Accurate wellbore trajectory prediction is a paramount challenge in subsurface engineering, governed by complex interactions between the drilling assembly and heterogeneous geological formations. This research establishes a comprehensive, mathematically rigorous framework for trajectory prediction that moves beyond empirical modeling to a geomechanically-informed, data-driven surrogate approach.The study leverages Log ASCII Standard …
We consider the task of learning a structured stabilizer decomposition of an arbitrary $n$-qubit quantum state $|\psi\rangle$: for $\epsilon > 0$, output a state $|\phi\rangle$ with stabilizer-rank $\textsf{poly}(1/\epsilon)$ such that $|\psi\rangle=|\phi\rangle+|\phi'\rangle$ where $|\phi'\rangle$ has stabilizer fidelity $< \epsilon$. We first show the existence of such decompositions using the recently established …
In this study, the global convergence properties of the Oja flow, a continuous-time algorithm for principal component extraction, was established for general square matrices. The Oja flow is a matrix differential equation on the Stiefel manifold designed to extract a dominant subspace. Although its analysis has traditionally been restricted to …
Based on a rigorous thermodynamic framework, this work develops a two-fluid magnetohydrodynamic model grounded in the Helmholtz free energy formalism. The model maintains full thermodynamic consistency by simultaneously satisfying energy conservation and entropy production laws in two-fluid systems. By analyzing the convex-concave structure of the Helmholtz free energy density, we …
Digital memcomputing machines (DMMs) have been designed to solve complex combinatorial optimization problems. Since DMMs are fundamentally classical dynamical systems, their ordinary differential equations (ODEs) can be efficiently simulated on modern computers. This provides a unique platform to study their performance under various conditions. An aspect that has received little …
We present a theoretical framework for deriving the general $n$-th order Fr\'echet derivatives of singular values in real rectangular matrices, by leveraging reduced resolvent operators from Kato's analytic perturbation theory for self-adjoint operators. Deriving closed-form expressions for higher-order derivatives of singular values is notoriously challenging through standard matrix-analysis techniques. To …
Recent advances in deep neural networks (DNNs) have significantly improved various audio processing applications, including speech enhancement, synthesis, and hearing-aid algorithms. DNN-based closed-loop systems have gained popularity in these applications due to their robust performance and ability to adapt to diverse conditions. Despite their effectiveness, current DNN-based closed-loop systems often …
Bitumen extraction for the production of synthetic crude oil in Canada's Athabasca Oil Sands industry has recently come under spotlight for being a significant source of greenhouse gas emission. A major cause of concern is methane, a greenhouse gas produced by the anaerobic biodegradation of hydrocarbons in oil sands residues, …
Quantum computing is an emerging field recognized for the significant speedup it offers over classical computing through quantum algorithms. However, designing and implementing quantum algorithms pose challenges due to the complex nature of quantum mechanics and the necessity for precise control over quantum states. Despite the significant advancements in AI, …
Gaussian process (GP) regression provides a flexible, nonparametric framework for probabilistic modeling, yet remains computationally demanding in large-scale applications. For one-dimensional data, state space (SS) models achieve linear-time inference by reformulating GPs as stochastic differential equations (SDEs). However, SS approaches are confined to gridded inputs and cannot handle multi-dimensional scattered …