Algorithms for Numerical Analysis in High Dimensions
SIAM Journal on Scientific Computing
Multivariate Regression and Machine Learning with Sums of Separable Functions
SIAM Journal on Scientific Computing
Journal of Computational Physics
| Hi-index | 0.01 |
We present an algorithm for learning the function that maps a material structure to its value on some property, given the value of this function on several structures. We pose this problem as one of learning (regressing) a function of many variables from scattered data. Each structure is first converted to a weighted set of points by a process that removes irrelevant translations and rotations but otherwise retains full information about the structure. Then, incorporating a weighted average for each structure, we construct the multivariate regression function as a sum of separable functions, following the paradigm of separated representations. The algorithm can treat all finite and periodic structures within a common framework, and in particular does not require all structures to lie on a common lattice. We show how the algorithm simplifies when the structures do lie on a common lattice, and we present numerical results for that case.