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Gaussian process latent variable models (GPLVMs) are a versatile family of unsupervised learning models commonly used for dimensionality reduction. However, common challenges in modeling data with GPLVMs include inadequate kernel…

Bayesian Federated Learning (BFL) enables uncertainty quantification and robust adaptation in distributed learning. In contrast to the frequentist approach, it estimates the posterior distribution of a global model, offering insights into…

One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…

Lattice gauge theories (LGTs) provide a powerful framework for studying non-perturbative phenomena in gauge theories. However, conventional approaches such as Monte Carlo (MC) simulations in imaginary time are limited, as they do not allow…

Digital twins (DTs) rely on continuous synchronization between physical systems and their virtual counterparts through online parameter estimation under uncertainty. In many practical settings, however, this task is challenged by low…

Accurate prediction of structural failure modes under seismic excitations is essential for seismic risk and resilience assessment. Traditional simulation-based approaches often result in imbalanced datasets dominated by non-failure or…

Designing estimation algorithms for systems governed by partial differential equations (PDEs) such as fluid flows is challenging due to the high-dimensional and oftentimes nonlinear nature of the dynamics, as well as their dependence on…

Machine-learning force fields (MLFFs) have emerged as a promising solution for speeding up ab initio molecular dynamics (MD) simulations, where accurate force predictions are critical but often computationally expensive. In this work, we…

Probabilistic load forecasting (PLF) is a key component in the extended tool-chain required for efficient management of smart energy grids. Neural networks are widely considered to achieve improved prediction performances, supporting highly…

Gaussian process latent variable models (GPLVM) are a flexible and non-linear approach to dimensionality reduction, extending classical Gaussian processes to an unsupervised learning context. The Bayesian incarnation of the GPLVM Titsias…

Stacking fault energies (SFEs) are vital parameters for understanding the deformation mechanisms in metals and alloys, with prior knowledge of SFEs from ab initio calculations being crucial for alloy design. Machine learning (ML) algorithms…

Low-rank matrix completion has achieved great success in many real-world data applications. A matrix factorization model that learns latent features is usually employed and, to improve prediction performance, the similarities between latent…

Probabilistic inference in high-dimensional state-space models is computationally challenging. For many spatiotemporal systems, however, prior knowledge about the dependency structure of state variables is available. We leverage this…

In this paper, we propose a novel Gaussian process-based moving horizon estimation (MHE) framework for unknown nonlinear systems. On the one hand, we approximate the system dynamics by the posterior means of the learned Gaussian processes…

Latent force models (LFMs) are flexible models that combine mechanistic modelling principles (i.e., physical models) with non-parametric data-driven components. Several key applications of LFMs need non-linearities, which results in…

Microstructural heterogeneity affects the macro-scale behavior of materials. Conversely, load distribution at the macro-scale changes the microstructural response. These up-scaling and down-scaling relations are often modeled using…

There is growing interest in using machine learning (ML) methods for structural metamodeling due to the substantial computational cost of traditional simulations. Purely data-driven strategies often face limitations in model robustness,…

In this work we propose an approximate Minimum Mean-Square Error (MMSE) filter for linear dynamic systems with Gaussian Mixture noise. The proposed estimator tracks each component of the Gaussian Mixture (GM) posterior with an individual…

Conventional radio frequency (RF) passive components modeling based on machine learning requires extensive electromagnetic (EM) simulations to cover geometric and frequency design spaces, creating computational bottlenecks. In this paper,…

Using state-space representation, mobile object positioning problems can be described as dynamic systems, with the state representing the unknown location and the observations being the information gathered from the location sensors. For…