Gaussian processes for modeling physical systems

Maximillian Fornitz Vording

Research output: Book/ReportPh.D. thesisResearch

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Abstract

The overall goal with this thesis is to investigate how we can use the theoretical understanding of a physical system to encode the internal structure of it in the kernels of Gaussian process models, so the models can give reliable predictions and guide future experiments even in settings with very limited observations. Theoretical and empirical results are provided that support this. The role of the kernel structure in the Gaussian process priors are analysed through two direct applications in pharmaceutical science and chemistry, first at a microscopic level for crystallised drugs and then at atomic level for molecular property prediction. The 1st application is for thermomechanical analysis of the properties of drugs, presented in the chapter 2. The physical system is a vibrating crystallised drug under temperature changes. To model changes in signal-to-noise ratios between measurement points, the distance between them in both time and space are incorporated into the generative model through a warped Gaussian process prior. We warp the Gaussian process prior into a truncated normal to restrict it to non-negative parameters suitable for fitting the resonance peak shapes. We show empirical results, that the GP prior with a squared exponential kernel improves the interpolation and tracking of resonance peaks in regions of low signal-to-noise ratios. The 2nd application on molecular property prediction, is presented throughout chapter 3. Here the theory behind graphs and how we can learn and/or design representations of them through message passing neural networks or graph convolutional Gaussian processes is introduced, while deriving new kernels on the space of edges from the existing basis functions. We extend the models to learn graph representations of molecules suitable for predicting their properties. Since molecular properties are dependent on internal degrees of freedom (dof) and inter-molecular
forces, a graph representation with 3 types of edges are chosen, one for each dof. We show that the models are invariant under rotation, translation and permutation of identical atoms. To train the Gaussian process, inter-domain inducing nodes for variational low-rank approximations is introduced. The proposed models are compared based on learning curves, where the Gaussian process model has lower test errors when trained on less than 64 molecules.
Original languageEnglish
PublisherTechnical University of Denmark
Number of pages160
Publication statusPublished - 2020

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