Doctor of Philosophy

dissertationStatistical learning theory has garnered attention during the last decade because it provides the theoretical and mathematical framework for solving pattern recognition problems, such as dimensionality reduction, clustering, and shape analysis. In statis

Adaptive weighting of Bayesian physics informed neural networks for multitask and multiscale forward and inverse problems

In this paper, we present a novel methodology for automatic adaptive weighting of Bayesian Physics-Informed Neural Networks (BPINNs), and we demonstrate that this makes it possible to robustly address multi-objective and multi-scale problems. BPINNs are a popular framework for data assimilation, combining the constraints of Uncertainty Quantification (UQ) and Partial Differential Equation (PDE). The relative weights of the BPINN target distribution terms are directly related to the inherent uncertainty in the respective learning tasks. Yet, they are usually manually set a-priori, that can lead to pathological behavior, stability concerns, and to conflicts between tasks which are obstacles that have deterred the use of BPINNs for inverse problems with multi-scale dynamics. The present weighting strategy automatically tunes the weights by considering the multi-task nature of target posterior distribution. We show that this remedies the failure modes of BPINNs and provides efficient exploration of the optimal Pareto front. This leads to better convergence and stability of BPINN training while reducing sampling bias. The determined weights moreover carry information about task uncertainties, reflecting noise levels in the data and adequacy of the PDE model. We demonstrate this in numerical experiments in Sobolev training, and compare them to analytically $\epsilon$-optimal baseline, and in a multi-scale Lokta-Volterra inverse problem. We eventually apply this framework to an inpainting task and an inverse problem, involving latent field recovery for incompressible flow in complex geometries

Auto-weighted Bayesian Physics-Informed Neural Networks and robust estimations for multitask inverse problems in pore-scale imaging of dissolution

In this article, we present a novel data assimilation strategy in pore-scale imaging and demonstrate that this makes it possible to robustly address reactive inverse problems incorporating Uncertainty Quantification (UQ). Pore-scale modeling of reactive flow offers a valuable opportunity to investigate the evolution of macro-scale properties subject to dynamic processes. Yet, they suffer from imaging limitations arising from the associated X-ray microtomography (X-ray microCT) process, which induces discrepancies in the properties estimates. Assessment of the kinetic parameters also raises challenges, as reactive coefficients are critical parameters that can cover a wide range of values. We account for these two issues and ensure reliable calibration of pore-scale modeling, based on dynamical microCT images, by integrating uncertainty quantification in the workflow. The present method is based on a multitasking formulation of reactive inverse problems combining data-driven and physics-informed techniques in calcite dissolution. This allows quantifying morphological uncertainties on the porosity field and estimating reactive parameter ranges through prescribed PDE models with a latent concentration field and dynamical microCT. The data assimilation strategy relies on sequential reinforcement incorporating successively additional PDE constraints. We guarantee robust and unbiased uncertainty quantification by straightforward adaptive weighting of Bayesian Physics-Informed Neural Networks (BPINNs), ensuring reliable micro-porosity changes during geochemical transformations. We demonstrate successful Bayesian Inference in 1D+Time and 2D+Time calcite dissolution based on synthetic microCT images with meaningful posterior distribution on the reactive parameters and dimensionless numbers

Low-Code/No-Code Artificial Intelligence Platforms for the Health Informatics Domain

In the contemporary health informatics space, Artificial Intelligence (AI) has become a necessity for the extraction of actionable knowledge in a timely manner. Low-code/No-Code (LCNC) AI Platforms enable domain experts to leverage the value that AI has to offer by lowering the technical skills overhead. We develop domain-specific, service-orientated platforms in the context of two subdomains of health informatics. We address in this work the core principles and the architectures of these platforms whose functionality we are constantly extending. Our work conforms to best practices with respect to the integration and interoperability of external services and provides process orchestration in a LCNC modeldriven fashion. We chose the CINCO product DIME and a bespoke tool developed in CINCO Cloud to serve as the underlying infrastructure for our LCNC platforms which address the requirements from our two application domains; public health and biomedical research. In the context of public health, an environment for building AI driven web applications for the automated evaluation of Web-based Health Information (WBHI). With respect to biomedical research, an AI driven workflow environment for the computational analysis of highly-plexed tissue images. We extended both underlying application stacks to support the various AI service functionality needed to address the requirements of the two application domains. The two case studies presented outline the methodology of developing these platforms through co-design with experts in the respective domains. Moving forward we anticipate we will increasingly re-use components which will reduce the development overhead for extending our existing platforms or developing new applications in similar domains