# Towards Real Time Thermal Simulations for Design Optimization using Graph Neural Networks

arXiv: https://arxiv.org/abs/2209.13348 · HTML: https://mlsanity.com/paper/2209.13348/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 14 references that are in the map.
- First posted on arXiv 21 Sep 2022.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)

## Built on by (most cited first, 3 of 3)

- [DeepOHeat-v1: Efficient Operator Learning for Fast and Trustworthy Thermal Simulation and Optimization in 3D-IC Design](https://mlsanity.com/paper/2504.03955/) (2025)
- [Unveiling the Unseen Potential of Graph Learning through MLPs: Effective Graph Learners Using Propagation-Embracing MLPs](https://mlsanity.com/paper/2311.11759/) (2023)
- [Reconstructing Unobservable Temperature Fields via Simulation-Aided Intelligent Sensing](https://mlsanity.com/paper/2606.04582/) (2026)

## Abstract (arXiv)

This paper presents a method to simulate the thermal behavior of 3D systems using a graph neural network. The method discussed achieves a significant speed-up with respect to a traditional finite-element simulation. The graph neural network is trained on a diverse dataset of 3D CAD designs and the corresponding finite-element simulations, representative of the different geometries, material properties and losses that appear in the design of electronic systems. We present for the transient thermal behavior of a test system. The accuracy of the network result for one-step predictions is remarkable (SI0.003% error). After 400 time steps, the accumulated error reaches SI0.78%. The computing time of each time step is SI50ms. Reducing the accumulated error is the current focus of our work. In the future, a tool such as the one we are presenting could provide nearly instantaneous approximations of the thermal behavior of a system that can be used for design optimization.