Accelerating multi‐dimensional interpolation using moving least‐squares on the GPU

Abstract

This paper focuses on designing and implementing parallel Moving Least Squares (MLS) interpolation algorithms by exploiting the Graphics Processing Unit (GPU) for the usage in Meshfree methods. The MLS method is an approach for scattered points' approximation / interpolation, which is commonly employed as the shape functions in various Meshfree methods. To improve the computational efficiency in building stiffness matrices in Meshfree methods, we are specifically interested in parallelizing the MLS interpolation on the GPU. The accelerated Meshfree methods can be employed to numerically analyze large deformations of soil and rock masses such as the landslides. In this paper, we first introduce our previously proposed method for finding the k nearest neighboring points located within the local region of the interest point in MLS. We then develop one sequential and three parallel implementations for each of three variations of the MLS interpolation, including the serial implementation, the parallel implementation on the multi-core CPU, the parallel implementation on a single GPU, and the parallel implementation on multi-GPUs.To evaluate the computational performance of our GPU implementations, five groups of benchmark tests are conducted in both two-dimensions and three-dimensions. We observe that our GPU implementations can achieve satisfied speedups over the sequential CPU implementation for varied sizes of testing data. To benefit the community, all source code and testing data related to the presented parallel MLS interpolation are publicly available.

Comparative investigation of parallel spatial interpolation algorithms for building large-scale digital elevation models

“…We have implemented the spatial interpolation algorithms of RBF (Ding et al, 2018b), MLS (Ding et al, 2018a), IDW (Mei, 2014), and AIDW (Mei, Xu & Xu, 2017) in our previous work. To evaluate the computational performance of the GPU-accelerated interpolation, we implement and compare (1) the sequential implementation, (2) the parallel implementation developed on a multicore CPU, (3) the parallel implementation using a single GPU, and (4) the parallel implementation using multiple GPUs.…”

Incomplete Road Information Imputation Using Parallel Interpolation to Enhance the Safety of Autonomous Driving

“…Other commonly used interpolation algorithms for estimating missing data include the MLS, RBF, adaptive IDW, and Kriging algorithms. Among them, the MLS needs to construct a matrix to solve when approximating the known data points [36]. If all the known point data are used to construct the matrix, the matrix will be too large to be stored.…”

“…However, to the best of the authors' knowledge, little work specifically focuses on imputating the incomplete road information that is induced by obstacles such as vehicles. Most studies estimate the missing values in time-series data using various machine learning algorithms and mathematical algorithms such as the Radial Basis Function (RBF) interpolation, the Support Vector Machine (SVM) regression, and the k-Nearest Neighbours (kNN) estimation [36]- [39].…”

Peer Review #2 of "Comparative investigation of parallel spatial interpolation algorithms for building large-scale digital elevation models (v0.1)"

“…We have implemented the spatial interpolation algorithms of RBF (Ding et al, 2018b), MLS (Ding et al, 2018a), IDW (Mei, 2014), and AIDW (Mei et al, 2017) in our previous work. To evaluate the computational performance of the GPU-accelerated interpolation, we implement and compare (1) the sequential implementation, (2) the parallel implementation developed on a multicore CPU, (3) the parallel implementation using a single GPU, and (4) the parallel implementation using multiple GPUs.…”