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The availability of large spatial data geocoded at accurate locations has fueled a growing interest in spatial modeling and analysis of point processes. The proposed research is motivated by the intensity estimation problem for large…

Data-driven design shows the promise of accelerating materials discovery but is challenging due to the prohibitive cost of searching the vast design space of chemistry, structure, and synthesis methods. Bayesian Optimization (BO) employs…

Materials design can be cast as an optimization problem with the goal of achieving desired properties, by varying material composition, microstructure morphology, and processing conditions. Existence of both qualitative and quantitative…

Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…

Reduced-rank regression recognises the possibility of a rank-deficient matrix of coefficients. We propose a novel Bayesian model for estimating the rank of the coefficient matrix, which obviates the need for post-processing steps and allows…

Physical parameterizations are used as representations of unresolved subgrid processes within weather and global climate models or coarse-scale turbulent models, whose resolutions are too coarse to resolve small-scale processes. These…

Physics-informed neural networks have emerged as a powerful tool in the scientific machine learning community, with applications to both forward and inverse problems. While they have shown considerable empirical success, significant…

Datasets in engineering applications are often limited and contaminated, mainly due to unavoidable measurement noise and signal distortion. Thus, using conventional data-driven approaches to build a reliable discriminative model, and…

We consider the problem of estimating an RF-device's location based on observations, such as received signal strength, from a set of transmitters with known locations. We survey the literature on this problem, showing that previous authors…

The latest Industrial revolution has helped industries in achieving very high rates of productivity and efficiency. It has introduced data aggregation and cyber-physical systems to optimize planning and scheduling. Although, uncertainty in…

Bayesian methods have been very successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model…

We develop a novel deep learning method for uncertainty quantification in stochastic partial differential equations based on Bayesian neural network (BNN) and Hamiltonian Monte Carlo (HMC). A BNN efficiently learns the posterior…

Numerical homogenization, i.e. the finite-dimensional approximation of solution spaces of PDEs with arbitrary rough coefficients, requires the identification of accurate basis elements. These basis elements are oftentimes found after a…

As large language models (LLMs) gain popularity in conducting prediction tasks in-context, understanding the sources of uncertainty in in-context learning becomes essential to ensuring reliability. The recent hypothesis of in-context…

Modeling the dynamics of flexible objects has become an emerging topic in the community as these objects become more present in many applications, e.g., soft robotics. Due to the properties of flexible materials, the movements of soft…

We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field…

The design of an experiment can be always be considered at least implicitly Bayesian, with prior knowledge used informally to aid decisions such as the variables to be studied and the choice of a plausible relationship between the…

In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…

Scientists use imaging to identify objects of interest and infer properties of these objects. The locations of these objects are often measured with error, which when ignored leads to biased parameter estimates and inflated variance.…

Physics-Informed Neural Networks (PINNs) are a novel computational approach for solving partial differential equations (PDEs) with noisy and sparse initial and boundary data. Although, efficient quantification of epistemic and aleatoric…