Transformer model improves radiative heat transfer simulations across resolutions
Beyond Affine Reconstruction: Multi-Resolution Transformer DeepONets for the Radiative Transfer Equation
Machine Learning
Summary
Radiative heat transfer calculations are very slow but important for simulating fires. The authors developed a new type of neural network that can handle input data at different resolutions without needing to reshape it. Their model predicts how radiation moves in these simulations more accurately and efficiently than prior methods. This approach also captures fine details better and needs fewer parameters, making it a promising tool for faster fire simulations.
What this means in practice
- •For fire simulation engineers: Run faster and more accurate radiative heat transfer calculations in fire models using a flexible neural operator that handles varied grid resolutions.
- •For computational fluid dynamics developers: Implement multi-resolution neural surrogates for radiative transfer to improve simulation detail and efficiency without extensive grid processing.
Authors
Tanguy Azéma, Marc Bocquet, Fatiha Nmira, Xiaoyi Lu, Jean-Louis Consalvi, Sibo Cheng
Abstract
Radiative heat transfer plays a dominant role in fire simulations, where solving the radiative transfer equation (RTE) is a computational bottleneck. Neural operators can accelerate these computations by learning solution operators from offline simulation data. However, conventional DeepONet surrogates rely on fixed-grid inputs and affine reconstruction, limiting their flexibility across resolutions and their approximation accuracy at a fixed latent dimension. In this paper, we develop a transformer-based DeepONet for multi-resolution RTE surrogate modelling. The proposed approach combines a Perceiver encoder, which maps temperature and absorption coefficient fields at different spatial resolutions into a fixed-size latent representation, with a cross-attention decoder that enables non-affine reconstruction of the radiative intensity. This architecture allows a single model to process inputs at varying resolutions without resampling them onto a common grid. We formulate a computable empirical version of a previously derived theoretical lower bound for affine reconstruction, enabling direct comparison with model errors on the same dataset. Experiments on a two-dimensional pool-fire dataset demonstrate that the proposed approach outperforms autoencoder-based DeepONets in predicting both radiative intensity and incident radiation, with fewer trainable parameters. Power spectral density analysis shows improved preservation of small-scale structures. Both affine baselines remain above the corresponding lower bound at all evaluated ranks, whereas the proposed model achieves a training error below it at one matched latent dimension, demonstrating the potential of non-affine reconstruction to overcome this representational limitation. Experiments on a dataset combining three spatial resolutions confirm the accuracy advantage of the approach at each input resolution.