arXiv subjects

Małgorzata J. Zimoń

Publications and source records attributed to Małgorzata J. Zimoń.

9 recordsLinked to original sources

arXiv2025

Learning Temporally Consistent Turbulence Between Sparse Snapshots via Diffusion Models

We investigate the statistical accuracy of temporally interpolated spatiotemporal flow sequences between sparse, decorrelated snapshots of turbulent flow fields using conditional Denoising Diffusion Probabilistic Models (DDPMs). The developed method is presented as a proof-of-concept generative surrogate for reconstructing coherent turbulent dynamics between sparse snapshots, demonstrated on a 2D Kolmogorov Flow, and a 3D Kelvin-Helmholtz Instability (KHI). We analyse the generated flow sequences through the lens of statistical turbulence, examining the time-averaged turbulent kinetic energy spectra over generated sequences, and temporal decay of turbulent structures. For the non-stationary Kelvin-Helmholtz Instability, we assess the ability of the proposed method to capture evolving flow statistics across the most strongly time-varying flow regime. We additionally examine instantaneous fields and physically motivated metrics at key stages of the KHI flow evolution.

physics.flu-dyn↗

arXiv2025

PCENet: High Dimensional Surrogate Modeling for Learning Uncertainty

Learning data representations under uncertainty is an important task that emerges in numerous scientific computing and data analysis applications. However, uncertainty quantification techniques are computationally intensive and become prohibitively expensive for high-dimensional data. In this study, we introduce a dimensionality reduction surrogate modeling (DRSM) approach for representation learning and uncertainty quantification that aims to deal with data of moderate to high dimensions. The approach involves a two-stage learning process: 1) employing a variational autoencoder to learn a low-dimensional representation of the input data distribution; and 2) harnessing polynomial chaos expansion (PCE) formulation to map the low dimensional distribution to the output target. The model enables us to (a) capture the system dynamics efficiently in the low-dimensional latent space, (b) learn under uncertainty, a representation of the data and a mapping between input and output distributions, (c) estimate this uncertainty in the high-dimensional data system, and (d) match high-order moments of the output distribution; without any prior statistical assumptions on the data. Numerical results are presented to illustrate the performance of the proposed method.

cs.LG↗

arXiv2025

Spectrally Decomposed Diffusion Models for Generative Turbulence Recovery

We investigate the statistical recovery of missing physics and turbulent phenomena in fluid flows using generative machine learning. Here we develop a two-stage super-resolution method using spectral filtering to restore the high-wavenumber components of a Kolmogorov flow. We include a rigorous examination of generated samples through the lens of statistical turbulence. By extending the prior methods to a combined super-resolution and conditional high-wavenumber generation, we demonstrate turbulence recovery on a 8x upsampling task, effectively doubling the range of recovered wavenumbers.

physics.flu-dyn↗

arXiv2025

Predicting Thermodynamics of Liquid Water from Time Series Analysis

Thermodynamics, introduced over two centuries ago, remains foundational to our understanding of physical, chemical, biological, and engineering systems. Its principles are traditionally grounded in the statistical mechanics framework, which explains macroscopic behavior from microscopic states. In this work, we propose an alternative approach that interprets thermodynamic behavior through the lenses of time series analysis, an approach commonly used in other fields, including finance, climate, and signal processing. We perform classical molecular dynamics simulations of liquid water, the most complex, anomalous, and important substance known, over a wide range of its phase diagram. By examining the temporal evolution of the hydrogen bond network (HBN) topology, we demonstrate that the dynamics of microscopic topological motifs populating the HBN encode the system's macroscopic thermodynamic behavior. Furthermore, our approach enables the prediction of thermodynamic properties in regions beyond those directly sampled in our simulations. We achieve this result by leveraging artificial intelligence to uncover patterns in temporally resolved data that are often lost through conventional averaging. This work offers new insights into the fundamental behavior of water and network-forming materials more broadly, establishing a new paradigm for understanding material properties beyond the classical confines of statistical mechanics.

