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Time discretization along with space discretization is important in the numerical simulation of subsurface flow applications for long run. In this paper, we derive theoretical convergence error estimates in discrete-time setting for…

Fully Homomorphic Encryption (FHE) allows for computation directly on encrypted data and enables privacy-preserving neural inference in the cloud. Prior work has focused on models with dense inputs (e.g., CNNs), with less attention given to…

Damping of structures and systems is often dominated by frictional dissipation in connections, the prediction of which remains a longstanding scientific challenge. Previous studies have shown that the actual topography of contact interfaces…

The manuscript addresses the problem of finding all solutions of power flow equations or other similar nonlinear system of algebraic equations. This problem arises naturally in a number of power systems contexts, most importantly in the…

Statistical models for networks with complex dependencies pose particular challenges for model selection and evaluation. In particular, many well-established statistical tools for selecting between models assume conditional independence of…

Polynomial chaos expansion (PCE) is a powerful surrogate model-based reliability analysis method. Generally, a PCE model with a higher expansion order is usually required to obtain an accurate surrogate model for some complex non-linear…

This paper presents a novel distributed approach for solving AC power flow (PF) problems. The optimization problem is reformulated into a distributed form using a communication structure corresponding to a hypergraph, by which complex…

An accurate and up-to-date topology is critical for situational awareness of a power grid; however, wrong switch statuses due to physical damage, communication error, or cyber-attack, can often result in topology errors. To maintain…

In this paper, we propose and study the asymptotic convergence and nonasymptotic global convergence rates (iteration-complexity) of an inertial under-relaxed version of the relative-error hybrid proximal extragradient (HPE) method for…

Over the past decade, Finite Element Method (FEM) has served as a foundational numerical framework for approximating the terms of Time Series Expansion (TSE) as solutions to transient Partial Differential Equation (PDE). However, the…

We propose a phase-difference estimation algorithm based on the tensor-network circuit compression, leveraging time-evolution data to pursue scalability and higher accuracy on a quantum phase estimation (QPE)-type algorithm. Using tensor…

Machine learning on encrypted data can address the concerns related to privacy and legality of sharing sensitive data with untrustworthy service providers. Fully Homomorphic Encryption (FHE) is a promising technique to enable machine…

Persistent entropy (PE) is an information-theoretic summary statistic of persistence barcodes that has been widely used to detect regime changes in complex systems. Despite its empirical success, a general theoretical understanding of when…

We propose a novel Skew Gradient Embedding (SGE) framework for systematically reformulating thermodynamically consistent partial differential equation (PDE) models-capturing both reversible and irreversible processes-as generalized gradient…

The pressure Poisson equation, central to the fractional step method in incompressible flow simulations, incurs high computational costs due to the iterative solution of large-scale linear systems. To address this challenge, we introduce…

As machine learning (ML) models become increasingly deployed through cloud infrastructures, the confidentiality of user data during inference poses a significant security challenge. Homomorphic Encryption (HE) has emerged as a compelling…

For time-critical IoT applications using deep learning, inference acceleration through distributed computing is a promising approach to meet a stringent deadline. In this paper, we implement a working prototype of a new distributed…

Current inference systems for Mixture-of-Experts (MoE) models primarily employ static parallelization strategies. However, these static approaches cannot consistently achieve optimal performance across different inference scenarios, as they…

In this paper, we provide a detailed convergence analysis for a first order stabilized linear semi-implicit numerical scheme for the nonlocal Cahn-Hilliard equation, which follows from consistency and stability estimates for the numerical…

A rapid fracture test in four-point bending is proposed to assess hydrogen embrittlement (HE) susceptibility of high strength martensitic steels. The novelty of this technique is the rapid rate of loading, whereas conventional approaches…