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arXiv Machine Learning

Surrogate Modeling of 3D Rayleigh-Benard Convection with Equivariant Autoencoders

The paper introduces an end‑to‑end equivariant surrogate model for three‑dimensional Rayleigh‑Bénard convection, combining an equivariant convolutional autoencoder with an equivariant convolutional LSTM that employs $G$‑steerable kernels. The architecture exploits $D_4$‑steerable kernels in vertically stacked layers and partial kernel sharing in the vertical direction to respect the system’s E(2) equivariance in the horizontal plane while handling broken translational symmetry vertically. Experiments show notable improvements in sample and parameter efficiency and better scaling to more complex dynamics.

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Advances in Scientific Machine Learning for Coupled Fluid Flow and Transport

This chapter reviews recent advances in Scientific Machine Learning (SciML) for modeling coupled fluid flow and transport phenomena governed by the incompressible Navier-Stokes and scalar transport equations. Such systems, found in applications like turbidity currents and thermal convection, feature strong nonlinear coupling and multiscale behavior that make high-fidelity simulations computationally expensive.

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arXiv AI
Jul 7

Conditional Clifford-Steerable CNNs for PDE Modeling

arXiv:2510. 14007v2 Announce Type: replace-cross Abstract: We introduce Conditional Clifford-Steerable CNNs (C-CSCNNs), a unified framework that incorporates equivariance to arbitrary pseudo-Euclidean groups and significantly improves the expressivity of standard CSCNNs.

By B\'alint L\'aszl\'o Szarvas, Maksim Zhdanov
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arXiv Machine Learning
Sep 2

Efficient Adaptation of ROMs for Unsteady Flows Using Data Assimilation

The paper presents a lightweight retraining strategy for a parameterized Reduced Order Model (ROM) that achieves full‑model accuracy using only a fraction of the computational effort and sparse observations. The ROM architecture combines a Variational Autoencoder for dimensionality reduction with a transformer network that evolves latent states while accounting for the Reynolds number as an external control variable. By leveraging the probabilistic VAE, the method generates trajectory ensembles and uncertainty estimates, and adapts to out‑of‑sample parameters through sparse data assimilation with an ensemble Kalman filter, focusing retraining on the autoencoder to correct latent manifold distortions.

By Isma\"el Zighed, Andrea N\'ovoa, Luca Magri, Taraneh Sayadi
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arXiv Machine Learning
Jul 3

Fourier Neural Operators for Rayleigh-B\'enard Convection

arXiv:2607. 02088v1 Announce Type: new Abstract: We propose an improved Fourier Neural Operator (FNO) for modeling two-dimensional Rayleigh-B\'enard convection by predicting time increments instead of full solutions, achieving higher accuracy than a standard FNO baseline.

By Chelsea Maria John, Thibaut Lunet, Sebastian G\"otschel, Andreas Herten, Stefan Kesselheim, Daniel Ruprecht
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arXiv AI
Jul 2

A Multi-Resolution Finite-Volume Inspired Deep Learning Framework for Spatiotemporal Dynamics Prediction

arXiv:2607. 00460v1 Announce Type: cross Abstract: Predicting complex spatiotemporal dynamics in physical processes often demands computationally expensive numerical methods or data-driven neural networks that suffer from high training costs, error accumulation, and limited generalizability to unseen parameters.

By Xin-Yang Liu, Xiantao Fan, Jian-Xun Wang
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