physics.chem-ph↗

arXiv2024

Concerning the Use of Turbulent Flow Data for Machine Learning

This article describes some common issues encountered in the use of Direct Numerical Simulation (DNS) turbulent flow data for machine learning. We focus on two specific issues; 1) the requirements for a fair validation set, and 2) the pitfalls in downsampling DNS data before training. We attempt to shed light on the impact these issues can have on machine learning and computer vision for turbulence. Further, we include statistical and spectral analysis for the homogenous isotropic turbulence from the John Hopkins Turbulence Database, a Kolmogorov flow, and a Rayleigh-Bénard Convection Cell using data generated by the authors, to concretely demonstrate these issues.

physics.flu-dyn↗

arXiv2024

Reducing data resolution for better super-resolution: Reconstructing turbulent flows from noisy observation

A super-resolution (SR) method for the reconstruction of Navier-Stokes (NS) flows from noisy observations is presented. In the SR method, first the observation data is averaged over a coarse grid to reduce the noise at the expense of losing resolution and, then, a dynamic observer is employed to reconstruct the flow field by reversing back the lost information. We provide a theoretical analysis, which indicates a chaos synchronization of the SR observer with the reference NS flow. It is shown that, even with noisy observations, the SR observer converges toward the reference NS flow exponentially fast, and the deviation of the observer from the reference system is bounded. Counter-intuitively, our theoretical analysis shows that the deviation can be reduced by increasing the lengthscale of the spatial average, i.e., making the resolution coarser. The theoretical analysis is confirmed by numerical experiments of two-dimensional NS flows. The numerical experiments suggest that there is a critical lengthscale for the spatial average, below which making the resolution coarser improves the reconstruction.

physics.flu-dyn↗

arXiv2023

Efficient Adaptive Stochastic Collocation Strategies for Advection-Diffusion Problems with Uncertain Inputs

Physical models with uncertain inputs are commonly represented as parametric partial differential equations (PDEs). That is, PDEs with inputs that are expressed as functions of parameters with an associated probability distribution. Developing efficient and accurate solution strategies that account for errors on the space, time and parameter domains simultaneously is highly challenging. Indeed, it is well known that standard polynomial-based approximations on the parameter domain can incur errors that grow in time. In this work, we focus on advection-diffusion problems with parameter-dependent wind fields. A novel adaptive solution strategy is proposed that allows users to combine stochastic collocation on the parameter domain with off-the-shelf adaptive timestepping algorithms with local error control. This is a non-intrusive strategy that builds a polynomial-based surrogate that is adapted sequentially in time. The algorithm is driven by a so-called hierarchical estimator for the parametric error and balances this against an estimate for the global timestepping error which is derived from a scaling argument.

math.NA↗

arXiv2022

Super Resolution for Turbulent Flows in 2D: Stabilized Physics Informed Neural Networks

We propose a new design of a neural network for solving a zero shot super resolution problem for turbulent flows. We embed Luenberger-type observer into the network's architecture to inform the network of the physics of the process, and to provide error correction and stabilization mechanisms. In addition, to compensate for decrease of observer's performance due to the presence of unknown destabilizing forcing, the network is designed to estimate the contribution of the unknown forcing implicitly from the data over the course of training. By running a set of numerical experiments, we demonstrate that the proposed network does recover unknown forcing from data and is capable of predicting turbulent flows in high resolution from low resolution noisy observations.

math.NA↗

arXiv2019

Thermal transients in a U-Bend

We study numerically the propagation of a hot thermal transient through a U-bend via an ensemble of wall-resolved large eddy simulations. Conjugate heat transfer between fluid and solid domains is accounted for. The flow is in a fully turbulent mixed convection regime, with a bulk Reynolds number of $10,000$, a Richardson number of $2.23$, and water as the working fluid (Prandtl number = $6$). These conditions lead to strong thermal stratification, with buoyancy-induced secondary flows, and the generation of a large and persistent recirculation region. The evolution of Dean vortices as the thermal transient passes is studied. It is found that baroclinic vorticity generation dominates over a large period of the transient, due to the thermal inertia of the wall. Gravitational buoyancy leads to a reversal of the counter-rotating vortex pair. The impact of this reversal on the swirl-switching and secondary-current losses is assessed. It is found that low frequency modes are suppressed in the reversed-vortex state.

physics.flu-dyn↗