Accelerating COBAYA3 on multi-core CPU and GPU systems using PARALUTION

COBAYA3 is a multi-physics system of codes which includes two 3D multi-group neutron diffusion codes, ANDES and COBAYA3-PBP, coupled with COBRA-TF, COBRA-IIIc and SUBCHANFLOW sub-channel thermal-hydraulic codes, for the simulation of LWR core transients. The 3D multi-group neutron diffusion equations are expressed in terms of a sparse linear system which can be solved using different iterative Krylov subspace solvers. The mathematical SPARSKIT library has been used for these purposes as it implements among others, external GMRES, PGMRES and BiCGStab solvers. Multi-core CPUs and graphical processing units (GPUs) provide high performance capabilities which are able to accelerate many scientific computations. To take advantage of these new hardware features in daily use computer codes, the integration of the PARALUTION library to solve sparse systems of linear equations is a good choice. It features several types of iterative solvers and preconditioners which can run on both multi-core CPUs and GPU devices without any modification from the interface point of view. This feature is due to the great portability obtained by the modular and flexible design of the library. By exploring this technology, namely the implementation of the PARALUTION library in COBAYA3, we are able to decrease the solution time of the sparse linear systems by a factor 5.15x on GPU and 2.56x on multi-core CPU using standard hardware. These obtained speedup factors in addition to the implementation details are discussed in this paper

Time Window Determination for Inference of Time-Varying Dynamics:Application to Cardiorespiratory Interaction

Interacting dynamical systems abound in nature, with examples ranging from biology and population dynamics, through physics and chemistry, to communications and climate. Often their states, parameters and functions are time-varying, because such systems interact with other systems and the environment, exchanging information and matter. A common problem when analysing time-series data from dynamical systems is how to determine the length of the time window for the analysis. When one needs to follow the time-variability of the dynamics, or the dynamical parameters and functions, the time window needs to be resolved first. We tackled this problem by introducing a method for adaptive determination of the time window for interacting oscillators, as modeled and scaled for the cardiorespiratory interaction. By investigating a system of coupled phase oscillators and utilizing the Dynamical Bayesian Inference method, we propose a procedure to determine the time window and the propagation parameter of the covariance matrix. The optimal values are determined so that the inferred parameters follow the dynamics of the actual ones and at the same time the error of the inference represented by the covariance matrix is minimal. The effectiveness of the methodology is presented on a system of coupled limit-cycle oscillators and on the cardiorespiratory interaction. Three cases of cardiorespiratory interaction were considered—measurement with spontaneous free breathing, one with periodic sine breathing and one with a-periodic time-varying breathing. The results showed that the cardiorespiratory coupling strength and similarity of form of coupling functions have greater values for slower breathing, and this variability follows continuously the change of the breathing frequency. The method can be applied effectively to other time-varying oscillatory interactions and carries important implications for analysis of general dynamical systems