Surrogate Modeling of 3D Rayleigh-Benard Convection with Equivariant Autoencoders
cs.LG, physics.flu-dyn
Submitted: 2025-05-19
Updated: 2026-09-11
Code: https://github.com/FynnFromme/equivariant-rb-forecasting
Project page: https://polymathic-ai.org/the_well/datasets
License: http://creativecommons.org/licenses/by/4.0/
The gist: The use of machine learning for modeling, understanding, and controlling large-scale physics systems is quickly gaining in popularity, with examples ranging from electromagnetism over nuclear fusion
Terminology
Abstract
The use of machine learning for modeling, understanding, and controlling large-scale physics systems is quickly gaining in popularity, with examples ranging from electromagnetism over nuclear fusion reactors and magneto-hydrodynamics to fluid mechanics and climate modeling. These systems - governed by partial differential equations - present unique challenges regarding the large number of degrees of freedom and the complex dynamics over many scales both in space and time, and additional measures to improve accuracy and sample efficiency are highly desirable. We present an end-to-end equivariant surrogate model consisting of an equivariant convolutional autoencoder and an equivariant convolutional LSTM using G-steerable kernels. As a case study, we consider the three-dimensional Rayleigh-Bénard convection, which describes the buoyancy-driven fluid flow between a heated bottom and a cooled top plate. While the system is E(2)-equivariant in the horizontal plane, the boundary conditions break the translational equivariance in the vertical direction. Our architecture leverages vertically stacked layers of D 4-steerable kernels, with additional partial kernel sharing in the vertical direction for further efficiency improvement. We demonstrate significant gains in sample and parameter efficiency, as well as a better scaling to more complex dynamics. The accompanying code is available under https://github.com/FynnFromme/equivariant-rb-forecasting.
Sources
- Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges
- 3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation
- Group-Convolutional Extended Dynamic Mode Decomposition
- Solving Partial Differential Equations with Equivariant Extreme Learning Machines
- P3D: Scalable Neural Surrogates for High-Resolution 3D Physics Simulations with Global Context
- PDE-Transformer: Efficient and Versatile Transformers for Physics Simulations
- 3DLinker: An E(3) Equivariant Variational Autoencoder for Molecular Linker Design
- Advanced deep-reinforcement-learning methods for flow control: group-invariant and positional-encoding networks improve learning speed and quality
- Generative Latent Neural PDE Solver using Flow Matching
- Learning Turbulent Flows with Generative Models: Super-resolution, Forecasting, and Sparse Flow Reconstruction
- U-Net: Convolutional Networks for Biomedical Image Segmentation
- High-level, high-resolution ocean modeling at all scales with Oceananigans
- Coordinate Independent Convolutional Networks -- Isometry and Gauge Equivariant Convolutions on Riemannian Manifolds
- diffSPH: Differentiable Smoothed Particle Hydrodynamics for Adjoint Optimization and Machine Learning
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