Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Learning Transient Convective Heat Transfer with Geometry Aware World Models

Onur T. Doganay, Alexander Klawonn, Martin Eigel, Hanno Gottschalk

TL;DR

This work addresses the need for real-time surrogates of transient, conjugate heat-transfer physics by extending a geometry-aware world-model based on LongVideoGAN to operate with arbitrary channel counts and dual conditioning: a global $c^{\mathrm{num}}$ and pixel-wise masks $c^{\mathrm{mask}}$. The proposed two-stage GAN (low-resolution plus super-resolution) learns long-horizon temporal dynamics while preserving geometry-specific effects, enabling near real-time generation of $C_{\mathrm{SIM}}$-channel state sequences for 2D buoyancy-driven flow with solid heat transfer. Evaluation on a transient CFD dataset shows strong reproduction of temporal and spatial correlations and mean-variance behavior for seen geometries and partial generalization to unseen configurations, with improvements over existing operator-learning approaches for long-horizon dynamics. Limitations include occasional generation-time jumps and reduced spatial fidelity for out-of-distribution geometries, motivating time-conditioned generation and 3D extensions for broader applicability in real-time digital twins and control contexts.

Abstract

Partial differential equation (PDE) simulations are fundamental to engineering and physics but are often computationally prohibitive for real-time applications. While generative AI offers a promising avenue for surrogate modeling, standard video generation architectures lack the specific control and data compatibility required for physical simulations. This paper introduces a geometry aware world model architecture, derived from a video generation architecture (LongVideoGAN), designed to learn transient physics. We introduce two key architecture elements: (1) a twofold conditioning mechanism incorporating global physical parameters and local geometric masks, and (2) an architectural adaptation to support arbitrary channel dimensions, moving beyond standard RGB constraints. We evaluate this approach on a 2D transient computational fluid dynamics (CFD) problem involving convective heat transfer from buoyancy-driven flow coupled to a heat flow in a solid structure. We demonstrate that the conditioned model successfully reproduces complex temporal dynamics and spatial correlations of the training data. Furthermore, we assess the model's generalization capabilities on unseen geometric configurations, highlighting both its potential for controlled simulation synthesis and current limitations in spatial precision for out-of-distribution samples.

Learning Transient Convective Heat Transfer with Geometry Aware World Models

TL;DR

This work addresses the need for real-time surrogates of transient, conjugate heat-transfer physics by extending a geometry-aware world-model based on LongVideoGAN to operate with arbitrary channel counts and dual conditioning: a global and pixel-wise masks . The proposed two-stage GAN (low-resolution plus super-resolution) learns long-horizon temporal dynamics while preserving geometry-specific effects, enabling near real-time generation of -channel state sequences for 2D buoyancy-driven flow with solid heat transfer. Evaluation on a transient CFD dataset shows strong reproduction of temporal and spatial correlations and mean-variance behavior for seen geometries and partial generalization to unseen configurations, with improvements over existing operator-learning approaches for long-horizon dynamics. Limitations include occasional generation-time jumps and reduced spatial fidelity for out-of-distribution geometries, motivating time-conditioned generation and 3D extensions for broader applicability in real-time digital twins and control contexts.

Abstract

Partial differential equation (PDE) simulations are fundamental to engineering and physics but are often computationally prohibitive for real-time applications. While generative AI offers a promising avenue for surrogate modeling, standard video generation architectures lack the specific control and data compatibility required for physical simulations. This paper introduces a geometry aware world model architecture, derived from a video generation architecture (LongVideoGAN), designed to learn transient physics. We introduce two key architecture elements: (1) a twofold conditioning mechanism incorporating global physical parameters and local geometric masks, and (2) an architectural adaptation to support arbitrary channel dimensions, moving beyond standard RGB constraints. We evaluate this approach on a 2D transient computational fluid dynamics (CFD) problem involving convective heat transfer from buoyancy-driven flow coupled to a heat flow in a solid structure. We demonstrate that the conditioned model successfully reproduces complex temporal dynamics and spatial correlations of the training data. Furthermore, we assess the model's generalization capabilities on unseen geometric configurations, highlighting both its potential for controlled simulation synthesis and current limitations in spatial precision for out-of-distribution samples.
Paper Structure (30 sections, 54 equations, 22 figures, 3 tables)

This paper contains 30 sections, 54 equations, 22 figures, 3 tables.

Table of Contents

  1. Keywords.
  2. Introduction
  3. Related Work
  4. Physics Informed Neural Networks.
  5. Operator Learning.
  6. Graph Neural Networks.
  7. Generative Models for State Snapshots.
  8. Video Generation Models.
  9. Fluid simulation using world models.
  10. Data Sets.
  11. Governing Equations of Convective Heat Transfer
  12. Equations.
  13. Boundary conditions and coupling.
  14. Architecture Overview and Conditioning
  15. Low-resolution GAN: Generator $G^\textrm{lr}$.
  16. ...and 15 more sections

Figures (22)

  • Figure 1: Architectures of the conditioned low-resolution generator (left, compare with Figure 3 in Brooks2022_lvg) and discriminator (right, compare with Figure 16 Brooks2022_lvg).
  • Figure 2: Mesh (a) and solution snapshot (b) of a CFD-simulation from the dataset. In this case, only on the bottom circle a positive heat source was defined. The upper circle is passive.
  • Figure 3: Parameterization of the reference problem
  • Figure 4: Frame-wise simulation mean values (blue) and standard deviation (blue, shaded) of the fields $T,u,v,p$ of experiment $x_a=0.20$.
  • Figure 5: Experiments $x_a\in\{0.20, 0.35, 0.48, 0.85\}$: Comparison of the generated (orange, dashed) and simulation (blue) mean values of the temperature $T$. Some of the $P=100$ GAN realizations are included and the curves are shifted via \ref{['eq:shift_alignment']}.
  • ...and 17 more figures