Using Gaussian Process Regression to Simulate the Vibrational Raman Spectra of Molecular Crystals

Vibrational properties of molecular crystals are constantly used as structural fingerprints, in order to identify both the chemical nature and the structural arrangement of molecules. The simulation of these properties is typically very costly, especially when dealing with response properties of materials to e.g. electric fields, which require a good description of the perturbed electronic density. In this work, we use Gaussian process regression (GPR) to predict the static polarizability and dielectric susceptibility of molecules and molecular crystals. We combine this framework with ab initio molecular dynamics to predict their anharmonic vibrational Raman spectra. We stress the importance of data representation, symmetry, and locality, by comparing the performance of different flavors of GPR. In particular, we show the advantages of using a recently developed symmetry-adapted version of GPR. As an examplary application, we choose Paracetamol as an isolated molecule and in different crystal forms. We obtain accurate vibrational Raman spectra in all cases with fewer than 1000 training points, and obtain improvements when using a GPR trained on the molecular monomer as a baseline for the crystal GPR models. Finally, we show that our methodology is transferable across polymorphic forms: we can train the model on data for one structure, and still be able to accurately predict the spectrum for a second polymorph. This procedure provides an independent route to access electronic structure properties when performing force-evaluations on empirical force-fields or machine-learned potential energy surfaces

Numerical Fitting-based Likelihood Calculation to Speed up the Particle Filter

The likelihood calculation of a vast number of particles is the computational bottleneck for the particle filter in applications where the observation information is rich. For fast computing the likelihood of particles, a numerical fitting approach is proposed to construct the Likelihood Probability Density Function (Li-PDF) by using a comparably small number of so-called fulcrums. The likelihood of particles is thereby analytically inferred, explicitly or implicitly, based on the Li-PDF instead of directly computed by utilizing the observation, which can significantly reduce the computation and enables real time filtering. The proposed approach guarantees the estimation quality when an appropriate fitting function and properly distributed fulcrums are used. The details for construction of the fitting function and fulcrums are addressed respectively in detail. In particular, to deal with multivariate fitting, the nonparametric kernel density estimator is presented which is flexible and convenient for implicit Li-PDF implementation. Simulation comparison with a variety of existing approaches on a benchmark 1-dimensional model and multi-dimensional robot localization and visual tracking demonstrate the validity of our approach.Comment: 42 pages, 17 figures, 4 tables and 1 appendix. This paper is a draft/preprint of one paper submitted to the IEEE Transaction