arXiv subjects

Iacopo Tirelli

Publications and source records attributed to Iacopo Tirelli.

6 recordsLinked to original sources

arXiv2026

Information decomposition for disentangled and interpretable manifold learning of fluid flows via variational autoencoders

We introduce an information-theoretic framework that uses variational autoencoders (VAEs) to extract compact, physically interpretable manifolds from high-dimensional flow-field data. To this end, the Kullback--Leibler (KL) divergence in the variational objective is decomposed into three complementary information-theoretic terms: the index-code mutual information, the total correlation, and the dimension-wise KL divergence. These terms explicitly regulate data compression, latent disentanglement, and geometric regularization. This establishes a principled basis for targeted latent-space design, allowing enhanced interpretability without sacrificing information capacity, a common drawback of heavily regularized VAE variants. The approach is evaluated on two synthetic unsteady flow datasets. First, we consider a flow around a cylinder in a channel with variable cylinder position, diameter, and Reynolds number. Later, we also consider the flow around a NACA 0012 airfoil at varying angles of attack and subjected to strong vortex gusts with variable intensity, position, and length scale. Comparisons with Principal Component Analysis, Isometric Feature Mapping, and $β$-VAE demonstrate clear advantages in disentanglement and physical interpretability. The learned latent coordinates successfully separate distinct physical effects. Moreover, the proposed method demonstrates strong robustness to variations in the loss-weighting parameters, despite involving a larger number of such parameters.

physics.flu-dyn↗

arXiv2026

Meshless Super-Resolution of Scattered Data via constrained RBFs and KNN-Driven Densification

We propose a novel meshless method to achieve super resolution from scattered data obtained from sparse, randomly positioned sensors such as the particle tracers of particle tracking velocimetry. The method combines K Nearest Neighbor Particle Tracking Velocimetry (KNN PTV, Tirelli et al. 2023) with meshless Proper Orthogonal Decomposition (meshless POD, Tirelli et al. 2025) and constrained Radial Basis Function regression (c RBFs, Sperotto et al. 2022). The main idea is to enhance the spatial resolution of flow fields by blending data from locally similar flow regions available in the time series. This similarity is assessed in terms of statistical coherency with leading features identified by meshless POD applied directly to scattered data, without interpolation onto a grid and relying instead on RBFs to compute the relevant inner products. The denser scattered distributions are then used within a constrained RBF framework to derive an analytical representation of the flow fields that incorporates physical constraints. The approach is fully meshless and does not require a grid at any stage, offering flexibility in complex geometries. An ablation study highlights the role of penalties and physical constraints in regularizing the regression and ensuring physically consistent reconstructions. The method is validated using three dimensional measurements of a jet flow in air. The assessment focuses on statistics, spectra, and modal analysis. Performance is evaluated against standard Particle Image Velocimetry, KNN PTV, and c RBFs. The results show improved accuracy, with an average error of about ten percent compared to twelve to thirteen percent for the other methods, nearly halved errors in reduced order reconstructions, and a higher frequency cutoff based on the noise floor.

physics.flu-dyn↗

arXiv2025

Full-domain POD modes from PIV asynchronous patches

A method is proposed to obtain full-domain spatial modes based on Proper Orthogonal Decomposition (POD) of Particle Image Velocimetry (PIV) measurements performed at different (overlapping) spatial locations. This situation occurs when large domains are covered by multiple non-simultaneous measurements and yet the large-scale flow field organization is to be captured. The proposed methodology leverages the definition of POD spatial modes as eigenvectors of the spatial correlation matrix, where local measurements, even when not obtained simultaneously, provide each a portion of the latter, which is then analyzed to synthesize the full-domain spatial modes. The measurement domain coverage is found to require regions overlapping by 50-75% to yield a smooth distribution of the modes. The procedure identifies structures twice as large as each measurement patch. The technique, referred to as Patch POD, is applied to planar PIV data of a submerged jet flow where the effect of patching is simulated by splitting the original PIV data. Patch POD is then extended to 3D robotic measurement around a wall-mounted cube. The results show that the patching technique enables global modal analysis over a domain covered with a multitude of non-simultaneous measurements.

