A data-driven approach for the closure of RANS models by the divergence of the Reynolds Stress Tensor

• URL: http://arxiv.org/abs/2203.16944v1
• Date: Thu, 31 Mar 2022 11:08:54 GMT
• Title: A data-driven approach for the closure of RANS models by the divergence of the Reynolds Stress Tensor
• Authors: Stefano Berrone and Davide Oberto
• Abstract summary: A new data-driven model to close and increase accuracy of RANS equations is proposed. The choice is driven by the presence of the divergence of RST in the RANS equations. Once this data-driven approach is trained, there is no need to run any turbulence model to close the equations.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In the present paper a new data-driven model to close and increase accuracy of RANS equations is proposed. It is based on the direct approximation of the divergence of the Reynolds Stress Tensor (RST) through a Neural Network (NN). This choice is driven by the presence of the divergence of RST in the RANS equations. Furthermore, once this data-driven approach is trained, there is no need to run any turbulence model to close the equations. Finally, it is well known that a good approximation of a function it is not necessarily a good approximation of its derivative. The architecture and inputs choices of the proposed network guarantee both Galilean and coordinates-frame rotation invariances by looking to a vector basis expansion of the divergence of the RST. Two well-known test cases are used to show advantages of the proposed method compared to classic turbulence models.

Related papers

• Straightness of Rectified Flow: A Theoretical Insight into Wasserstein Convergence [54.580605276017096]
  Diffusion models have emerged as a powerful tool for image generation and denoising. Recently, Liu et al. designed a novel alternative generative model Rectified Flow (RF) RF aims to learn straight flow trajectories from noise to data using a sequence of convex optimization problems.
  arXiv  Detail & Related papers  (2024-10-19T02:36:11Z)
• Nonuniform random feature models using derivative information [10.239175197655266]
  We propose nonuniform data-driven parameter distributions for neural network initialization based on derivative data of the function to be approximated. We address the cases of Heaviside and ReLU activation functions, and their smooth approximations (sigmoid and softplus) We suggest simplifications of these exact densities based on approximate derivative data in the input points that allow for very efficient sampling and lead to performance of random feature models close to optimal networks in several scenarios.
  arXiv  Detail & Related papers  (2024-10-03T01:30:13Z)
• von Mises Quasi-Processes for Bayesian Circular Regression [57.88921637944379]
  We explore a family of expressive and interpretable distributions over circle-valued random functions. The resulting probability model has connections with continuous spin models in statistical physics. For posterior inference, we introduce a new Stratonovich-like augmentation that lends itself to fast Markov Chain Monte Carlo sampling.
  arXiv  Detail & Related papers  (2024-06-19T01:57:21Z)
• Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariance [52.093434664236014]
  Recent diffusion models provide a promising zero-shot solution to noisy linear inverse problems without retraining for specific inverse problems. Inspired by this finding, we propose to improve recent methods by using more principled covariance determined by maximum likelihood estimation.
  arXiv  Detail & Related papers  (2024-02-03T13:35:39Z)
• A deep implicit-explicit minimizing movement method for option pricing in jump-diffusion models [0.0]
  We develop a novel deep learning approach for pricing European basket options written on assets that follow jump-diffusion dynamics. The option pricing problem is formulated as a partial integro-differential equation, which is approximated via a new implicit-explicit minimizing movement time-stepping approach.
  arXiv  Detail & Related papers  (2024-01-12T18:21:01Z)
• Enhancing Data-Assimilation in CFD using Graph Neural Networks [0.0]
  We present a novel machine learning approach for data assimilation applied in fluid mechanics, based on adjoint-optimization augmented by Graph Neural Networks (GNNs) models. We obtain our results using direct numerical simulations based on a Finite Element Method (FEM) solver; a two-fold interface between the GNN model and the solver allows the GNN's predictions to be incorporated into post-processing steps of the FEM analysis.
  arXiv  Detail & Related papers  (2023-11-29T19:11:40Z)
• A probabilistic, data-driven closure model for RANS simulations with aleatoric, model uncertainty [1.8416014644193066]
  We propose a data-driven, closure model for Reynolds-averaged Navier-Stokes (RANS) simulations that incorporates aleatoric, model uncertainty. A fully Bayesian formulation is proposed, combined with a sparsity-inducing prior in order to identify regions in the problem domain where the parametric closure is insufficient.
  arXiv  Detail & Related papers  (2023-07-05T16:53:31Z)
• Joint Bayesian Inference of Graphical Structure and Parameters with a Single Generative Flow Network [59.79008107609297]
  We propose in this paper to approximate the joint posterior over the structure of a Bayesian Network. We use a single GFlowNet whose sampling policy follows a two-phase process. Since the parameters are included in the posterior distribution, this leaves more flexibility for the local probability models.
  arXiv  Detail & Related papers  (2023-05-30T19:16:44Z)
• Variational Laplace Autoencoders [53.08170674326728]
  Variational autoencoders employ an amortized inference model to approximate the posterior of latent variables. We present a novel approach that addresses the limited posterior expressiveness of fully-factorized Gaussian assumption. We also present a general framework named Variational Laplace Autoencoders (VLAEs) for training deep generative models.
  arXiv  Detail & Related papers  (2022-11-30T18:59:27Z)
• Improving predictions of Bayesian neural nets via local linearization [79.21517734364093]
  We argue that the Gauss-Newton approximation should be understood as a local linearization of the underlying Bayesian neural network (BNN) Because we use this linearized model for posterior inference, we should also predict using this modified model instead of the original one. We refer to this modified predictive as "GLM predictive" and show that it effectively resolves common underfitting problems of the Laplace approximation.
  arXiv  Detail & Related papers  (2020-08-19T12:35:55Z)
• Mean-Field Approximation to Gaussian-Softmax Integral with Application to Uncertainty Estimation [23.38076756988258]
  We propose a new single-model based approach to quantify uncertainty in deep neural networks. We use a mean-field approximation formula to compute an analytically intractable integral. Empirically, the proposed approach performs competitively when compared to state-of-the-art methods.
  arXiv  Detail & Related papers  (2020-06-13T07:32:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.