Generative Diffusion Models for Synthetic High-Fidelity Lagrangian Turbulence Data

Основные понятия

A machine learning approach based on state-of-the-art diffusion models can generate single-particle trajectories in three-dimensional turbulence at high Reynolds numbers, accurately reproducing the statistical and topological properties exhibited by particle trajectories in turbulence.

Аннотация

The authors present a data-driven model based on generative diffusion models (DMs) that can faithfully reproduce the statistical and geometrical properties of particles advected by high-Reynolds-number turbulent flows. The key highlights are:

The DM model is able to generate single-particle trajectories in three-dimensional turbulence that closely match the ground-truth data from direct numerical simulations (DNS) across a wide range of statistical benchmarks, including the fat-tail distribution for velocity increments, the anomalous power law, and the increased intermittency around the dissipative scale.

The model exhibits strong generalizability, producing events of higher intensity and rarity that still adhere to the realistic turbulence statistics, overcoming the limitations of the training dataset.

The DM model can accurately capture the scale-by-scale local scaling exponents, a stringent test that requires reproducing the rate of variation of the local scaling properties over a wide range of frequencies/time lags.

The progressive enrichment of signal properties during the backward diffusion process in the DM provides insights into the fundamental physical model learned by the DM to generate the correct set of multi-time fluctuations.

The ability to generate high-quality synthetic Lagrangian turbulence data can enable new applications and models that require large, well-validated datasets, overcoming the challenges of obtaining real-world Lagrangian data.

Статистика

The ratio of the largest to the smallest time scales in the turbulent flow, τL/τη, is proportional to the Taylor Reynolds number, Rλ, which varies from a few thousand in laboratory experiments to millions in atmospheric and astrophysical contexts.
The non-Gaussian fat tails in the probability density functions (PDFs) of velocity and acceleration become more pronounced with increasing Rλ, resulting in rare-but-intense fluctuations of up to 50-60 standard deviations.
The generalized flatness, which quantifies the intermittency, can be order of magnitude larger than the expected values in the presence of Gaussian statistics.

Цитаты

"Lagrangian turbulence lies at the core of numerous applied and fundamental problems related to the physics of dispersion and mixing in engineering, bio-fluids, atmosphere, oceans, and astrophysics."
"Despite exceptional theoretical, numerical, and experimental efforts conducted over the past thirty years, no existing models are capable of faithfully reproducing statistical and topological properties exhibited by particle trajectories in turbulence."
"Remarkably, our model exhibits strong generalization properties, enabling the synthesis of events with intensities never encountered during the training phase."

Ключевые выводы из

Synthetic Lagrangian Turbulence by Generative Diffusion Models

by Tianyi Li,Lu... в arxiv.org 04-30-2024

https://arxiv.org/pdf/2307.08529.pdf

Дополнительные вопросы

How can the DM model be extended to generate multi-particle Lagrangian trajectories and study relative dispersion problems

To extend the DM model to generate multi-particle Lagrangian trajectories and study relative dispersion problems, we can modify the input and output structure of the model. Currently, the DM model is designed to generate single-particle trajectories by learning the statistical properties of the Lagrangian turbulence from DNS data. By expanding the input to include multiple initial conditions for particles and adjusting the output to provide trajectories for each particle, the model can be trained to generate ensembles of Lagrangian trajectories. This extension would allow for the study of relative dispersion problems, where the separation and interaction of multiple particles in a turbulent flow can be analyzed. By considering the correlations and interactions between particles, the model can provide insights into dispersion patterns, clustering behavior, and the evolution of particle trajectories in complex flow environments.

Can the DM model be adapted to handle different flow configurations, such as varying boundary conditions, forcing mechanisms, or higher Reynolds numbers

Adapting the DM model to handle different flow configurations, such as varying boundary conditions, forcing mechanisms, or higher Reynolds numbers, involves adjusting the training data and model architecture. To accommodate different flow conditions, the training dataset should include a diverse range of flow scenarios with varying parameters. By exposing the model to a wide range of conditions during training, it can learn to generalize and adapt to different flow configurations. Additionally, the model architecture can be enhanced to incorporate conditional inputs that specify the flow conditions, allowing the model to generate trajectories based on specific parameters. By conditioning the generation process on different flow configurations, the DM model can be tailored to handle a variety of scenarios, making it more versatile and applicable to a broader range of turbulent flow conditions.

What insights can be gained by factorizing the data with wavelet decomposition and implementing DMs to synthesize the wavelet coefficients, conditioning on the low-frequency ones

Factorizing the data with wavelet decomposition and implementing DMs to synthesize the wavelet coefficients, conditioning on the low-frequency ones, can provide valuable insights into the multiscale features of the turbulence. Wavelet decomposition is a powerful tool for analyzing signals at different scales and frequencies, making it ideal for capturing the complex and hierarchical nature of turbulent flows. By decomposing the input data into wavelet coefficients representing different frequency bands, the DM model can learn to generate trajectories that exhibit the characteristic features of turbulence at various scales. Conditioning the generation process on the low-frequency wavelet coefficients allows the model to capture the global flow structures and interactions, while incorporating the high-frequency components enables the model to reproduce the fine-scale details and fluctuations present in turbulent flows. This approach can enhance the model's ability to generate realistic and detailed Lagrangian trajectories that accurately reflect the multiscale properties of turbulence.