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Neural network frameworks such as PyTorch and TensorFlow are the workhorses of numerous machine learning applications ranging from object recognition to machine translation. While these frameworks are versatile and straightforward to use,…
$T, p$ flash calculations determine the correct number of phases at phase equilibrium and their compositions for fixed temperature and pressure. They are essential for chemical process simulation and optimization. The convex envelope method…
This work develops a polygonal finite element method (PFEM) for the analysis of steady-state and transient thermal stresses in two dimensional continua. The method employs Wachspress rational basis functions to construct conforming…
Thermal power flow (TPF) is an important task for various control purposes in 4 Th generation district heating grids with multiple decentral heat sources and meshed grid structures. Computing the TPF, i.e., determining the grid state…
The Poisson-Nernst-Planck (PNP) equations are one of the most effective model for describing electrostatic interactions and diffusion processes in ion solution systems, and have been widely used in the numerical simulations of biological…
In this paper, we present a numerical scheme for the diffuse-interface model in [Abels, Garcke, Gr\"un, M3AS 22(3), 2012] for two-phase flow of immiscible, incompressible fluids. As that model is in particular consistent with…
This paper presents a Graphics Processing Units (GPUs) acceleration method of an iterative scheme for gas-kinetic model equations. Unlike the previous GPU parallelization of explicit kinetic schemes, this work features a fast converging…
Currently existing energy-stable parametric finite element methods for surface diffusion flow and other flows are usually limited to first-order accuracy in time. Designing a high-order algorithm for geometric flows that can also be…
The modeling of atmospheric processes in the context of weather and climate simulations is an important and computationally expensive challenge. The temporal integration of the underlying PDEs requires a very large number of time steps,…
Important computational physics problems are often large-scale in nature, and it is highly desirable to have robust and high performing computational frameworks that can quickly address these problems. However, it is no trivial task to…
In this work, we consider two-stage quadratic optimization problems under ellipsoidal uncertainty. In the first stage, one needs to decide upon the values of a subset of optimization variables (control variables). In the second stage, the…
Rapid and accurate wildfire detection is crucial for emergency response and environmental management. In airborne and spaceborne missions, real-time algorithms must distinguish between no fire, active fire, and post-fire conditions, and…
We consider the problem of modeling high-speed flows using machine learning methods. While most prior studies focus on low-speed fluid flows in which uniform time-stepping is practical, flows approaching and exceeding the speed of sound…
We perform an exploratory study of a new approach for evaluating Feynman integrals numerically. We apply the recently-proposed framework of physics-informed deep learning to train neural networks to approximate the solution to the…
Artificial Intelligence (AI) applications, such as Large Language Models, are primarily driven and executed by Graphics Processing Units (GPUs). These GPU programs (kernels) consume substantial amounts of energy, yet software developers…
Linear algebra operations, which are ubiquitous in machine learning, form major performance bottlenecks. The High-Performance Computing community invests significant effort in the development of architecture-specific optimized kernels, such…
With the continuous improvement of on-chip integrated voltage regulators (IVRs) and fast, adaptive frequency control, dynamic voltage-frequency scaling (DVFS) transition times have shrunk from the microsecond to the nanosecond regime,…
The escalating adoption of diffusion models for applications such as image generation demands efficient parallel inference techniques to manage their substantial computational cost. However, existing diffusion parallelism inference schemes…
X-ray ptychography imaging at synchrotron facilities like the Advanced Photon Source (APS) involves controlling instrument hardwares to collect a set of diffraction patterns from overlapping coherent illumination spots on extended samples,…
A growing number of Machine Learning Frameworks recently made Deep Learning accessible to a wider audience of engineers, scientists, and practitioners, by allowing straightforward use of complex neural network architectures and algorithms.…