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We present methods for the direct characterization of quantum dynamics (DCQD) in which both the principal and ancilla systems undergo noisy processes. Using a concatenated error detection code, we discriminate between located and unlocated…
The decomposition of oceanic flow into its balanced and unbalanced motions carries theoretical and practical significance for the oceanographic community. These two motions have distinct dynamical characteristics and affect the transport of…
We develop a new generalization of Koopman operator theory that incorporates the effects of inputs and control. Koopman spectral analysis is a theoretical tool for the analysis of nonlinear dynamical systems. Moreover, Koopman is intimately…
One of the simplest and least resource-intensive methods to suppress decoherence for qubit operations, namely, dynamical decoupling (DD), is investigated for a broad range of realistic noise sources with time-retarded feedback. By way of…
Dynamic Mode Decomposition (DMD) is a popular data-driven analysis technique used to decompose complex, nonlinear systems into a set of modes, revealing underlying patterns and dynamics through spectral analysis. This review presents a…
Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a…
This work proposes a general framework for capturing noise-driven transitions in spatially extended non-equilibrium systems and explains the emergence of coherent patterns beyond the instability onset. The framework relies on stochastic…
Operational forecasting centers are investing in decadal (1-10 year) forecast systems to support long-term decision making for a more climate-resilient society. One method that has previously been employed is the Dynamic Mode Decomposition…
Linear dimensionality reduction methods are commonly used to extract low-dimensional structure from high-dimensional data. However, popular methods disregard temporal structure, rendering them prone to extracting noise rather than…
This work is focussed on the inversion task of inferring the distribution over parameters of interest leading to multiple sets of observations. The potential to solve such distributional inversion problems is driven by increasing…
In this work, Dynamic Mode Decomposition (DMD) and Proper Orthogonal Decomposition (POD) methodologies are applied to hydroacoustic dataset computed using Large Eddy Simulation (LES) coupled with Ffowcs Williams and Hawkings (FWH) analogy.…
Distributed Acoustic Sensing (DAS) is a promising technology introducing a new paradigm in the acquisition of high-resolution seismic data. However, DAS data often show weak signals compared to the background noise, especially in tough…
Data-driven methods for establishing quantum optimal control (QOC) using time-dependent control pulses tailored to specific quantum dynamical systems and desired control objectives are critical for many emerging quantum technologies. We…
Diffusion models (DMs) have rapidly emerged as a powerful framework for image generation and restoration. However, existing DMs are primarily trained in a supervised manner by using a large corpus of clean images. This reliance on clean…
This work proposes convolutional-sparse-coded dynamic mode decomposition (CSC-DMD) by unifying extended dynamic mode decomposition (EDMD) and convolutional sparse coding. EDMD is a data driven analysis method for describing a nonlinear…
In this paper a signal denoising scheme based on Empirical mode decomposition (EMD) is presented. The denoising method is a fully data driven approach. Noisy signal is decomposed adaptively into intrinsic oscillatory components called…
Understanding the spectrum of noise acting on a qubit can yield valuable information about its environment, and crucially underpins the optimization of dynamical decoupling protocols that can mitigate such noise. However, extracting…
In a variational denoising model, weight in the data fidelity term plays the role of enhancing the noise-removal capability. It is profoundly correlated with noise information, while also balancing the data fidelity and regularization…
Reconstruction-based anomaly detection models achieve their purpose by suppressing the generalization ability for anomaly. However, diverse normal patterns are consequently not well reconstructed as well. Although some efforts have been…
A novel approach to reduced-order modeling of high-dimensional time varying systems is proposed. It leverages the formalism of the Dynamic Mode Decomposition technique together with the concept of balanced realization. It is assumed that…