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The Optimal Power Flow (OPF) problem is a fundamental building block for the optimization of electrical power systems. It is nonlinear and nonconvex and computes the generator setpoints for power and voltage, given a set of load demands. It…

The DC Optimal Power Flow (DC-OPF) problem is fundamental to power system operations, requiring rapid solutions for real-time grid management. While traditional optimization solvers provide optimal solutions, their computational cost…

We introduce new second-order adaptive low-dissipation central-upwind (LDCU) schemes for the one- and two-dimensional hyperbolic systems of conservation laws. The new adaptive LDCU schemes employ the LDCU numerical fluxes (recently proposed…

We develop several efficient numerical schemes which preserve exactly the global constraints for constrained gradient flows. Our schemes are based on the SAV approach combined with the Lagrangian multiplier approach. They are as efficient…

Generative modeling techniques such as Diffusion and Flow Matching have achieved significant successes in generating designable and diverse protein backbones. However, many current models are computationally expensive, requiring hundreds or…

Generative models based on flow matching have attracted significant attention for their simplicity and superior performance in high-resolution image synthesis. By leveraging the instantaneous change-of-variables formula, one can directly…

Flow Matching models achieve state-of-the-art image generation quality but incur substantial inference cost due to iterative denoising through large Transformer networks. We observe that different layer groups within a Transformer exhibit…

Class imbalance poses new challenges when it comes to classifying data streams. Many algorithms recently proposed in the literature tackle this problem using a variety of data-level, algorithm-level, and ensemble approaches. However, there…

A machine-learning strategy for investigating the stability of fluid flow problems is proposed herein. The goal is to provide a simple yet robust methodology to find a nonlinear mapping from the parametric space to an indicator representing…

In this paper, the acceleration of algorithms using a design of a field programmable gate array (FPGA) as a prototype of a static dataflow architecture is discussed. The static dataflow architecture using operators interconnected by…

We propose a novel scheme to numerically solve scalar conservation laws on networks without the necessity to solve Riemann problems at the junction. The scheme is derived using the relaxation system introduced in [Jin and Xin, Comm. Pure…

Resolvent analysis is a powerful tool for modeling and analyzing turbulent flows and in particular provides an approximation of coherent flow structures. Despite recent algorithmic advances, computing resolvent modes for flows with more…

Lax-Wendroff flux reconstruction (LWFR) schemes have high order of accuracy in both space and time despite having a single internal time step. Here, we design a Jacobian-free LWFR type scheme to solve the special relativistic hydrodynamics…

Computational fluid dynamics (CFD) requires a vast amount of compute cycles on contemporary large-scale parallel computers. Hence, performance optimization is a pivotal activity in this field of computational science. Not only does it…

In this paper we present advanced representation learning study on integrating deep learning techniques and sparse approximation, including diffusion models, for advanced flow field analysis and reconstruction. Key applications include…

Flow-based traffic measurement is a very challenging problem: Managing counters for each individual traffic flow in hardware resources knowingly struggle to scale with high-speed links. In this paper we propose a novel lattice theory-based…

We consider a class of optimal power flow (OPF) applications where some loads offer a modulation service in exchange for an activation fee. These applications can be modeled as multi-period formulations of the OPF with discrete variables…

Phase-transition models are an important family of non-equilibrium continuum traffic flow models, offering properties like replicating complex traffic phenomena, maintaining anisotropy, and promising potentials for accommodating automated…

Traditional simulations on High-Performance Computing (HPC) systems typically involve modeling very large domains and/or very complex equations. HPC systems allow running large models, but limits in performance increase that have become…

The Maximum Flow (Max-Flow) problem is a cornerstone in graph theory and combinatorial optimization, aiming to determine the largest possible flow from a designated source node to a sink node within a capacitated flow network. It has…