Małgorzata J. Zimoń

Mykhaylo Zayats, Małgorzata J. Zimoń, Kyongmin Yeo et al.

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.

Mohammed Sardar, Małgorzata J. Zimoń, Samuel Draycott et al.

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.

Paz Fink Shustin, Shashanka Ubaru, Małgorzata J. Zimoń et al.

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.