Topological Analysis of Ensembles of Hydrodynamic Turbulent Flows -- An Experimental Study

• URL: http://arxiv.org/abs/2207.14080v1
• Date: Thu, 28 Jul 2022 13:36:00 GMT
• Title: Topological Analysis of Ensembles of Hydrodynamic Turbulent Flows -- An Experimental Study
• Authors: Florent Nauleau, Fabien Vivodtzev, Thibault Bridel-Bertomeu, Heloise Beaugendre, Julien Tierny
• Abstract summary: We document the usage of the persistence diagram of the maxima of flow enstrophy (an established vorticity indicator) for the topological representation of 180 ensemble members. We document five main hypotheses reported by domain experts, describing their expectations regarding the variability of the flows generated by the distinct solver configurations.
• Score: 4.976815699476328
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This application paper presents a comprehensive experimental evaluation of the suitability of Topological Data Analysis (TDA) for the quantitative comparison of turbulent flows. Specifically, our study documents the usage of the persistence diagram of the maxima of flow enstrophy (an established vorticity indicator), for the topological representation of 180 ensemble members, generated by a coarse sampling of the parameter space of five numerical solvers. We document five main hypotheses reported by domain experts, describing their expectations regarding the variability of the flows generated by the distinct solver configurations. We contribute three evaluation protocols to assess the validation of the above hypotheses by two comparison measures: (i) a standard distance used in scientific imaging (the L2 norm) and (ii) an established topological distance between persistence diagrams (the L2-Wasserstein metric). Extensive experiments on the input ensemble demonstrate the superiority of the topological distance (ii) to report as close to each other flows which are expected to be similar by domain experts, due to the configuration of their vortices. Overall, the insights reported by our study bring an experimental evidence of the suitability of TDA for representing and comparing turbulent flows, thereby providing to the fluid dynamics community confidence for its usage in future work. Also, our flow data and evaluation protocols provide to the TDA community an application-approved benchmark for the evaluation and design of further topological distances.

