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In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a…

There has been significant recent interest in parallel graph processing due to the need to quickly analyze the large graphs available today. Many graph codes have been designed for distributed memory or external memory. However, today even…

As supercomputers become larger with powerful Graphics Processing Unit (GPU), traditional direct eigensolvers struggle to keep up with the hardware evolution and scale efficiently due to communication and synchronization demands.…

Message-passing graph neural network interatomic potentials (GNN-IPs), particularly those with equivariant representations such as NequIP, are attracting significant attention due to their data efficiency and high accuracy. However,…

Monte Carlo simulation is widely used to numerically solve stochastic differential equations. Although the method is flexible and easy to implement, it may be slow to converge. Moreover, an inaccurate solution will result when using large…

Visual SLAM systems combine visual tracking with global loop closure to maintain a consistent map and accurate localization. Loop closure is a computationally expensive process as we need to search across the whole map for matches. This…

The growth of connected intelligent devices in the Internet of Things has created a pressing need for real-time processing and understanding of large volumes of analogue data. The difficulty in boosting the computing speed renders digital…

Supercomputers are equipped with an increasingly large number of cores to use computational power as a way of solving problems that are otherwise intractable. Unfortunately, getting serial algorithms to run in parallel to take advantage of…

In this paper we present an optimized parallel implementation of a flexible MAP decoder for synchronization error correcting codes, supporting a very wide range of code sizes and channel conditions. On mid-range GPUs we demonstrate decoding…

Real-world node embedding applications often contain hundreds of billions of edges with high-dimension node features. Scaling node embedding systems to efficiently support these applications remains a challenging problem. In this paper we…

Furthering our understanding of many of today's interesting problems in plasma physics---including plasma based acceleration and magnetic reconnection with pair production due to quantum electrodynamic effects---requires large-scale kinetic…

We present a new adaptive parallel algorithm for the challenging problem of multi-dimensional numerical integration on massively parallel architectures. Adaptive algorithms have demonstrated the best performance, but efficient many-core…

A parallel computer system is a collection of processing elements that communicate and cooperate to solve large computational problems efficiently. To achieve this, at first the large computational problem is partitioned into several tasks…

Simulations of systems with quenched disorder are extremely demanding, suffering from the combined effect of slow relaxation and the need of performing the disorder average. As a consequence, new algorithms, improved implementations, and…

Neural networks achieve strong empirical performance, but robustness concerns still hinder deployment in safety-critical applications. Formal verification provides robustness guarantees, but current methods face a scalability-completeness…

The acceleration of sparse matrix computations on modern many-core processors, such as the graphics processing units (GPUs), has been recognized and studied over a decade. Significant performance enhancements have been achieved for many…

In this work we apply model averaging to parallel training of deep neural network (DNN). Parallelization is done in a model averaging manner. Data is partitioned and distributed to different nodes for local model updates, and model…

Solving exactly Combinatorial Optimization Problems (COPs) using a Branch-and-Bound (B&B) algorithm requires a huge amount of computational resources. Therefore, we recently investigated designing B&B algorithms on top of graphics…

The vision of super computer at every desk can be realized by powerful and highly parallel CPUs or GPUs or APUs. Graphics processors once specialized for the graphics applications only, are now used for the highly computational intensive…

This paper first presents a parallel solution for the Flowshop Scheduling Problem in parallel environment, and then proposes a novel load balancing strategy. The proposed Proportional Fairness Strategy (PFS) takes computational performance…