Learning Transient Convective Heat Transfer with Geometry Aware World Models

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.

💡 Research Summary

The paper addresses the computational bottleneck of traditional partial‑differential‑equation (PDE) solvers for real‑time engineering applications by proposing a geometry‑aware world‑model that learns transient convective heat transfer from data. Building on LongVideoGAN, a video‑generation GAN originally designed for temporally coherent RGB videos, the authors adapt the architecture to handle an arbitrary number of physical channels (temperature, pressure, velocity components, density, etc.) and to incorporate both global physical parameters and local geometric information as conditioning inputs.

Two conditioning mechanisms are introduced. First, global parameters such as heat‑source power or gravitational acceleration are encoded as style vectors and injected into the low‑resolution generator, allowing the model to modulate long‑term dynamics. Second, binary masks representing solid obstacles or heat‑source shapes are expanded to match the channel dimension and fed to both the low‑resolution and super‑resolution generators, thereby providing spatially varying geometry cues. This dual conditioning enables the network to synthesize realistic spatio‑temporal fields for unseen configurations.

The authors generate a bespoke dataset of 10 000 transient CFD simulations of buoyancy‑driven flow coupled with heat conduction in a solid domain. The fluid is modeled by the compressible 2‑D Navier–Stokes equations with gravity, closed by the ideal‑gas law, while the solid obeys a heat‑conduction equation with a constant volumetric heat source. Interface conditions enforce temperature continuity and heat‑flux balance; no‑slip walls and isothermal far‑field boundaries complete the problem definition. The dataset spans a wide range of geometries (different obstacle shapes and positions) and heat‑source powers, providing both in‑distribution (seen) and out‑of‑distribution (unseen) test sets.

Architecturally, the model consists of a hierarchical two‑stage GAN. The low‑resolution generator produces long sequences (e.g., 64 × 64 pixels, 200 frames) using 3‑D convolutions, style‑based modulation, and the global‑parameter vector. The super‑resolution generator refines each frame to 256 × 256 pixels with a sliding‑window approach, leveraging the geometry mask to preserve fine boundary details. A 3‑D convolutional discriminator evaluates spatio‑temporal realism across all physical channels. Training combines the standard adversarial loss with physics‑informed L2 losses on temperature and velocity, a boundary‑condition penalty, and a regularization term on the style vectors. Adam optimizer (β1 = 0.0, β2 = 0.99) is used for 200 epochs with a batch size of 16.

Evaluation employs a suite of metrics: channel‑wise L2 error, mean absolute temperature deviation, a temporal energy‑conservation metric, and structural similarity (SSIM) for visual fidelity. On the in‑distribution test set the model achieves average temperature L2 error of 2.3 % and velocity L2 error of 3.1 %, with SSIM ≈ 0.92, indicating high fidelity both numerically and visually. The model accurately reproduces the long‑term temperature rise and the complex vortex structures characteristic of buoyancy‑driven flow. For out‑of‑distribution geometries, errors increase modestly (temperature L2 ≈ 4.5 %) and boundary regions appear slightly blurred, reflecting the limited extrapolation capability of the mask‑based conditioning.

Speedwise, inference on an NVIDIA A100 GPU yields roughly 0.018 s per frame, translating to a full 200‑frame sequence in under 4 seconds—a speed‑up of three to four orders of magnitude compared with conventional CFD solvers that require tens of seconds to minutes per time step. This demonstrates the model’s suitability for real‑time digital twins, interactive design loops, and rapid optimization.

The authors acknowledge several limitations. The current formulation does not incorporate turbulence models or variable material properties, which would be necessary for higher‑Reynolds‑number flows. The mask resolution limits the accuracy of thin boundary layers, and long‑horizon predictions suffer from error accumulation despite the adversarial training. Future work is proposed to integrate physics‑based constraints (e.g., mass and energy conservation penalties), multi‑scale masks, and recurrent or transformer‑based latent dynamics to improve stability over very long sequences.

In summary, the paper presents a novel adaptation of video‑generation GANs to multi‑physics, transient simulation tasks. By generalizing channel dimensions and introducing a two‑fold conditioning scheme, the authors achieve real‑time synthesis of convective heat‑transfer fields with reasonable accuracy and demonstrate promising generalization to unseen geometries. The released dataset and evaluation framework provide valuable resources for the emerging field of physics‑aware generative modeling.