Related papers

• GeodesicNVS: Probability Density Geodesic Flow Matching for Novel View Synthesis [54.39598154430305]
  We propose a Data-to-Data Flow Matching framework that learns deterministic transformations directly between paired views.<n>PDG-FM constrains flow trajectories using geodesic interpolants derived from probability density metrics of pretrained diffusion models.<n>These results highlight the advantages of incorporating data-dependent geometric regularization into deterministic flow matching for consistent novel view generation.
  arXiv  Detail & Related papers  (2026-03-01T09:30:11Z)
• Flow-Based Density Ratio Estimation for Intractable Distributions with Applications in Genomics [80.05951561886123]
  We leverage condition-aware flow matching to derive a single dynamical formulation for tracking density ratios along generative trajectories.<n>We demonstrate competitive performance on simulated benchmarks for closed-form ratio estimation, and show that our method supports versatile tasks in single-cell genomics data analysis.
  arXiv  Detail & Related papers  (2026-02-27T17:27:55Z)
• Improving Bayesian inference in PTA data analysis: importance nested sampling with Normalizing Flows [0.0]
  We present a detailed study of Bayesian inference for pulsar timing array data with a focus on enhancing efficiency, robustness and speed.<n>We integrate the i-nessai sampler and benchmark its performance on realistic, simulated datasets.<n>Results highlight the potential of flow-based nested sampling to accelerate PTA analyses while preserving the quality of the inference.
  arXiv  Detail & Related papers  (2025-11-03T17:29:46Z)
• Demystifying Network Foundation Models [14.775836458250799]
  This work presents a systematic investigation into the latent knowledge encoded within Network Foundation Models (NFMs)<n>We evaluate four state-of-the-art NFMs, revealing that they all exhibit significant anisotropy, inconsistent feature sensitivity patterns.<n>Our work identifies numerous limitations across all models and demonstrates that addressing them can significantly improve model performance.
  arXiv  Detail & Related papers  (2025-09-27T03:53:46Z)
• Guided Diffusion Sampling on Function Spaces with Applications to PDEs [111.87523128566781]
  We propose a general framework for conditional sampling in PDE-based inverse problems.<n>This is accomplished by a function-space diffusion model and plug-and-play guidance for conditioning.<n>Our method achieves an average 32% accuracy improvement over state-of-the-art fixed-resolution diffusion baselines.
  arXiv  Detail & Related papers  (2025-05-22T17:58:12Z)
• A Unifying Information-theoretic Perspective on Evaluating Generative Models [5.524685807042777]
  Several recent approaches utilize "precision" and "recall," borrowed from the classification domain, to individually quantify the output fidelity (realism) and output diversity (representation of the real data variation) We unify a class of kth-nearest-neighbors (kNN)-based metrics under an information-theoretic lens using approaches from kNN density estimation. We propose a tri-dimensional metric composed of Precision Cross-Entropy (PCE), Recall Cross-Entropy (RCE), and Recall Entropy (RE)
  arXiv  Detail & Related papers  (2024-12-18T21:17:02Z)
• Distributionally Robust Instrumental Variables Estimation [10.765695227417865]
  We propose a distributionally robust framework for instrumental variables (IV) estimation. We show that Wasserstein DRIVE could be preferable in practice, particularly when the practitioner is uncertain about model assumptions or distributional shifts in data.
  arXiv  Detail & Related papers  (2024-10-21T04:33:38Z)
• A Likelihood Based Approach to Distribution Regression Using Conditional Deep Generative Models [6.647819824559201]
  We study the large-sample properties of a likelihood-based approach for estimating conditional deep generative models. Our results lead to the convergence rate of a sieve maximum likelihood estimator for estimating the conditional distribution.
  arXiv  Detail & Related papers  (2024-10-02T20:46:21Z)
• FUSE: Fast Unified Simulation and Estimation for PDEs [11.991297011923004]
  We argue that solving both problems within the same framework can lead to consistent gains in accuracy and robustness. We present the capabilities of the proposed methodology for predicting continuous and discrete biomarkers in full-body haemodynamics simulations.
  arXiv  Detail & Related papers  (2024-05-23T13:37:26Z)
• Diffusion posterior sampling for simulation-based inference in tall data settings [53.17563688225137]
  Simulation-based inference ( SBI) is capable of approximating the posterior distribution that relates input parameters to a given observation. In this work, we consider a tall data extension in which multiple observations are available to better infer the parameters of the model. We compare our method to recently proposed competing approaches on various numerical experiments and demonstrate its superiority in terms of numerical stability and computational cost.
  arXiv  Detail & Related papers  (2024-04-11T09:23:36Z)
• Revisiting the Evaluation of Image Synthesis with GANs [55.72247435112475]
  This study presents an empirical investigation into the evaluation of synthesis performance, with generative adversarial networks (GANs) as a representative of generative models. In particular, we make in-depth analyses of various factors, including how to represent a data point in the representation space, how to calculate a fair distance using selected samples, and how many instances to use from each set.
  arXiv  Detail & Related papers  (2023-04-04T17:54:32Z)
• Validation Diagnostics for SBI algorithms based on Normalizing Flows [55.41644538483948]
  This work proposes easy to interpret validation diagnostics for multi-dimensional conditional (posterior) density estimators based on NF. It also offers theoretical guarantees based on results of local consistency. This work should help the design of better specified models or drive the development of novel SBI-algorithms.
  arXiv  Detail & Related papers  (2022-11-17T15:48:06Z)
• Gauge-equivariant flow models for sampling in lattice field theories with pseudofermions [51.52945471576731]
  This work presents gauge-equivariant architectures for flow-based sampling in fermionic lattice field theories using pseudofermions as estimators for the fermionic determinant. This is the default approach in state-of-the-art lattice field theory calculations, making this development critical to the practical application of flow models to theories such as QCD.
  arXiv  Detail & Related papers  (2022-07-18T21:13:34Z)
• Robust Topological Inference in the Presence of Outliers [18.6112824677157]
  The distance function to a compact set plays a crucial role in the paradigm of topological data analysis. Despite its stability to perturbations in the Hausdorff distance, persistent homology is highly sensitive to outliers. We propose a $textitmedian-of-means$ variant of the distance function ($textsfMoM Dist$), and establish its statistical properties.
  arXiv  Detail & Related papers  (2022-06-03T19:45:43Z)
• Evaluating the Adversarial Robustness for Fourier Neural Operators [78.36413169647408]
  Fourier Neural Operator (FNO) was the first to simulate turbulent flow with zero-shot super-resolution. We generate adversarial examples for FNO based on norm-bounded data input perturbations. Our results show that the model's robustness degrades rapidly with increasing perturbation levels.
  arXiv  Detail & Related papers  (2022-04-08T19:19:42Z)
• Leveraging Global Parameters for Flow-based Neural Posterior Estimation [90.21090932619695]
  Inferring the parameters of a model based on experimental observations is central to the scientific method. A particularly challenging setting is when the model is strongly indeterminate, i.e., when distinct sets of parameters yield identical observations. We present a method for cracking such indeterminacy by exploiting additional information conveyed by an auxiliary set of observations sharing global parameters.
  arXiv  Detail & Related papers  (2021-02-12T12:23:13Z)
• On Deep Instrumental Variables Estimate [21.003925102068298]
  "Deep Instrumental Variable (IV)" is a framework based on deep neural networks to address endogeneity. We consider a two-stage estimator using deep neural networks in the linear instrumental variables model. We show that the second-stage estimator achieves the semiparametric efficiency bound.
  arXiv  Detail & Related papers  (2020-04-30T17:03:00Z)

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.