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Bayesian methods in machine learning, such as Gaussian processes, have great advantages com-pared to other techniques. In particular, they provide estimates of the uncertainty associated with a prediction. Extending the Bayesian approach to…

Anomaly detection is a fundamental task in machine learning and data mining, with significant applications in cybersecurity, industrial fault diagnosis, and clinical disease monitoring. Traditional methods, such as statistical modeling and…

Nonlinear dynamics are ubiquitous in science and engineering applications, but the physics of most complex systems is far from being fully understood. Discovering interpretable governing equations from measurement data can help us…

Fine-scale simulation of complex systems governed by multiscale partial differential equations (PDEs) is computationally expensive and various multiscale methods have been developed for addressing such problems. In addition, it is…

Control barrier functions are widely used to synthesize safety-critical controls. However, the presence of Gaussian-type noise in dynamical systems can generate unbounded signals and potentially result in severe consequences. Although…

A crucial task in predictive maintenance is estimating the remaining useful life of physical systems. In the last decade, deep learning has improved considerably upon traditional model-based and statistical approaches in terms of predictive…

We propose an efficient transfer Bayesian optimization method, which finds the maximum of an expensive-to-evaluate black-box function by using data on related optimization tasks. Our method uses auxiliary information that represents the…

Bayesian calibration of black-box computer models offers an established framework to obtain a posterior distribution over model parameters. Traditional Bayesian calibration involves the emulation of the computer model and an additive model…

System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along…

Recent studies have shown that ensemble approaches could not only improve accuracy and but also estimate model uncertainty in deep learning. However, it requires a large number of parameters according to the increase of ensemble models for…

A Bayesian approach is developed for the inference of an eddy-diffusivity field from Lagrangian trajectory data. The motion of Lagrangian particles is modelled by a stochastic differential equation associated with the advection-diffusion…

Bayesian methods are particularly effective for addressing inverse problems due to their ability to manage uncertainties inherent in the inference process. However, employing these methods with costly forward models poses significant…

Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…

Equation learning aims to infer differential equation models from data. While a number of studies have shown that differential equation models can be successfully identified when the data are sufficiently detailed and corrupted with…

Compared to point estimates calculated by standard neural networks, Bayesian neural networks (BNN) provide probability distributions over the output predictions and model parameters, i.e., the weights. Training the weight distribution of a…

Diffusion models have become fundamental tools for modeling data distributions in machine learning. Despite their success, these models face challenges when generating data with extreme brightness values, as evidenced by limitations…

A common task in experimental sciences is to fit mathematical models to real-world measurements to improve understanding of natural phenomenon (reverse-engineering or inverse modeling). When complex dynamical systems are considered, such as…

Learning dynamical systems from incomplete or noisy data is inherently ill-posed, as a single observation may correspond to multiple plausible futures. While physics-based ensemble forecasting relies on perturbing initial states to capture…

Anomalous diffusion occurs in a wide range of systems, including protein transport within cells, animal movement in complex habitats, pollutant dispersion in groundwater, and nanoparticle motion in synthetic materials. Accurately estimating…

Network models provide a powerful framework for analysing single-cell count data, facilitating the characterisation of cellular identities, disease mechanisms, and developmental trajectories. However, uncertainty modeling in unsupervised…