Diagnostics of Data-Driven Models: Uncertainty Quantification of PM7 Semi-Empirical Quantum Chemical Method.

We report an evaluation of a semi-empirical quantum chemical method PM7 from the perspective of uncertainty quantification. Specifically, we apply Bound-to-Bound Data Collaboration, an uncertainty quantification framework, to characterize (a) variability of PM7 model parameter values consistent with the uncertainty in the training data and (b) uncertainty propagation from the training data to the model predictions. Experimental heats of formation of a homologous series of linear alkanes are used as the property of interest.

Tracking transience: a method for dynamic monitoring of biological events in Arabidopsis thaliana biosensors.

The activation and level of expression of an endogenous, stress-responsive biosensor (bioreporter) can be visualized in real-time and non-destructively using highly accessible equipment (fluorometer). Biosensor output can be linked to computer-controlled systems to enable feedback-based control of a greenhouse environment. Today's agriculture requires an ability to precisely and rapidly assess the physiological stress status of plants in order to optimize crop yield.

Interval prediction of molecular properties in parametrized quantum chemistry.

The accurate evaluation of molecular properties lies at the core of predictive physical models. Most reliable quantum-chemical calculations are limited to smaller molecular systems while purely empirical approaches are limited in accuracy and reliability. A promising approach is to employ a quantum-mechanical formalism with simplifications and to compensate for the latter with parametrization.

Sensitivity analysis of uncertainty in model prediction.

Data Collaboration is a framework designed to make inferences from experimental observations in the context of an underlying model. In the prior studies, the methodology was applied to prediction on chemical kinetics models, consistency of a reaction system, and discrimination among competing reaction models. The present work advances Data Collaboration by developing sensitivity analysis of uncertainty in model prediction with respect to uncertainty in experimental observations and model parameters.

Model discrimination using data collaboration.

This paper introduces a practical data-driven method to discriminate among large-scale kinetic reaction models. The approach centers around a computable measure of model/data mismatch. We introduce two provably convergent algorithms that were developed to accommodate large ranges of uncertainty in the model parameters.