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Bayes’s Theorem is a powerful tool for the quantitative analysis of measurements and numerical calculations in many fields of study, by enabling systematic incorporation of prior knowledge and of correlations and covariance between elements of the measurements and calculations. Probabilistic Bayesian analysis can address “Inverse Problems,” in which causal factors are deduced from measurements that are influenced by them, thereby testing model formulations and constraining model parameters. Probabilistic Bayesian analysis can also be applied to challenging computations, such as the emulation of complex simulations and image de–noising. Probabilistic Bayesian calculations are often highly demanding computationally, however, requiring Machine Learning (ML)-based methods for the efficient utilization of practically obtainable resources.
The goal of this project is to develop and implement general ML-based approaches to Bayesian probabilistic analysis methods, including uncertainty quantification, emulation, inference, and de–noising, for application to a broad range of Nuclear Physics (NP) research areas. These areas include the measurement of the mass and fundamental nature of the neutrino; study of the Quark-Gluon Plasma that filled the early universe; and mapping of natural and anthropogenic radiation environments. Project PIs are Nuclear Physicists with leading roles in each of these areas, and data scientists developing state–of–the–art ML-based methods for probabilistic Bayesian analysis.
The figure shows a schematic representation of the key computational requirements for probabilistic Bayesian analysis and Uncertainty quantification (UQ) of several elements of this project. The left column indicates the various data sources, while the right column specifies the target analyses. The middle box places each element in a two-dimensional space of computational complexity of the forward model (vertical) and posterior parameter space dimensionality (horizontal), both of which vary by several orders of magnitude.
The project explores several probabilistic Bayesian analysis methods to address these challenges, within a common framework. This comprehensive approach will provide insight into the applicability and performance of such ML-based methods for analyses of widely differing character.
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