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The problem of solving a system of polynomial equations is one of the most fundamental problems in applied mathematics. Among them, the problem of solving a system of binomial equations form a important subclass for which specialized…
The growth of large language models (LLMs) increases challenges of accelerating distributed training across multiple GPUs in different data centers. Moreover, concerns about data privacy and data exhaustion have heightened interest in…
Solving parametric partial differential equations (PDEs) presents significant challenges for data-driven methods due to the sensitivity of spatio-temporal dynamics to variations in PDE parameters. Machine learning approaches often struggle…
In recent years graphical processing units (GPUs) have become a powerful tool in scientific computing. Their potential to speed up highly parallel applications brings the power of high performance computing to a wider range of users.…
We report numerical results on solving constrained linear-quadratic model predictive control (MPC) problems by exploiting graphics processing units (GPUs). The presented method reduces the MPC problem by eliminating the state variables and…
The edge computing paradigm has emerged to handle cloud computing issues such as scalability, security and low response time among others. This new computing trend heavily relies on ubiquitous embedded systems on the edge. Performance and…
Data compression and decompression have become vital components of big-data applications to manage the exponential growth in the amount of data collected and stored. Furthermore, big-data applications have increasingly adopted GPUs due to…
Solving partial differential equations is difficult. Recently proposed neural resolution-invariant models, despite their effectiveness and efficiency, usually require equispaced spatial points of data. However, sampling in spatial domain is…
Fast power system state estimation (SE) solution is of paramount importance for achieving real-time decision making in power grid operations. Semidefinite programming (SDP) reformulation has been shown effective to obtain the global optimum…
Starting from the single graphics processing unit (GPU) version of the Smoothed Particle Hydrodynamics (SPH) code DualSPHysics, a multi-GPU SPH program is developed for free-surface flows. The approach is based on a spatial decomposition…
The sparse pseudo-input Gaussian process (SPGP) is a new approximation method for speeding up GP regression in the case of a large number of data points N. The approximation is controlled by the gradient optimization of a small set of M…
Multiscale mixed methods based on non-overlapping domain decompositions can efficiently handle the solution of significant subsurface flow problems in very heterogeneous formations of interest to the industry, especially when implemented on…
Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…
Hypergraph partitioning is a recurring NP-hard problem in engineering; its efficient solution at scale hinges on parallelism. This work proposes a GPU-centric algorithm for multi-level hypergraph partitioning aimed at a specific set of…
The main goal in many fields in the empirical sciences is to discover causal relationships among a set of variables from observational data. PC algorithm is one of the promising solutions to learn underlying causal structure by performing a…
This work presents a convex-optimization-based framework for analysis and control of nonlinear partial differential equations. The approach uses a particular weak embedding of the nonlinear PDE, resulting in a linear equation in the space…
Optimization with time-dependent partial differential equations (PDEs) as constraints {appears} in many science and engineering applications. The associated first-order necessary optimality system consists of one forward and one backward…
Imposing known physical constraints, such as conservation laws, during neural network training introduces an inductive bias that can improve accuracy, reliability, convergence, and data efficiency for modeling physical dynamics. While such…
Restricted solid on solid surface growth models can be mapped onto binary lattice gases. We show that efficient simulation algorithms can be realized on GPUs either by CUDA or by OpenCL programming. We consider a deposition/evaporation…
We consider differential Lyapunov and Riccati equations, and generalized versions thereof. Such equations arise in many different areas and are especially important within the field of optimal control. In order to approximate their…