# Variational Rank Reduction Autoencoders for Generative Thermal Design

arXiv: https://arxiv.org/abs/2509.08515 · HTML: https://mlsanity.com/paper/2509.08515/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 65 references that are in the map.
- First posted on arXiv 10 Sep 2025.

## Builds on (most cited first, 30 of 34)

- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Topological Autoencoders](https://mlsanity.com/paper/1906.00722/) (2019)
- [A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs](https://mlsanity.com/paper/2001.04001/) (2020)
- [Deep Generative Models in Engineering Design: A Review](https://mlsanity.com/paper/2110.10863/) (2021)
- [Latent Neural Operator for Solving Forward and Inverse PDE Problems](https://mlsanity.com/paper/2406.03923/) (2024)
- [POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition](https://mlsanity.com/paper/2101.11845/) (2021)
- [β-Variational autoencoders and transformers for reduced-order modelling of fluid flows](https://mlsanity.com/paper/2304.03571/) (2023)
- [Gaussian Process Prior Variational Autoencoders](https://mlsanity.com/paper/1810.11738/) (2018)
- [Learning two-phase microstructure evolution using neural operators and autoencoder architectures](https://mlsanity.com/paper/2204.07230/) (2022)
- [Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modeling](https://mlsanity.com/paper/2102.13156/) (2021)
- [Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoders](https://mlsanity.com/paper/2201.05136/) (2022)
- [Geom-DeepONet: A Point-cloud-based Deep Operator Network for Field Predictions on 3D Parameterized Geometries](https://mlsanity.com/paper/2403.14788/) (2024)
- [Deep Generative Models through the Lens of the Manifold Hypothesis: A Survey and New Connections](https://mlsanity.com/paper/2404.02954/) (2024)
- [Towards extraction of orthogonal and parsimonious non-linear modes from turbulent flows](https://mlsanity.com/paper/2109.01514/) (2021)
- [A graph convolutional autoencoder approach to model order reduction for parametrized PDEs](https://mlsanity.com/paper/2305.08573/) (2023)
- [Deep learning of thermodynamics-aware reduced-order models from data](https://mlsanity.com/paper/2007.03758/) (2020)
- [Solving inverse-PDE problems with physics-aware neural networks](https://mlsanity.com/paper/2001.03608/) (2020)
- [Discovering Sparse Interpretable Dynamics from Partial Observations](https://mlsanity.com/paper/2107.10879/) (2021)
- [Extracting Interpretable Physical Parameters from Spatiotemporal Systems using Unsupervised Learning](https://mlsanity.com/paper/1907.06011/) (2019)
- [PI-VAE: Physics-Informed Variational Auto-Encoder for stochastic differential equations](https://mlsanity.com/paper/2203.11363/) (2022)
- [Physics-Informed Geometry-Aware Neural Operator](https://mlsanity.com/paper/2408.01600/) (2024)
- [Inferring turbulent velocity and temperature fields and their statistics from Lagrangian velocity measurements using physics-informed Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2407.15727/) (2024)
- [Physics-Enhanced Machine Learning: a position paper for dynamical systems investigations](https://mlsanity.com/paper/2405.05987/) (2024)
- [Physics-guided Deep Markov Models for Learning Nonlinear Dynamical Systems with Uncertainty](https://mlsanity.com/paper/2110.08607/) (2021)
- [Physics perception in sloshing scenes with guaranteed thermodynamic consistency](https://mlsanity.com/paper/2106.13301/) (2021)
- [Nonlinear model reduction for operator learning](https://mlsanity.com/paper/2403.18735/) (2024)
- [Thermodynamically Consistent Latent Dynamics Identification for Parametric Systems](https://mlsanity.com/paper/2506.08475/) (2025)
- [An unsupervised latent/output physics-informed convolutional-LSTM network for solving partial differential equations using peridynamic differential operator](https://mlsanity.com/paper/2210.12177/) (2022)
- [An adaptive artificial neural network-based generative design method for layout designs](https://mlsanity.com/paper/2101.12410/) (2021)
- [LatentPINNs: Generative physics-informed neural networks via a latent representation learning](https://mlsanity.com/paper/2305.07671/) (2023)

## Built on by (most cited first, 1 of 1)

- [Generative Parametric Design (GPD): A framework for real-time geometry generation and on-the-fly multiparametric approximation](https://mlsanity.com/paper/2512.11748/) (2025)

## Abstract (arXiv)

Generative thermal design for complex geometries is fundamental in many areas of engineering, yet it faces two main challenges: the high computational cost of high-fidelity simulations and the limitations of conventional generative models. Approaches such as autoencoders (AEs) and variational autoencoders (VAEs) often produce unstructured latent spaces with discontinuities, which restricts their capacity to explore designs and generate physically consistent solutions. To address these limitations, we propose a hybrid framework that combines Variational Rank-Reduction Autoencoders (VRRAEs) with Deep Operator Networks (DeepONets). The VRRAE introduces a truncated SVD within the latent space, leading to continuous, interpretable, and well-structured representations that mitigate posterior collapse and improve geometric reconstruction. The DeepONet then exploits this compact latent encoding in its branch network, together with spatial coordinates in the trunk network, to predict temperature gradients efficiently and accurately. This hybrid approach not only enhances the quality of generated geometries and the accuracy of gradient prediction, but also provides a substantial advantage in inference efficiency compared to traditional numerical solvers. Overall, the study underscores the importance of structured latent representations for operator learning and highlights the potential of combining generative models and operator networks in thermal design and broader engineering applications.