12949/) (2023)
- [A Thermal Machine Learning Solver For Chip Simulation](https://mlsanity.com/paper/2209.04741/) (2022)
- [Separable Operator Networks](https://mlsanity.com/paper/2407.11253/) (2024)
- [DeepOHeat-v1: Efficient Operator Learning for Fast and Trustworthy Thermal Simulation and Optimization in 3D-IC Design](https://mlsanity.com/paper/2504.03955/) (2025)
- [Therm-FM: Foundation Model is ALL YOU NEED for 3D-ICs Thermal Simulation](https://mlsanity.com/paper/2605.22663/) (2026)

## Abstract (arXiv)

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 (kappa2(Ah) ≈ 6 × 104) 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 kappa2 to kappa, 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× faster.