# Multi-fidelity Generative Deep Learning Turbulent Flows

arXiv: https://arxiv.org/abs/2006.04731 · HTML: https://mlsanity.com/paper/2006.04731/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2020.

## Built on by (most cited first, 21 of 21)

- [Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons](https://mlsanity.com/paper/2201.07766/) (2022)
- [Bayesian Conditional Diffusion Models for Versatile Spatiotemporal Turbulence Generation](https://mlsanity.com/paper/2311.07896/) (2023)
- [Transfer Learning on Multi-Fidelity Data](https://mlsanity.com/paper/2105.00856/) (2021)
- [Physics-enhanced deep surrogates for partial differential equations](https://mlsanity.com/paper/2111.05841/) (2021)
- [Multi-fidelity surrogate modeling using long short-term memory networks](https://mlsanity.com/paper/2208.03115/) (2022)
- [Multi-fidelity reduced-order surrogate modeling](https://mlsanity.com/paper/2309.00325/) (2023)
- [Use of Multifidelity Training Data and Transfer Learning for Efficient Construction of Subsurface Flow Surrogate Models](https://mlsanity.com/paper/2204.11138/) (2022)
- [CoNFiLD-inlet: Synthetic Turbulence Inflow Using Generative Latent Diffusion Models with Neural Fields](https://mlsanity.com/paper/2411.14378/) (2024)
- [State estimation with limited sensors -- A deep learning based approach](https://mlsanity.com/paper/2101.11513/) (2021)
- [Inverse Aerodynamic Design of Gas Turbine Blades using Probabilistic Machine Learning](https://mlsanity.com/paper/2108.10163/) (2021)
- [GrADE: A graph based data-driven solver for time-dependent nonlinear partial differential equations](https://mlsanity.com/paper/2108.10639/) (2021)
- [Generative Learning for Forecasting the Dynamics of Complex Systems](https://mlsanity.com/paper/2402.17157/) (2024)
- [Multi-fidelity physics constrained neural networks for dynamical systems](https://mlsanity.com/paper/2402.02031/) (2024)
- [Neural network based generation of a 1-dimensional stochastic field with turbulent velocity statistics](https://mlsanity.com/paper/2211.11580/) (2022)
- [A multiscale and multicriteria Generative Adversarial Network to synthesize 1-dimensional turbulent fields](https://mlsanity.com/paper/2307.16580/) (2023)
- [Learning Effective Dynamics across Spatio-Temporal Scales of Complex Flows](https://mlsanity.com/paper/2502.07990/) (2025)
- [Multi-fidelity Reinforcement Learning Control for Complex Dynamical Systems](https://mlsanity.com/paper/2504.05588/) (2025)
- [Progressive multi-fidelity learning with neural networks for physical system predictions](https://mlsanity.com/paper/2510.13762/) (2025)
- [Graph Laplacian-based Bayesian Multi-fidelity Modeling](https://mlsanity.com/paper/2409.08211/) (2024)
- [A few-shot graph Laplacian-based approach for improving the accuracy of low-fidelity data](https://mlsanity.com/paper/2304.04862/) (2023)
- [Data-driven Modeling of Parameterized Nonlinear Fluid Dynamical Systems with a Dynamics-embedded Conditional Generative Adversarial Network](https://mlsanity.com/paper/2412.17978/) (2024)

## Abstract (arXiv)

In computational fluid dynamics, there is an inevitable trade off between accuracy and computational cost. In this work, a novel multi-fidelity deep generative model is introduced for the surrogate modeling of high-fidelity turbulent flow fields given the solution of a computationally inexpensive but inaccurate low-fidelity solver. The resulting surrogate is able to generate physically accurate turbulent realizations at a computational cost magnitudes lower than that of a high-fidelity simulation. The deep generative model developed is a conditional invertible neural network, built with normalizing flows, with recurrent LSTM connections that allow for stable training of transient systems with high predictive accuracy. The model is trained with a variational loss that combines both data-driven and physics-constrained learning. This deep generative model is applied to non-trivial high Reynolds number flows governed by the Navier-Stokes equations including turbulent flow over a backwards facing step at different Reynolds numbers and turbulent wake behind an array of bluff bodies. For both of these examples, the model is able to generate unique yet physically accurate turbulent fluid flows conditioned on an inexpensive low-fidelity solution.