Symbolic Regression of Data-Driven Reduced Order Model Closures for Under-Resolved, Convection-Dominated Flows

• URL: http://arxiv.org/abs/2502.04703v1
• Date: Fri, 07 Feb 2025 07:14:41 GMT
• Title: Symbolic Regression of Data-Driven Reduced Order Model Closures for Under-Resolved, Convection-Dominated Flows
• Authors: Simone Manti, Ping-Hsuan Tsai, Alessandro Lucantonio, Traian Iliescu,
• Abstract summary: Data-driven closures correct the standard reduced order models (ROMs) to increase their accuracy in under-resolved, convection-dominated flows.<n>We propose a novel symbolic regression (SR) data-driven ROM closure strategy, which combines the advantages of current approaches and eliminates their drawbacks.<n>New data-driven SR-ROM closures yield ROMs that are interpretable, parsimonious, accurate, generalizable, and robust.
• Score: 41.94295877935867
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Data-driven closures correct the standard reduced order models (ROMs) to increase their accuracy in under-resolved, convection-dominated flows. There are two types of data-driven ROM closures in current use: (i) structural, with simple ansatzes (e.g., linear or quadratic); and (ii) machine learning-based, with neural network ansatzes. We propose a novel symbolic regression (SR) data-driven ROM closure strategy, which combines the advantages of current approaches and eliminates their drawbacks. As a result, the new data-driven SR closures yield ROMs that are interpretable, parsimonious, accurate, generalizable, and robust. To compare the data-driven SR-ROM closures with the structural and machine learning-based ROM closures, we consider the data-driven variational multiscale ROM framework and two under-resolved, convection-dominated test problems: the flow past a cylinder and the lid-driven cavity flow at Reynolds numbers Re = 10000, 15000, and 20000. This numerical investigation shows that the new data-driven SR-ROM closures yield more accurate and robust ROMs than the structural and machine learning ROM closures.

Related papers

• AutoTurb: Using Large Language Models for Automatic Algebraic Model Discovery of Turbulence Closure [15.905369652489505]
  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.
  arXiv  Detail & Related papers  (2024-10-14T16:06:35Z)
• Registration by Regression (RbR): a framework for interpretable and flexible atlas registration [9.123448432479858]
  We propose Registration by Regression (RbR), a novel atlas registration framework that is highly robust and flexible. RbR predicts the atlas coordinates for every voxel of the input scan (i.e., every voxel is a keypoint), and then uses closed-form expressions to quickly fit transforms. Experiments on independent public datasets show that RbR yields more accurate registration than competing keypoint approaches.
  arXiv  Detail & Related papers  (2024-04-25T17:30:38Z)
• Multilinear Kernel Regression and Imputation via Manifold Learning [5.482532589225551]
  MultiL-KRIM builds on the intuitive concept of spaces to tangent and incorporates collaboration among point-cloud neighbors (regressors) directly into the data-modeling term of the loss function. Two important application domains showcase the functionality of MultiL-KRIM: time-varying-graph-signal (TVGS) recovery, and reconstruction of highly accelerated dynamic-magnetic-resonance-imaging (dMRI) data.
  arXiv  Detail & Related papers  (2024-02-06T02:50:42Z)
• Bounding data reconstruction attacks with the hypothesis testing interpretation of differential privacy [78.32404878825845]
  Reconstruction Robustness (ReRo) was recently proposed as an upper bound on the success of data reconstruction attacks against machine learning models. Previous research has demonstrated that differential privacy (DP) mechanisms also provide ReRo, but so far, only Monte Carlo estimates of a tight ReRo bound have been shown.
  arXiv  Detail & Related papers  (2023-07-08T08:02:47Z)
• Federated Latent Class Regression for Hierarchical Data [5.110894308882439]
  Federated Learning (FL) allows a number of agents to participate in training a global machine learning model without disclosing locally stored data. We propose a novel probabilistic model, Hierarchical Latent Class Regression (HLCR), and its extension to Federated Learning, FEDHLCR. Our inference algorithm, being derived from Bayesian theory, provides strong convergence guarantees and good robustness to overfitting. Experimental results show that FEDHLCR offers fast convergence even in non-IID datasets.
  arXiv  Detail & Related papers  (2022-06-22T00:33:04Z)
• Physics Guided Machine Learning for Variational Multiscale Reduced Order Modeling [58.720142291102135]
  We propose a new physics guided machine learning (PGML) paradigm to increase the accuracy of reduced order models (ROMs) at a modest computational cost. The hierarchical structure of the ROM basis and the variational multiscale (VMS) framework enable a natural separation of the resolved and unresolved ROM spatial scales. Modern PGML algorithms are used to construct novel models for the interaction among the resolved and unresolved ROM scales.
  arXiv  Detail & Related papers  (2022-05-25T00:07:57Z)
• Stress-Testing LiDAR Registration [52.24383388306149]
  We propose a method for selecting balanced registration sets, which are challenging sets of frame-pairs from LiDAR datasets. Perhaps unexpectedly, we find that the fastest and simultaneously most accurate approach is a version of advanced RANSAC.
  arXiv  Detail & Related papers  (2022-04-16T05:10:55Z)
• SreaMRAK a Streaming Multi-Resolution Adaptive Kernel Algorithm [60.61943386819384]
  Existing implementations of KRR require that all the data is stored in the main memory. We propose StreaMRAK - a streaming version of KRR. We present a showcase study on two synthetic problems and the prediction of the trajectory of a double pendulum.
  arXiv  Detail & Related papers  (2021-08-23T21:03:09Z)
• A Hypergradient Approach to Robust Regression without Correspondence [85.49775273716503]
  We consider a variant of regression problem, where the correspondence between input and output data is not available. Most existing methods are only applicable when the sample size is small. We propose a new computational framework -- ROBOT -- for the shuffled regression problem.
  arXiv  Detail & Related papers  (2020-11-30T21:47:38Z)

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.