arXiv subjects

Diana A. Bistrian

Publications and source records attributed to Diana A. Bistrian.

6 recordsLinked to original sources

arXiv2026

High-Fidelity Digital Twin Data Models by Randomized Dynamic Mode Decomposition and Deep Learning with Applications in Fluid Dynamics

The purpose of this paper is the identification of high-fidelity digital twin data models from numerical code outputs by non-intrusive techniques (i.e., not requiring Galerkin projection of the governing equations onto the reduced modes basis). In this paper the author defines the concept of the digital twin data model (DTM) as a model of reduced complexity that has the main feature of mirroring the original process behavior. The significant advantage of a DTM is to reproduce the dynamics with high accuracy and reduced costs in CPU time and hardware for settings difficult to explore because of the complexity of the dynamics over time. This paper introduces a new framework for creating efficient digital twin data models by combining two state-of-the-art tools: randomized dynamic mode decomposition and deep learning artificial intelligence. It is shown that the outputs are consistent with the original source data with the advantage of reduced complexity. The DTMs are investigated in the numerical simulation of three shock wave phenomena with increasing complexity. The author performs a thorough assessment of the performance of the new digital twin data models in terms of numerical accuracy and computational efficiency.

cs.LG↗

arXiv2026

Hankel-Koopman Finite-Horizon Energy Decomposition of Coupled Experimental Data: A Three-Phase Data-Driven Twin Forecasting Framework

This paper introduces a unified three-phase data-driven twin framework for finite-horizon forecasting of physical quantities from coupled experimental measurements. The framework combines a new Hankel--Koopman finite-horizon energy decomposition with orthogonal modes and an inverse-calibrated multi-output nonlinear autoregressive model with exogenous inputs. The nonlinear dynamics are identified and simulated in the Hankel coefficient space over a prescribed calibration window. Candidate models are then evaluated after anti-diagonal recovery and reconstruction of the corresponding trajectories in the physical measurement space. The resulting simulated channel trajectories serve as exogenous inputs to a recursive forecasting model for the quantity of interest. In this way, the proposed framework integrates reduced-order representation, nonlinear dynamical identification, measurement reconstruction, and explainable forecasting. The mathematical analysis specializes Koopman delay-coordinate theory to the serialized multichannel Hankel lift and establishes its compatibility with the shifted Hankel representation. It also proves the orthogonality of the modes and the finite-horizon modal energy decomposition, together with the existence, uniqueness, inverse stability, and forward stability of the identified models under explicitly stated hypotheses. In a solar-power-plant case study, the framework yields consistently high correlations and low relative errors across all considered forecast horizons, demonstrating its ability to preserve the temporal evolution of the quantity of interest during recursive forecasting.

math.NA↗

arXiv2024

Mathematical Considerations on Randomized Orthgonal Decomposition Method for Developing Twin Data Models

This paper introduces the approach of Randomized Orthogonal Decomposition (ROD) for producing twin data models in order to overcome the drawbacks of existing reduced order modelling techniques. When compared to Fourier empirical decomposition, ROD provides orthonormal shape modes that maximize their projection on the data space, which is a significant benefit. A shock wave event described by the viscous Burgers equation model is used to illustrate and evaluate the novel method. The new twin data model is thoroughly evaluated using certain criteria of numerical accuracy and computational performance.

math.NA↗

arXiv2024

Reduced-order modelling based on Koopman operator theory

The present study focuses on a subject of significant interest in fluid dynamics: the identification of a model with decreased computational complexity from numerical code output using Koopman operator theory. A reduced-order modelling method that incorporates a novel strategy for identifying the most impactful Koopman modes was used to numerically approximate the Koopman composition operator.

math.NA↗

arXiv2022

Sketching Methods for Dynamic Mode Decomposition in Spherical Shallow Water Equations

Dynamic mode decomposition (DMD) is an emerging methodology that has recently attracted computational scientists working on nonintrusive reduced order modeling. One of the major strengths that DMD possesses is having ground theoretical roots from the Koopman approximation theory. Indeed, DMD may be viewed as the data-driven realization of the famous Koopman operator. Nonetheless, the stable implementation of DMD incurs computing the singular value decomposition of the input data matrix. This, in turn, makes the process computationally demanding for high dimensional systems. In order to alleviate this burden, we develop a framework based on sketching methods, wherein a sketch of a matrix is simply another matrix which is significantly smaller, but still sufficiently approximates the original system. Such sketching or embedding is performed by applying random transformations, with certain properties, on the input matrix to yield a compressed version of the initial system. Hence, many of the expensive computations can be carried out on the smaller matrix, thereby accelerating the solution of the original problem. We conduct numerical experiments conducted using the spherical shallow water equations as a prototypical model in the context of geophysical flows. The performance of several sketching approaches is evaluated for capturing the range and co-range of the data matrix. The proposed sketching-based framework can accelerate various portions of the DMD algorithm, compared to classical methods that operate directly on the raw input data. This eventually leads to substantial computational gains that are vital for digital twinning of high dimensional systems.

math.NA↗

arXiv2019

Sampling and resolution characteristics in reduced order models of shallow water equations: intrusive vs non-intrusive

We investigate the sensitivity of reduced order models (ROMs) to training data resolution as well as sampling rate. In particular, we consider proper orthogonal decomposition (POD), coupled with Galerkin projection (POD-GP), as an intrusive reduced order modeling technique. For non-intrusive ROMs, we consider two frameworks. The first is using dynamic mode decomposition (DMD), and the second is based on artificial neural networks (ANNs). For ANN, we utilized a residual deep neural network, and for DMD we have studied two versions of DMD approaches; one with hard thresholding and the other with sorted bases selection. Also, we highlight the differences between mean-subtracting the data (i.e., centering) and using the data without mean-subtraction. We tested these ROMs using a system of 2D shallow water equations for four different numerical experiments, adopting combinations of sampling rates and resolutions. For these cases, we found that the DMD basis obtained with hard threshodling is sensitive to sampling rate, performing worse at very high rates. The sorted DMD algorithm helps to mitigate this problem and yields more stabilized and converging solution. Furthermore, we demonstrate that both DMD approaches with mean subtraction provide significantly more accurate results than DMD with mean-subtracting the data. On the other hand, POD is relatively insensitive to sampling rate and yields better representation of the flow field. Meanwhile, resolution has little effect on both POD and DMD performances. Therefore, we preferred to train the neural network in POD space, since it is more stable and better represents our dataset. Numerical results reveal that an artificial neural network on POD subspace (POD-ANN) performs remarkably better than POD-GP and DMD in capturing system dynamics, even with a small number of modes.

physics.flu-dyn↗