Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms

We present a mathematical framework for constructing and analyzing parallel algorithms for lattice Kinetic Monte Carlo (KMC) simulations. The resulting algorithms have the capacity to simulate a wide range of spatio-temporal scales in spatially distributed, non-equilibrium physiochemical processes with complex chemistry and transport micro-mechanisms. The algorithms can be tailored to specific hierarchical parallel architectures such as multi-core processors or clusters of Graphical Processing Units (GPUs). The proposed parallel algorithms are controlled-error approximations of kinetic Monte Carlo algorithms, departing from the predominant paradigm of creating parallel KMC algorithms with exactly the same master equation as the serial one. Our methodology relies on a spatial decomposition of the Markov operator underlying the KMC algorithm into a hierarchy of operators corresponding to the processors' structure in the parallel architecture. Based on this operator decomposition, we formulate Fractional Step Approximation schemes by employing the Trotter Theorem and its random variants; these schemes, (a) determine the communication schedule} between processors, and (b) are run independently on each processor through a serial KMC simulation, called a kernel, on each fractional step time-window. Furthermore, the proposed mathematical framework allows us to rigorously justify the numerical and statistical consistency of the proposed algorithms, showing the convergence of our approximating schemes to the original serial KMC. The approach also provides a systematic evaluation of different processor communicating schedules.Comment: 34 pages, 9 figure

Learning cloth manipulation with demonstrations

Recent advances in Deep Reinforcement learning and computational capabilities of GPUs have led to variety of research being conducted in the learning side of robotics. The main aim being that of making autonomous robots that are capable of learning how to solve a task on their own with minimal requirement for engineering on the planning, vision, or control side. Efforts have been made to learn the manipulation of rigid objects through the help of human demonstrations, specifically in the tasks such as stacking of multiple blocks on top of each other, inserting a pin into a hole, etc. These Deep RL algorithms successfully learn how to complete a task involving the manipulation of rigid objects, but autonomous manipulation of textile objects such as clothes through Deep RL algorithms is still not being studied in the community. The main objectives of this work involve, 1) implementing the state of the art Deep RL algorithms for rigid object manipulation and getting a deep understanding of the working of these various algorithms, 2) Creating an open-source simulation environment for simulating textile objects such as clothes, 3) Designing Deep RL algorithms for learning autonomous manipulation of textile objects through demonstrations.Peer ReviewedPreprin

Quantum Hidden Subgroup Algorithms: The Devil Is in the Details

We conjecture that one of the main obstacles to creating new non-abelian quantum hidden subgroup algorithms is the correct choice of a transversal.Comment: 5 pages, to appear in April 2004 Proceedings of SPIE on Quantum Information and Computatio

Creating explanatory visualizations of algorithms for active learning

Visualizations have been used to explain algorithms to learners, in order to help them understand complex processes. These ‘explanatory visualizations’ can help learners understand computer algorithms and data-structures. But most are created by an educator and merely watched by the learner. In this paper, we explain how we get learners to plan and develop their own explanatory visualizations of algorithms. By actively developing their own visualizations learners gain a deeper insight of the algorithms that they are explaining. These depictions can also help other learners understand the algorithm