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Uncertainty quantification for image data is dominated by complex deep learning methods, yet the field lacks an interpretable, mathematically grounded baseline. We propose Bayesian scattering to fill this gap, serving as a first-step…

Raman spectroscopy is an important tool for studies of molecules, liquids and solids. While Raman spectra can be obtained theoretically from molecular dynamics (MD) simulations, this requires the calculation of the electronic polarizability…

Bayesian estimation is a powerful theoretical paradigm for the operation of quantum sensors. However, the Bayesian method for statistical inference generally suffers from demanding calibration requirements that have so far restricted its…

Efficiently quantifying predictive uncertainty in medical images remains a challenge. While Bayesian neural networks (BNN) offer predictive uncertainty, they require substantial computational resources to train. Although Bayesian…

Uncertainty quantification is vital for safety-critical Deep Learning applications like medical image segmentation. We introduce BA U-Net, an uncertainty-aware model for MRI segmentation that integrates Bayesian Neural Networks with…

In Hezaveh et al. 2017 we showed that deep learning can be used for model parameter estimation and trained convolutional neural networks to determine the parameters of strong gravitational lensing systems. Here we demonstrate a method for…

Several recent works encourage the use of a Bayesian framework when assessing performance and fairness metrics of a classification algorithm in a supervised setting. We propose the Uncertainty Matters (UM) framework that generalizes a…

Uncertainty quantification in automated image analysis is highly desired in many applications. Typically, machine learning models in classification or segmentation are only developed to provide binary answers; however, quantifying the…

Learning unbiased models on imbalanced datasets is a significant challenge. Rare classes tend to get a concentrated representation in the classification space which hampers the generalization of learned boundaries to new test examples. In…

Representing and quantifying uncertainty in physical parameterisations is a central challenge in weather and climate modelling, and approaches are often developed separately for different timescales. Here, we introduce a unified framework…

Reliable models of the thermodynamic properties of materials are critical for industrially relevant applications that require a good understanding of equilibrium phase diagrams, thermal and chemical transport, and microstructure evolution.…

Background: Many mathematical models have now been employed across every area of systems biology. These models increasingly involve large numbers of unknown parameters, have complex structure which can result in substantial evaluation time…

Scientific Machine Learning (SciML) integrates physics and data into the learning process, offering improved generalization compared with purely data-driven models. Despite its potential, applications of SciML in prognostics remain limited,…

Physics-informed extreme learning machine (PIELM) has recently received significant attention as a rapid version of physics-informed neural network (PINN) for solving partial differential equations (PDEs). The key characteristic is to fix…

Inverse problems can be described as limited-data problems in which the signal of interest cannot be observed directly. A physics-based forward model that relates the signal with the observations is typically needed. Unfortunately, unknown…

Climate models are generally calibrated manually by comparing selected climate statistics, such as the global top-of-atmosphere energy balance, to observations. The manual tuning only targets a limited subset of observational data and…

High-quality calibrated uncertainty estimates are crucial for numerous real-world applications, especially for deep learning-based deployed ML systems. While Bayesian deep learning techniques allow uncertainty estimation, training them with…

A representation of the cause-effect mechanism is needed to enable artificial intelligence to represent how the world works. Bayesian Networks (BNs) have proven to be an effective and versatile tool for this task. BNs require constructing a…

Fault diagnosis of mechanical equipment involves data collection, feature extraction, and pattern recognition but is often hindered by the imbalanced nature of industrial data, introducing significant uncertainty and reducing diagnostic…

Recent advances in machine unlearning have focused on developing algorithms to remove specific training samples from a trained model. In contrast, we observe that not all models are equally easy to unlearn. Hence, we introduce a family of…