High Performance Multivariate Geospatial Statistics on Manycore Systems

TL;DR

This paper presents a scalable high-performance framework for multivariate geospatial modeling and inference on manycore systems, enabling efficient analysis of large environmental datasets with improved accuracy and computational speed.

Contribution

It introduces a novel parallel computing framework using low-rank matrix approximations and task-based scheduling for large-scale multivariate geospatial analysis.

Findings

Low-rank approximation improves performance over exact methods.

Framework maintains accuracy in parameter estimation and prediction.

Scalability demonstrated on various high-performance computing systems.

Abstract

Modeling and inferring spatial relationships and predicting missing values of environmental data are some of the main tasks of geospatial statisticians. These routine tasks are accomplished using multivariate geospatial models and the cokriging technique. The latter requires the evaluation of the expensive Gaussian log-likelihood function, which has impeded the adoption of multivariate geospatial models for large multivariate spatial datasets. However, this large-scale cokriging challenge provides a fertile ground for supercomputing implementations for the geospatial statistics community as it is paramount to scale computational capability to match the growth in environmental data coming from the widespread use of different data collection technologies. In this paper, we develop and deploy large-scale multivariate spatial modeling and inference on parallel hardware architectures. To tackle the increasing complexity in matrix operations and the massive concurrency in parallel systems, we leverage low-rank matrix approximation techniques with task-based programming models and schedule the asynchronous computational tasks using a dynamic runtime system. The proposed framework provides both the dense and the approximated computations of the Gaussian log-likelihood function. It demonstrates accuracy robustness and performance scalability on a variety of computer systems. Using both synthetic and real datasets, the low-rank matrix approximation shows better performance compared to exact computation, while preserving the application requirements in both parameter estimation and prediction accuracy. We also propose a novel algorithm to assess the prediction accuracy after the online parameter estimation. The algorithm quantifies prediction performance and provides a benchmark for measuring the efficiency and accuracy of several approximation techniques in multivariate spatial modeling.