Machine learning for fluid flow reconstruction from limited measurements

Dubois, Pierre; Gomez, Thomas; Planckaert, Laurent; Perret, Laurent

doi:10.1016/j.jcp.2021.110733

Cited by 41 publications

(9 citation statements)

References 51 publications

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“…In turbulent flow problems, the state-space is high-dimensional, owing to the complex spatio-temporal dynamics involved. However, low dimensional features can be extracted, making relevant the use of dimensionality reduction techniques [39]. Reconstruction and prediction problems are therefore equivalent to the estimation of the reduced or latent state, thus making the use of encoder-decoder based architecture a natural choice.…”

Section: Deep Learning Methodsmentioning

confidence: 99%

Autoregressive Transformers for Data-Driven Spatio-Temporal Learning of Turbulent Flows

Patil¹,

Viquerat²,

Hachem³

2022

Preprint

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A convolutional encoder-decoder-based transformer model has been developed to autoregressively train on spatio-temporal data of turbulent flows. It works by predicting future fluid flow fields from the previously predicted fluid flow field to ensure long-term predictions without diverging.The model exhibits significant agreements for a priori assessments, and the a posterior predictions, after a considerable number of simulation steps, exhibit predicted variances. Autoregressive training and prediction of a posteriori states is the primary step towards the development of more complex data-driven turbulence models and simulations.

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Section: Deep Learning Methodsmentioning

confidence: 99%

Autoregressive Transformers for Data-Driven Spatio-Temporal Learning of Turbulent Flows

Patil¹,

Viquerat²,

Hachem³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…This capability is essential across various engineering domains, where obtaining comprehensive full-field flow information is challenging due to complex setups, prohibitive computational costs, or the inherent sparsity and noise in direct measurements. Traditional approaches have primarily adopted deterministic models, incorporating dimensionality reduction techniques like POD or DNN-based autoencoders [62][63][64]. Although these methods have demonstrated some success in flow reconstruction, they often struggle with accuracy, robustness, and scalability, particularly in large-scale, complex turbulent flow scenarios [65].…”

Section: Flow Reconstruction From Sparse Sensor Measurementsmentioning

confidence: 99%

CoNFiLD: Conditional Neural Field Latent Diffusion Model Generating Spatiotemporal Turbulence

Wang,

Du,

Parikh

et al. 2024

Preprint

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This study introduces the Conditional Neural Field Latent Diffusion (CoNFiLD) model, a novel generative learning framework designed for rapid simulation of intricate spatiotemporal dynamics in chaotic and turbulent systems within three-dimensional irregular domains. Traditional eddy-resolved numerical simulations, despite offering detailed flow predictions, encounter significant limitations due to their extensive computational demands, restricting their applications in broader engineering contexts. In contrast, deep learning-based surrogate models promise efficient, data-driven solutions. However, their effectiveness is often compromised by a reliance on deterministic frameworks, which fall short in accurately capturing the chaotic and stochastic nature of turbulence. The CoNFiLD model addresses these challenges by synergistically integrating conditional neural field encoding with latent diffusion processes, enabling the memory-efficient and robust probabilistic generation of spatiotemporal turbulence under varied conditions. Leveraging Bayesian conditional sampling, the model can seamlessly adapt to a diverse range of turbulence generation scenarios without the necessity for retraining, covering applications from zero-shot full-field flow reconstruction using sparse sensor measurements to super-resolution generation and spatiotemporal flow data restoration. Comprehensive numerical experiments across a variety of inhomogeneous, anisotropic turbulent flows with irregular geometries have been conducted to evaluate the model's versatility and efficacy, showcasing its transformative potential in the domain of turbulence generation and the broader modeling of spatiotemporal dynamics.

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“…With the development of deep learning technology, researchers leveraged DNNs to build parameterized ROMs [12] for better dimensionality reduction, such as autoencoder [13,14] and generative model [15,16], and establish deep regression model for high precision of coefficient estimation [17]. Due to the powerful representational ability, these DNN methods can provide more competitive performance than traditional ROMs [18,19]. However, two stages of ROMs building and coefficients estimation will both introduce errors to influence reconstruction accuracy, and it has poor interpretability in conducting coefficients estimation.…”

Section: Introductionmentioning

confidence: 99%

RecFNO: a resolution-invariant flow and heat field reconstruction method from sparse observations via Fourier neural operator

Zhao¹,

Chen²,

Gong³

et al. 2023

Preprint

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Perception of the full state is an essential technology to support the monitoring, analysis, and design of physical systems, one of whose challenges is to recover global field from sparse observations. Well-known for brilliant approximation ability, deep neural networks have been attractive to data-driven flow and heat field reconstruction studies. However, limited by network structure, existing researches mostly learn the reconstruction mapping in finite-dimensional space and has poor transferability to variable resolution of outputs. In this paper, we extend the new paradigm of neural operator and propose an end-to-end physical field reconstruction method with both excellent performance and mesh transferability named RecFNO. The proposed method aims to learn the mapping from sparse observations to flow and heat field in infinite-dimensional space, contributing to a more powerful nonlinear fitting capacity and resolution-invariant characteristic. Firstly, according to different usage scenarios, we develop three types of embeddings to model the sparse observation inputs: MLP, mask, and Voronoi embedding. The MLP embedding is propitious to more sparse input, while the others benefit from spatial information preservation and perform better with the increase of observation data. Then, we adopt stacked Fourier layers to reconstruct physical field in Fourier space that regularizes the overall recovered field by Fourier modes superposition. Benefiting from the operator in infinite-dimensional space, the proposed method obtains remarkable accuracy and better resolution transferability among meshes. The experiments conducted on fluid mechanics and thermology problems show that the proposed method outperforms existing POD-based and CNN-based methods in most cases and has the capacity to achieve zero-shot super-resolution.

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Machine learning for fluid flow reconstruction from limited measurements

Cited by 41 publications

References 51 publications

Autoregressive Transformers for Data-Driven Spatio-Temporal Learning of Turbulent Flows

Autoregressive Transformers for Data-Driven Spatio-Temporal Learning of Turbulent Flows

CoNFiLD: Conditional Neural Field Latent Diffusion Model Generating Spatiotemporal Turbulence

RecFNO: a resolution-invariant flow and heat field reconstruction method from sparse observations via Fourier neural operator

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