Recent advances in generative AI offer promising solutions for synthetic data generation but often rely on large datasets for effective training. To address this limitation, we propose a novel generative model that learns from limited data by incorporating physical constraints into a Variational Autoencoder (VAE) framework. Specifically, we extend VAE with a physics-based generator to capture underlying dynamics, while unmodeled dynamics are learned via a latent Gaussian Process VAE (GPVAE) component. We further introduce a regularization term that balances the physical model and data-driven discrepancy, promoting both interpretability and fidelity to real-world observations. We evaluate the proposed method on both real and simulated data, demonstrating that the Physics-Informed GPVAE (PIGPVAE) outperforms state-of-the-art methods in terms of diversity and accuracy of the generated samples, even under small-data conditions. Additionally, we demonstrate that PIGPVAE can produce realistic samples beyond the observed distribution, highlighting its robustness and usefulness under distribution shifts.

Forecasting indoor temperatures is of paramount importance to achieve efficient control of HVAC systems. In this task, the limited data availability presents a challenge as most of the available data is acquired during standard operation where extreme scenarios and transitory regimes such as major temperature increases or decreases are de-facto excluded. Acquisition of such data requires significant energy consumption and a dedicated facility, hindering the quantity and diversity of available data. To acquire such data, we make use of such a facility referred to as the Test-cell. Cost related constraints however do not allow for continuous year-around acquisition.To address this, we investigate the efficacy of data augmentation techniques, particularly leveraging state-of-the-art AI-based methods for synthetic data generation. Inspired by practical and experimental motivations, we explore fusion strategies of real and synthetic data to improve forecasting models. This approach alleviates the need for continuously acquiring extensive time series data, especially in contexts involving repetitive heating and cooling cycles in buildings. Our evaluation methodology for synthetic data synthesis involves a dual-focused approach: firstly, we assess the performance of synthetic data generators independently, particularly focusing on SoTA AI-based methods; secondly, we measure the utility of incorporating synthetically augmented data in a subsequent downstream tasks (forecasting). In the forecasting tasks, we employ a simple model in two distinct scenarios: 1) we first examine an augmentation technique that combines real and synthetically generated data to expand the training dataset, 2) Second, we delve into utilizing synthetic data to tackle dataset imbalances. Our results highlight the potential of synthetic data augmentation in enhancing forecasting accuracy while mitigating training variance. Through empirical experiments, we show significant improvements achievable by integrating synthetic data, thereby paving the way for more robust forecasting models in low-data regime.

Background The essential hypertension phenotype results from an interplay between genetic and environmental factors. The influence of lifestyle exposures such as excess adiposity, alcohol consumption, tobacco use, diet, and activity patterns on blood pressure (BP) is well established. Additionally, polygenic risk scores for BP traits are associated with clinically significant phenotypic variation. However, interactions between genetic and environmental risk factors in hypertension morbidity and mortality are poorly characterized. Methods and Results We used genotype and phenotype data from up to 49 234 participants from the HUNT (Trøndelag Health Study) to model gene–environment interactions between genome‐wide polygenic risk scores for systolic BP and diastolic BP and 125 environmental exposures. Among the 125 environmental exposures assessed, 108 and 100 were independently associated with SBP and DBP, respectively. Of these, 12 interactions were identified for genome‐wide PRSs for systolic BP and 4 for genome‐wide polygenic risk scores for diastolic BP, 2 of which were overlapping ( P < 2 × 10 −4 ). We found evidence for gene‐dependent influence of lifestyle factors such as cardiorespiratory fitness, dietary patterns, and tobacco exposure, as well as biomarkers such as serum cholesterol, creatinine, and alkaline phosphatase on BP. Conclusions Individuals that are genetically susceptible to high BP may be more vulnerable to common acquired risk factors for hypertension, but these effects appear to be modifiable. The gene‐dependent influence of several common acquired risk factors indicates the potential of genetic data combined with lifestyle assessments in risk stratification, and gene–environment‐informed risk modeling in the prevention and management of hypertension.

