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We propose VarFA, a variational inference factor analysis framework that extends existing factor analysis models for educational data mining to efficiently output uncertainty estimation in the model's estimated factors. Such uncertainty…

Accuracy and generalization capabilities are key objectives when learning dynamical system models. To obtain such models from limited data, current works exploit prior knowledge and assumptions about the system. However, the fusion of…

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…

Recent works have presented promising results from the application of machine learning (ML) to the modeling of flow rates in oil and gas wells. Encouraging results and advantageous properties of ML models, such as computationally cheap…

We investigate the use of normalizing flow (NF) models as flexible priors in Bayesian inference via Markov Chain Monte Carlo (MCMC) sampling for iterative Bayesian calibration. Trained on posteriors from previous analyses, these models can…

Bayesian inference with computationally expensive likelihood evaluations remains a significant challenge in many scientific domains. We propose normalizing flow regression (NFR), a novel offline inference method for approximating posterior…

Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…

Inverse problems, which involve estimating parameters from incomplete or noisy observations, arise in various fields such as medical imaging, geophysics, and signal processing. These problems are often ill-posed, requiring regularization…

This study proposes a novel approach to quantifying uncertainties of constitutive relations inferred from noisy experimental data using inverse modelling. We focus on electrochemical systems in which charged species (e.g., Lithium ions) are…

Continuum-scale material deformation models, such as crystal plasticity, can significantly enhance their predictive accuracy by incorporating input from lower-scale (i.e., mesoscale) models. The procedure to generate and extract the…

Modeling and synthesizing image noise is an important aspect in many computer vision applications. The long-standing additive white Gaussian and heteroscedastic (signal-dependent) noise models widely used in the literature provide only a…

Multi-fidelity methods are prominently used when cheaply-obtained, but possibly biased and noisy, observations must be effectively combined with limited or expensive true data in order to construct reliable models. This arises in both…

Prior specification for nonparametric Bayesian inference involves the difficult task of quantifying prior knowledge about a parameter of high, often infinite, dimension. Realistically, a statistician is unlikely to have informed opinions…

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…

Noise and uncertainty are usually the enemy of machine learning, noise in training data leads to uncertainty and inaccuracy in the predictions. However, we develop a machine learning architecture that extracts crucial information out of the…

Especially when facing reliability data with limited information (e.g., a small number of failures), there are strong motivations for using Bayesian inference methods. These include the option to use information from physics-of-failure or…

Model Updating is frequently used in Structural Health Monitoring to determine structures' operating conditions and whether maintenance is required. Data collected by sensors are used to update the values of some initially unknown…

In this work, we study the problem of learning the volatility under market microstructure noise. Specifically, we consider noisy discrete time observations from a stochastic differential equation and develop a novel computational method to…

Artificial neural networks will always make a prediction, even when completely uncertain and regardless of the consequences. This obliviousness of uncertainty is a major obstacle towards their adoption in practice. Techniques exist,…

What happens to the optimal interpretation of noisy data when there exists more than one equally plausible interpretation of the data? In a Bayesian model-learning framework the answer depends on the prior expectations of the dynamics of…