Learning Physics between Digital Twins with Low-Fidelity Models and Physics-Informed Gaussian Processes

A digital twin is a computer model that represents an individual, for example, a component, a patient or a process. In many situations, we want to gain knowledge about an individual from its data while incorporating imperfect physical knowledge and also learn from data from other individuals. In this paper, we introduce a fully Bayesian methodology for learning between digital twins in a setting where the physical parameters of each individual are of interest. A model discrepancy term is incorporated in the model formulation of each personalized model to account for the missing physics of the low-fidelity model. To allow sharing of information between individuals, we introduce a Bayesian Hierarchical modelling framework where the individual models are connected through a new level in the hierarchy. Our methodology is demonstrated in two case studies, a toy example previously used in the literature extended to more individuals and a cardiovascular model relevant for the treatment of Hypertension. The case studies show that 1) models not accounting for imperfect physical models are biased and over-confident, 2) the models accounting for imperfect physical models are more uncertain but cover the truth, 3) the models learning between digital twins have less uncertainty than the corresponding independent individual models, but are not over-confident.Comment: 33 pages, 19 figure

Quantile based modelling of diurnal temperature range with the five-parameter lambda distribution

Diurnal temperature range is an important variable in climate science that can provide information regarding climate variability and climate change. Changes in diurnal temperature range can have implications for hydrology, human health and ecology, among others. Yet, the statistical literature on modelling diurnal temperature range is lacking. In this paper we propose to model the distribution of diurnal temperature range using the five-parameter lambda (FPL) distribution. Additionally, in order to model diurnal temperature range with explanatory variables, we propose a distributional quantile regression model that combines quantile regression with marginal modelling using the FPL distribution. Inference is performed using the method of quantiles. The models are fitted to 30 years of daily observations of diurnal temperature range from 112 weather stations in the southern part of Norway. The flexible FPL distribution shows great promise as a model for diurnal temperature range, and performs well against competing models. The distributional quantile regression model is fitted to diurnal temperature range data using geographic, orographic and climatological explanatory variables. It performs well and captures much of the spatial variation in the distribution of diurnal temperature range in Norway.Comment: 28 pages, 9 figures; v2: revision of the introduction, more references added and minor corrections of the tex

Spatial modelling improves genetic evaluation in smallholder breeding programs

Background Breeders and geneticists use statistical models to separate genetic and environmental effects on phenotype. A common way to separate these effects is to model a descriptor of an environment, a contemporary group or herd, and account for genetic relationship between animals across environments. However, separating the genetic and environmental effects in smallholder systems is challenging due to small herd sizes and weak genetic connectedness across herds. We hypothesised that accounting for spatial relationships between nearby herds can improve genetic evaluation in smallholder systems. Furthermore, geographically referenced environmental covariates are increasingly available and could model underlying sources of spatial relationships. The objective of this study was therefore, to evaluate the potential of spatial modelling to improve genetic evaluation in dairy cattle smallholder systems. Methods We performed simulations and real dairy cattle data analysis to test our hypothesis. We modelled environmental variation by estimating herd and spatial effects. Herd effects were considered independent, whereas spatial effects had distance-based covariance between herds. We compared these models using pedigree or genomic data. Results The results show that in smallholder systems (i) standard models do not separate genetic and environmental effects accurately, (ii) spatial modelling increases the accuracy of genetic evaluation for phenotyped and non-phenotyped animals, (iii) environmental covariates do not substantially improve the accuracy of genetic evaluation beyond simple distance-based relationships between herds, (iv) the benefit of spatial modelling was largest when separating the genetic and environmental effects was challenging, and (v) spatial modelling was beneficial when using either pedigree or genomic data. Conclusions We have demonstrated the potential of spatial modelling to improve genetic evaluation in smallholder systems. This improvement is driven by establishing environmental connectedness between herds, which enhances separation of genetic and environmental effects. We suggest routine spatial modelling in genetic evaluations, particularly for smallholder systems. Spatial modelling could also have a major impact in studies of human and wild populations

Uncertainty propagation through a point model for steady-state two-phase pipe flow

Uncertainty propagation is used to quantify the uncertainty in model predictions in the presence of uncertain input variables. In this study, we analyze a steady-state point-model for two-phase gas-liquid flow. We present prediction intervals for holdup and pressure drop that are obtained from knowledge of the measurement error in the variables provided to the model. The analysis also uncovers which variables the predictions are most sensitive to. Sensitivity indices and prediction intervals are calculated by two different methods, Monte Carlo and polynomial chaos. The methods give similar prediction intervals, and they agree that the predictions are most sensitive to the pipe diameter and the liquid viscosity. However, the Monte Carlo simulations require fewer model evaluations and less computational time. The model predictions are also compared to experiments while accounting for uncertainty, and the holdup predictions are accurate, but there is bias in the pressure drop estimatespublishedVersio

Modeling dependency structures in 450k DNA methylation data

Motivation: DNA methylation has been shown to be spatially dependent across chromosomes. Previous studies have focused on the influence of genomic context on the dependency structure, while not considering differences in dependency structure between individuals. Results: We modeled spatial dependency with a flexible framework to quantify the dependency structure, focusing on inter-individual differences by exploring the association between dependency parameters and technical and biological variables. The model was applied to a subset of the Finnish Twin Cohort study (N = 1611 individuals). The estimates of the dependency parameters varied considerably across individuals, but were generally consistent across chromosomes within individuals. The variation in dependency parameters was associated with bisulfite conversion plate, zygosity, sex and age. The age differences presumably reflect accumulated environmental exposures and/or accumulated small methylation differences caused by stochastic mitotic events, establishing recognizable, individual patterns more strongly seen in older individuals.Peer reviewe