Michail Spitieris

Michail Spitieris, Ingelin Steinsland

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.

Olav Finne Praesteng Larsen, Massimiliano Ruocco, Michail Spitieris et al.

Access to trajectory data is a key requirement for developing and validating Air Traffic Management (ATM) solutions, yet many secondary and regional airports face severe data scarcity. This limits the applicability of machine learning methods and the ability to perform large-scale simulations or "what-if" analyses. In this paper, we investigate whether generative models trained on data-rich airports can be efficiently adapted to data-scarce airports using transfer learning. We adapt state-of-the-art diffusion- and flow-matching-based architectures to the aviation domain and evaluate their transferability between Zurich (source) and Dublin (target) landing trajectory datasets. Models are pretrained on Zurich and fine-tuned on Dublin with varying amounts of local data, ranging from 0% to 100%. Results show that diffusion-based models achieve competitive performance with as little as 5% of the Dublin data and reach baseline-level performance around 20%, consistently outperforming models trained from scratch across metrics and visual inspections. Latent flow matching and latent diffusion models also benefit from pretraining, though with more variable gains, while flow matching models show weaker generalization. Despite challenges in capturing rare trajectory patterns, these findings demonstrate the potential of transfer learning to substantially reduce data requirements for trajectory generation in ATM, enabling realistic synthetic data generation even in environments with limited historical records.

Michail Spitieris, Massimiliano Ruocco, Abdulmajid Murad et al.

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 to enhance performance. Specifically, we extend the VAE architecture by incorporating physical models in the generative process, enabling it to capture underlying dynamics more effectively. While physical models provide valuable insights, they struggle to capture complex temporal dependencies present in real-world data. To bridge this gap, we introduce a discrepancy term to account for unmodeled dynamics, represented within a latent Gaussian Process VAE (GPVAE). Furthermore, we apply regularization to ensure the generated data aligns closely with observed data, enhancing both the diversity and accuracy of the synthetic samples. The proposed method is applied to indoor temperature data, achieving state-of-the-art performance. Additionally, we demonstrate that PIGPVAE can produce realistic samples beyond the observed distribution, highlighting its robustness and usefulness under distribution shifts.

Zachari Thiry, Massimiliano Ruocco, Alessandro Nocente et al.

Forecasting indoor temperatures is important 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. Cost related constraints however do not allow for continuous year-around acquisition. To address this, we investigate the efficacy of data augmentation techniques leveraging SoTA 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. In our evaluation 1) we assess the performance of synthetic data generators independently, particularly focusing on SoTA AI-based methods; 2) we measure the utility of incorporating synthetically augmented data in a subsequent forecasting tasks where 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) 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.

Michail Spitieris, Ingelin Steinsland

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.