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Solving multiscale diffusion problems is often computationally expensive due to the spatial and temporal discretization challenges arising from high-contrast coefficients. To address this issue, a partially explicit temporal splitting…
Numerical solution of discrete PDEs corresponding to saddle point problems is highly relevant to physical systems such as Stokes flow. However, scaling up numerical solvers for such systems is often met with challenges in efficiency and…
Integrating renewable resources within the transmission grid at a wide scale poses significant challenges for economic dispatch as it requires analysis with more optimization parameters, constraints, and sources of uncertainty. This…
Markov Chain Monte Carlo (MCMC) algorithms are standard approaches to solve imaging inverse problems and quantify estimation uncertainties, a key requirement in absence of ground-truth data. To improve estimation quality, Plug-and-Play MCMC…
The multi-frontal direct solver is the state-of-the-art algorithm for the direct solution of sparse linear systems. This paper provides computational complexity and memory usage estimates for the application of the multi-frontal direct…
Performing Bayesian inference on large spatio-temporal models requires extracting inverse elements of large sparse precision matrices for marginal variances, as well as estimating model hyperparameters. Although direct matrix factorizations…
Sparse General Matrix Multiply (SpGEMM) is key for various High-Performance Computing (HPC) applications such as genomics and graph analytics. Using the semiring abstraction, many algorithms can be formulated as SpGEMM, allowing…
Exponential growth in global computing demand is exacerbated due to the higher-energy requirements of conventional architectures, primarily due to energy-intensive data movement. In-memory computing with Resistive Random Access Memory…
As the need for computational power and efficiency rises, parallel systems become increasingly popular among various scientific fields. While multiple core-based architectures have been the center of attention for many years, the rapid…
The multi-resolution approximation (MRA) of Gaussian processes was recently proposed to conduct likelihood-based inference for massive spatial data sets. An advantage of the methodology is that it can be parallelized. We implemented the MRA…
Machine learning approaches have recently been leveraged as a substitute or an aid for physical/mathematical modeling approaches to dynamical systems. To develop an efficient machine learning method dedicated to modeling and prediction of…
We present GSPMD, an automatic, compiler-based parallelization system for common machine learning computations. It allows users to write programs in the same way as for a single device, then give hints through a few annotations on how to…
Quantum circuit simulations play a critical role in bridging the gap between theoretical quantum algorithms and their practical realization on physical quantum hardware, yet they face computational challenges due to the exponential growth…
Large, sparse linear systems are pervasive in modern science and engineering, and Krylov subspace solvers are an established means of solving them. Yet convergence can be slow for ill-conditioned matrices, so practical deployments usually…
Diverse scientific and engineering research areas deal with discrete, time-stamped changes in large systems of interacting delay differential equations. Simulating such complex systems at scale on high-performance computing clusters demands…
Scalable Gaussian process (GP) inference is essential for sequential decision-making tasks, yet improving GP scalability remains a challenging problem with many open avenues of research. This paper focuses on iterative GPs, where iterative…
We consider the swelling of hydrogels as an example of a chemo-mechanical problem with strong coupling between the mechanical balance relations and the mass diffusion. The problem is cast into a minimization formulation using a…
Iterative algorithms are instrumental in modern numerical simulation for solving systems arising from the discretization of PDEs. They face however significant challenges in industrial applications, such as slow convergence, limit cycle…
To address the challenge of performance portability, and facilitate the implementation of electronic structure solvers, we developed the Basic Matrix Library (BML) and Parallel, Rapid O(N) and Graph-based Recursive Electronic Structure…
Recent years have seen a huge development in spatial modelling and prediction methodology, driven by the increased availability of remote-sensing data and the reduced cost of distributed-processing technology. It is well known that…