physics.flu-dyn↗

arXiv2025

A meshless method to compute the proper orthogonal decomposition and its variants from scattered data

Complex phenomena can be better understood when broken down into a limited number of simpler "components". Linear statistical methods such as the principal component analysis and its variants are widely used across various fields of applied science to identify and rank these components based on the variance they represent in the data. These methods can be seen as factorisations of the matrix collecting all the data, assuming it consists of time series sampled from fixed points in space. However, when data sampling locations vary over time, as with mobile monitoring stations in meteorology and oceanography or with particle tracking velocimetry in experimental fluid dynamics, advanced interpolation techniques are required to project the data onto a fixed grid before the factorisation. This interpolation is often expensive and inaccurate. This work proposes a method to decompose scattered data without interpolating. The approach employs physics-constrained radial basis function regression to compute inner products in space and time. The method provides an analytical and mesh-independent decomposition in space and time, demonstrating higher accuracy. Our approach allows distilling the most relevant "components" even for measurements whose natural output is a distribution of data scattered in space and time, maintaining high accuracy and mesh independence.

physics.data-an↗

arXiv2023

A simple trick to improve the accuracy of PIV/PTV data

Particle Image Velocimetry (PIV) estimates velocities through correlations of particle images within interrogation windows, leading to a spatial modulation of the velocity field. Although in principle Particle Tracking Velocimetry (PTV) estimates locally a non-modulated particle displacement, to exploit the scattered data from PTV it is necessary to interpolate these data on a structured grid, which implies a spatial modulation effect that biases the resulting velocity field. This systematic error due to finite spatial resolution inevitably depends on the interrogation window size and on the interparticle spacing. It must be observed that all these operations (cross-correlation, direct interpolation or averaging in windows) induce modulation on both the mean and the fluctuating part. We introduce a simple trick to reduce this systematic error source of PIV/PTV measurements exploiting ensemble statistics. Ensemble Particle Tracking Velocimetry (EPTV) can be leveraged to obtain the high-resolution mean flow by merging the different instantaneous realisations. The mean flow can be estimated with EPTV, and the fluctuating part can be measured from PIV/PTV. The high-resolution mean can then be superposed to the instantaneous fluctuating part to obtain velocity fields with lower systematic error. The methodology is validated against datasets with a progressively increasing level of complexity: two virtual experiments based on direct numerical simulations (DNS) of the wake of a fluidic pinball and a channel flow and the experimental data of a turbulent boundary layer. For all the cases both PTV and PIV are analysed.

physics.flu-dyn↗

arXiv2022

An end-to-end KNN-based PTV approach for high-resolution measurements and uncertainty quantification

We introduce a novel end-to-end approach to improving the resolution of PIV measurements. The method blends information from different snapshots without the need for time-resolved measurements on grounds of similarity of flow regions in different snapshots. The main hypothesis is that, with a sufficiently large ensemble of statistically-independent snapshots, the identification of flow structures that are morphologically similar but occurring at different time instants is feasible. Measured individual vectors from different snapshots with similar flow organisation can thus be merged, resulting in an artificially increased particle concentration. This allows to refine the interrogation region and, consequently, increase the spatial resolution. The measurement domain is split in subdomains. The similarity is enforced only on a local scale, i.e. morphologically-similar regions are sought only among subdomains corresponding to the same flow region. The identification of locally-similar snapshots is based on unsupervised K-nearest neighbours search in a space of significant flow features. Such features are defined in terms of a Proper Orthogonal Decomposition, performed in subdomains on the original low-resolution data, obtained either with standard cross-correlation or with binning of Particle Tracking Velocimetry data with a relatively large bin size. A refined bin size is then selected according to the number of "sufficiently close" snapshots identified. The statistical dispersion of the velocity vectors within the bin is then used to estimate the uncertainty and to select the optimal K which minimises it. The method is tested and validated against datasets with a progressively increasing level of complexity: two virtual experiments based on direct simulations of the wake of a fluidic pinball and a channel flow and the experimental data collected in a turbulent boundary layer.

physics.flu-dyn↗