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Increased usage of automated tools like deep learning in medical image segmentation has alleviated the bottleneck of manual contouring. This has shifted manual labour to quality assessment (QA) of automated contours which involves detecting…

Finite element analysis (FEA) has been widely used to generate simulations of complex and nonlinear systems. Despite its strength and accuracy, the limitations of FEA can be summarized into two aspects: a) running high-fidelity FEA often…

Knowing whether a Quantum Machine Learning model would perform well on a given dataset before training it can help to save critical resources. However, gathering a priori information about model performance (e.g., training speed, critical…

In the context of Monte Carlo (MC) simulation of particle transport Uncertainty Quantification (UQ) addresses the issue of predicting non statistical errors affecting the physical results, i.e. errors deriving mainly from uncertainties in…

Estimating quantum entropies and divergences is an important problem in quantum physics, information theory, and machine learning. Quantum neural estimators (QNEs), which utilize a hybrid classical-quantum architecture, have recently…

Deep learning-based object pose estimators are often unreliable and overconfident especially when the input image is outside the training domain, for instance, with sim2real transfer. Efficient and robust uncertainty quantification (UQ) in…

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…

The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to…

In large-scale statistical modeling, reducing data size through subsampling is essential for balancing computational efficiency and statistical accuracy. We propose a new method, Principal Component Analysis guided Quantile Sampling…

Recently, introducing Tensor Decomposition (TD) techniques into unsupervised feature selection (UFS) has been an emerging research topic. A tensor structure is beneficial for mining the relations between different modes and helps relieve…

For regression tasks, standard Gaussian processes (GPs) provide natural uncertainty quantification (UQ), while deep neural networks (DNNs) excel at representation learning. Deterministic UQ methods for neural networks have successfully…

Inverse problems are ubiquitous in modern scientific studies and involve recovering an underlying signal from noisy observations often transformed by a measurement operator. These problems are frequently ill-posed, particularly in imaging,…

The forward problems of pattern formation have been greatly empowered by extensive theoretical studies and simulations, however, the inverse problem is less well understood. It remains unclear how accurately one can use images of pattern…

Quantitative magnetic resonance imaging (qMRI) requires multi-phase acqui-sition, often relying on reduced data sampling and reconstruction algorithms to accelerate scans, which inherently poses an ill-posed inverse problem. While many…

There are essentially three kinds of approaches to Uncertainty Quantification (UQ): (A) robust optimization, (B) Bayesian, (C) decision theory. Although (A) is robust, it is unfavorable with respect to accuracy and data assimilation. (B)…

Uncertainty quantification for inverse problems in imaging has drawn much attention lately. Existing approaches towards this task define uncertainty regions based on probable values per pixel, while ignoring spatial correlations within the…

Parametric uncertainty in nonlinear dynamical systems can fundamentally alter bifurcation behaviour, leading to qualitative response changes. Predicting operating margins/envelopes under such uncertainties is critical but challenging:…

Quantum thermodynamic uncertainty relations establish fundamental trade-offs between the precision achievable in quantum systems and associated thermodynamic quantities such as entropy production or dynamical activity. While foundational,…

Data-driven surrogate models offer quick approximations to complex numerical and experimental systems but typically lack uncertainty quantification, limiting their reliability in safety-critical applications. While Bayesian methods provide…

This paper provides a comparative study of modern uncertainty quantification (UQ) methods. To greatly enhance real-time performance, both differential algebra (DA) and a directional differential algebra (DDA) approach are employed. This can…