Aims Hypertension is a major modifiable cause of morbidity and mortality that affects over 1 billion people worldwide. Blood pressure (BP) traits have a strong genetic component that can be quantified with polygenic risk scores (PRSs). To date, the performance of BP PRSs has mainly been assessed in adults, and less is known about polygenic hypertension risk in childhood.Methods and results Multiple PRSs for systolic BP (SBP), diastolic BP (DBP), and pulse pressure were developed using either genome-wide significant weights, pruning and thresholding, or Bayesian regression. Among 87 total PRSs, the top performer for each trait was applied in independent cohorts of children and adult to assess genotype-phenotype associations and disease risk across the lifespan. Differences between those with low (1st decile), average (2nd-9th decile), and high (10th decile) PRS emerge in the first years of life and are maintained throughout adulthood. These diverging BP trajectories also seem to affect cardiovascular and renal disease risk, with increased risk observed among those in the top decile and reduced risk among those in the bottom decile of the polygenic risk distribution compared with the rest of the population.Conclusion Genetic risk factors are associated with BP traits across the lifespan, beginning in the first years of life. Given the importance of exposure time in disease pathogenesis and the early rise in BP levels among those genetically susceptible, PRSs may help identify high-risk individuals prior to hypertension onset, facilitate primordial prevention, and reduce the burden of this public health challenge. A high genetic risk of elevated blood pressure (BP) is associated with increased BP from early childhood and throughout the lifespan. Inherited predispositions also affect the risk of cardiovascular morbidity and mortality, yet this appears to be modified by the absence or presence of hypertension, indicating that genetic hypertension risk is not deterministic, and that controlling BP can and should be done across the polygenic risk distribution. Given that differences in BP emerge early in life as a function of genetic risk, polygenic risk scores have the potential to reduce the duration of exposure to high BP by identifying high-risk individuals from birth, and thereby attenuate lifelong disease risk. Graphical Abstract

We introduce a computational efficient data-driven framework suitable for quantifying the uncertainty in physical parameters and model formulation of computer models, represented by differential equations. We construct physics-informed priors, which are multi-output GP priors that encode the model's structure in the covariance function. This is extended into a fully Bayesian framework that quantifies the uncertainty of physical parameters and model predictions. Since physical models often are imperfect descriptions of the real process, we allow the model to deviate from the observed data by considering a discrepancy function. For inference, Hamiltonian Monte Carlo is used. Further, approximations for big data are developed that reduce the computational complexity from $\mathcal{O}(N^3)$ to $\mathcal{O}(N\cdot m^2),$ where $m \ll N.$ Our approach is demonstrated in simulation and real data case studies where the physics are described by time-dependent ODEs describe (cardiovascular models) and space-time dependent PDEs (heat equation). In the studies, it is shown that our modelling framework can recover the true parameters of the physical models in cases where 1) the reality is more complex than our modelling choice and 2) the data acquisition process is biased while also producing accurate predictions. Furthermore, it is demonstrated that our approach is computationally faster than traditional Bayesian calibration methods.

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.

This work is motivated by personalized digital twins based on observations and physical models for treatment and prevention of Hypertension. The models commonly used are simplification of the real process and the aim is to make inference about physically interpretable parameters. To account for model discrepancy we propose to set up the estimation problem in a Bayesian calibration framework. This naturally solves the inverse problem accounting for and quantifying the uncertainty in the model formulation, in the parameter estimates and predictions. We focus on the inverse problem, i.e. to estimate the physical parameters given observations. The models we consider are the two and three parameters Windkessel models (WK2 and WK3). These models simulate the blood pressure waveform given the blood inflow and a set of physically interpretable calibration parameters. The third parameter in WK3 function as a tuning parameter. The WK2 model offers physical interpretable parameters and therefore we adopt it as a computer model choice in a Bayesian calibration formulation. In a synthetic simulation study, we simulate noisy data from the WK3 model. We estimate the model parameters using conventional methods, i.e. least squares optimization and through the Bayesian calibration framework. It is demonstrated that our formulation can reconstruct the blood pressure waveform of the complex model, but most importantly can learn the parameters according to known mathematical connections between the two models. We also successfully apply this formulation to a real case study, where data was obtained from a pilot randomized controlled trial study. Our approach is successful for both the simulation study and the real cases.