# Physics-Preserving Latent Compression for Zero-Shot Resolution Transfer in 3D Turbulence

arXiv: https://arxiv.org/abs/2606.21781 · HTML: https://mlsanity.com/paper/2606.21781/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 46 references that are in the map.
- First posted on arXiv 19 Jun 2026.

## Builds on (most cited first, 25 of 25)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Cosmos World Foundation Model Platform for Physical AI](https://mlsanity.com/paper/2501.03575/) (2025)
- [LTX-Video: Realtime Video Latent Diffusion](https://mlsanity.com/paper/2501.00103/) (2024)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Diffusion Transformers with Representation Autoencoders](https://mlsanity.com/paper/2510.11690/) (2025)
- [Multiwavelet-based Operator Learning for Differential Equations](https://mlsanity.com/paper/2109.13459/) (2021)
- [Geometric GAN](https://mlsanity.com/paper/1705.02894/) (2017)
- [U-NO: U-shaped Neural Operators](https://mlsanity.com/paper/2204.11127/) (2022)
- [Deep Compression Autoencoder for Efficient High-Resolution Diffusion Models](https://mlsanity.com/paper/2410.10733/) (2024)
- [A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction](https://mlsanity.com/paper/2211.14680/) (2022)
- [Learned Coarse Models for Efficient Turbulence Simulation](https://mlsanity.com/paper/2112.15275/) (2021)
- [WF-VAE: Enhancing Video VAE by Wavelet-Driven Energy Flow for Latent Video Diffusion Model](https://mlsanity.com/paper/2411.17459/) (2024)
- [Identifying and Solving Conditional Image Leakage in Image-to-Video Diffusion Model](https://mlsanity.com/paper/2406.15735/) (2024)
- [Language-Conditioned World Modeling for Visual Navigation](https://mlsanity.com/paper/2603.26741/) (2026)
- [Learning PDE Solvers with Physics and Data: A Unifying View of Physics-Informed Neural Networks and Neural Operators](https://mlsanity.com/paper/2601.14517/) (2026)
- [PEST: Physics-Enhanced Swin Transformer for 3D Turbulence Simulation](https://mlsanity.com/paper/2602.10150/) (2026)
- [FlowRefiner: Flow Matching-Based Iterative Refinement for 3D Turbulent Flow Simulation](https://mlsanity.com/paper/2604.17149/) (2026)
- [Conditional neural field for spatial dimension reduction of turbulence data: a comparison study](https://mlsanity.com/paper/2510.25135/) (2025)

## Built on by (most cited first, 3 of 3)

- [TIDE: A Physically Diverse 3D Turbulence Benchmark Dataset for Advancing Scientific Machine Learning](https://mlsanity.com/paper/2608.04222/) (2026)
- [Staying on the Attractor: Supervising Neural Surrogates of 3D Turbulence Where They Leave It](https://mlsanity.com/paper/2609.32864/) (2026)
- [Learn the Dynamics, Enforce the Physics: Generative Latent Operators for High-Dimensional Beam Evolution](https://mlsanity.com/paper/2610.14537/) (2026)

## Abstract (arXiv)

High-resolution turbulence modeling is essential for scientific computing, but remains constrained by the cost of direct numerical simulation and the scarcity of full-resolution data. Existing scientific compressors reduce storage but typically operate on per-frame representations, whereas learned compressors yield compact latents that are often resolution-dependent and weakly aligned with the physics of turbulence. This raises the need for a compression framework that reduces data size, preserves physical diagnostics, and transfers from low-resolution training fields to high-resolution test fields without retraining. In this paper, we propose Physics-Preserving Latent Compression (PPLC), a patch-local latent compressor for three-dimensional turbulence. Motivated by inertial-range scale similarity, PPLC treats fixed-size patches as transferable units and applies a shared variational autoencoder independently of the global grid size. It combines exact mean preservation, zero-mean fluctuation encoding, an invertible Haar wavelet front-end, shift-consistency regularization, and overlap-aware reconstruction. Instantiated on forced isotropic turbulence, PPLC is trained only on stride-downsampled 256^3 fields and transfers zero-shot to 1024^3 fields. Experiments show that PPLC improves the balance between reconstruction accuracy and physical fidelity over classical and learned baselines, keeping diagnostics such as dissipation, enstrophy, energy spectra, and incompressibility closer to the ground truth. Beyond turbulence compression, PPLC offers a general strategy for physics-preserving latent representations that support data-efficient scientific surrogate modeling.