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Motivation: Recent work has demonstrated the feasibility of using non-numerical, qualitative data to parameterize mathematical models. However, uncertainty quantification (UQ) of such parameterized models has remained challenging because of…

Verifying and explaining the behavior of neural networks is becoming increasingly important, especially when they are deployed in safety-critical applications. In this paper, we study verification problems for Binarized Neural Networks…

Deep neural network controllers for autonomous driving have recently benefited from significant performance improvements, and have begun deployment in the real world. Prior to their widespread adoption, safety guarantees are needed on the…

Modern deep learning tools are remarkably effective in addressing intricate problems. However, their operation as black-box models introduces increased uncertainty in predictions. Additionally, they contend with various challenges,…

The accessibility of spatially distributed data, enabled by affordable sensors, field, and numerical experiments, has facilitated the development of data-driven solutions for scientific problems, including climate change, weather…

Uncertainty in state or model parameters is common in robotics and typically handled by acquiring system measurements that yield information about the uncertain quantities of interest. Inputs to a nonlinear dynamical system yield outcomes…

This paper develops a Bayesian network-based method for the calibration of multi-physics models, integrating various sources of uncertainty with information from computational models and experimental data. We adopt the Kennedy and O'Hagan…

In this work, we introduce a generalized framework for multiscale state-space modeling that incorporates nested nonlinear dynamics, with a specific focus on Bayesian learning under switching regimes. Our framework captures the complex…

Deep-learning models for traffic data prediction can have superior performance in modeling complex functions using a multi-layer architecture. However, a major drawback of these approaches is that most of these approaches do not offer…

This chapter explores neural networks, topological data analysis, and topological deep learning techniques, alongside statistical Bayesian methods, for processing images, time series, and graphs to maximize the potential of artificial…

Deep neural networks offer numerous potential applications across geoscience, for example, one could argue that they are the state-of-the-art method for predicting faults in seismic datasets. In quantitative reservoir characterization…

In context-specific applications such as robotics, telecommunications, and healthcare, artificial intelligence systems often face the challenge of limited training data. This scarcity introduces epistemic uncertainty, i.e., reducible…

Consistent experiment data are crucial to adjust parameters of physics models and to determine best estimates of observables. However, often experiment data are not consistent due to unrecognized systematic errors. Standard methods of…

Bayesian inference is a popular approach to calibrating uncertainties, but it can underpredict such uncertainties when model misspecification is present, impacting its reliability to inform decision making. Recently, the statistics and…

This study aims to comprehensively investigate the deep ensemble approach, an approximate Bayesian inference, in the multi-output regression task for predicting the aerodynamic performance of a missile configuration. To this end, the effect…

Bayesian neural networks (BNNs) allow rigorous uncertainty quantification in deep learning, but often come at a prohibitive computational cost. We propose three different innovative architectures of partial trace-class Bayesian neural…

The electromagnetic nucleon form-factors data are studied with artificial feed forward neural networks. As a result the unbiased model-independent form-factor parametrizations are evaluated together with uncertainties. The Bayesian approach…

We develop a theoretical framework for frame synchronization, also known as block synchronization, in the quantum domain which makes it possible to attach classical and quantum metadata to quantum information over a noisy channel even when…

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…

Bayesian inference provides a rigorous methodology for estimation and uncertainty quantification of parameters in geophysical forward models. Badlands (basin and landscape dynamics model) is a landscape evolution model that simulates…