Scalable Empirical Dynamic Modeling With Parallel Computing and Approximate k-NN Search

Abstract

Empirical Dynamic Modeling (EDM) is a mathematical framework for modeling and predicting non-linear time series data. Although EDM is increasingly adopted in various research fields, its application to large-scale data has been limited due to its high computational cost. This article presents kEDM, a high-performance implementation of EDM for analyzing large-scale time series datasets. kEDM adopts the Kokkos performance-portable programming model to efficiently run on both CPU and GPU while sharing a single code base. We also conduct hardware-specific optimization of performance-critical kernels. kEDM achieved up to $6.58\times $ speedup in pairwise causal inference of real-world biology datasets compared to an existing EDM implementation. Furthermore, we integrate multiple approximate k-NN search algorithms into EDM to enable the analysis of extremely large datasets that were intractable with conventional EDM based on exhaustive k-NN search. EDM-based time series forecast enhanced with approximate k-NN search demonstrated up to $790\times $ speedup compared to conventional Simplex projection with less than 1% increase in MAPE.

Keywords

• Empirical dynamic modeling
• high-performance computing
• time-series analysis
• performance portability
• high-performance data analytics