AutoTurb: Using Large Language Models for Automatic Algebraic Model Discovery of Turbulence Closure

• URL: http://arxiv.org/abs/2410.10657v1
• Date: Mon, 14 Oct 2024 16:06:35 GMT
• Title: AutoTurb: Using Large Language Models for Automatic Algebraic Model Discovery of Turbulence Closure
• Authors: Yu Zhang, Kefeng Zheng, Fei Liu, Qingfu Zhang, Zhenkun Wang,
• Abstract summary: In this work, a novel framework using LLMs to automatically discover expressions for correcting the Reynolds stress model is proposed. The proposed method is performed for separated flow over periodic hills at Re = 10,595. It is demonstrated that the corrective RANS can improve the prediction for both the Reynolds stress and mean velocity fields.
• Score: 15.905369652489505
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Symbolic regression (SR) methods have been extensively investigated to explore explicit algebraic Reynolds stress models (EARSM) for turbulence closure of Reynolds-averaged Navier-Stokes (RANS) equations. The deduced EARSM can be readily implemented in existing computational fluid dynamic (CFD) codes and promotes the identification of physically interpretable turbulence models. The existing SR methods, such as genetic programming, sparse regression, or artificial neural networks, require user-defined functional operators, a library of candidates, or complex optimization algorithms. In this work, a novel framework using LLMs to automatically discover algebraic expressions for correcting the RSM is proposed. The direct observation of Reynolds stress and the indirect output of the CFD simulation are both involved in the training process to guarantee data consistency and avoid numerical stiffness. Constraints of functional complexity and convergence are supplementally imposed in the objective function on account of the tremendous flexibility of LLMs. The evolutionary search is employed for global optimization. The proposed method is performed for separated flow over periodic hills at Re = 10,595. The generalizability of the discovered model is verified on a set of 2D turbulent separated flow configurations with different Reynolds numbers and geometries. It is demonstrated that the corrective RANS can improve the prediction for both the Reynolds stress and mean velocity fields. Compared with algebraic models discovered by other works, the discovered model performs better in accuracy and generalization capability. The proposed approach provides a promising paradigm for using LLMs to improve turbulence modeling for a given class of flows.

Related papers

• Using Parametric PINNs for Predicting Internal and External Turbulent Flows [6.387263468033964]
  We build upon the previously proposed RANS-PINN framework, which only focused on predicting flow over a cylinder. We investigate its accuracy in predicting relevant turbulent flow variables for both internal and external flows.
  arXiv  Detail & Related papers  (2024-10-24T17:08:20Z)
• Reference Trustable Decoding: A Training-Free Augmentation Paradigm for Large Language Models [79.41139393080736]
  Large language models (LLMs) have rapidly advanced and demonstrated impressive capabilities. We propose Reference Trustable Decoding (RTD), a paradigm that allows models to quickly adapt to new tasks without fine-tuning.
  arXiv  Detail & Related papers  (2024-09-30T10:48:20Z)
• Understanding Reinforcement Learning-Based Fine-Tuning of Diffusion Models: A Tutorial and Review [63.31328039424469]
  This tutorial provides a comprehensive survey of methods for fine-tuning diffusion models to optimize downstream reward functions. We explain the application of various RL algorithms, including PPO, differentiable optimization, reward-weighted MLE, value-weighted sampling, and path consistency learning.
  arXiv  Detail & Related papers  (2024-07-18T17:35:32Z)
• Koopman-Based Surrogate Modelling of Turbulent Rayleigh-Bénard Convection [4.248022697109535]
  We use a Koopman-inspired architecture called the Linear Recurrent Autoencoder Network (LRAN) for learning reduced-order dynamics in convection flows. A traditional fluid dynamics method, the Kernel Dynamic Mode Decomposition (KDMD) is used to compare the LRAN. We obtained more accurate predictions with the LRAN than with KDMD in the most turbulent setting.
  arXiv  Detail & Related papers  (2024-05-10T12:15:02Z)
• Recurrent neural networks and transfer learning for elasto-plasticity in woven composites [0.0]
  This article presents Recurrent Neural Network (RNN) models as a surrogate for computationally intensive meso-scale simulation of woven composites. A mean-field model generates a comprehensive data set representing elasto-plastic behavior. In simulations, arbitrary six-dimensional strain histories are used to predict stresses under random walking as the source task and cyclic loading conditions as the target task.
  arXiv  Detail & Related papers  (2023-11-22T14:47:54Z)
• Amortizing intractable inference in large language models [56.92471123778389]
  We use amortized Bayesian inference to sample from intractable posterior distributions. We empirically demonstrate that this distribution-matching paradigm of LLM fine-tuning can serve as an effective alternative to maximum-likelihood training. As an important application, we interpret chain-of-thought reasoning as a latent variable modeling problem.
  arXiv  Detail & Related papers  (2023-10-06T16:36:08Z)
• 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)
• Score-based Diffusion Models in Function Space [140.792362459734]
  Diffusion models have recently emerged as a powerful framework for generative modeling. We introduce a mathematically rigorous framework called Denoising Diffusion Operators (DDOs) for training diffusion models in function space. We show that the corresponding discretized algorithm generates accurate samples at a fixed cost independent of the data resolution.
  arXiv  Detail & Related papers  (2023-02-14T23:50:53Z)
• Latent Variable Representation for Reinforcement Learning [131.03944557979725]
  It remains unclear theoretically and empirically how latent variable models may facilitate learning, planning, and exploration to improve the sample efficiency of model-based reinforcement learning. We provide a representation view of the latent variable models for state-action value functions, which allows both tractable variational learning algorithm and effective implementation of the optimism/pessimism principle. In particular, we propose a computationally efficient planning algorithm with UCB exploration by incorporating kernel embeddings of latent variable models.
  arXiv  Detail & Related papers  (2022-12-17T00:26:31Z)
• Accurate Discharge Coefficient Prediction of Streamlined Weirs by Coupling Linear Regression and Deep Convolutional Gated Recurrent Unit [2.4475596711637433]
  The present study proposes data-driven modeling techniques, as an alternative to CFD simulation, to predict the discharge coefficient based on an experimental dataset. It is found that the proposed three layer hierarchical DL algorithm consists of a convolutional layer coupled with two subsequent GRU levels, which is also hybridized with the LR method, leads to lower error metrics.
  arXiv  Detail & Related papers  (2022-04-12T01:59:36Z)
• Fast Distributionally Robust Learning with Variance Reduced Min-Max Optimization [85.84019017587477]
  Distributionally robust supervised learning is emerging as a key paradigm for building reliable machine learning systems for real-world applications. Existing algorithms for solving Wasserstein DRSL involve solving complex subproblems or fail to make use of gradients. We revisit Wasserstein DRSL through the lens of min-max optimization and derive scalable and efficiently implementable extra-gradient algorithms.
  arXiv  Detail & Related papers  (2021-04-27T16:56:09Z)

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.