Validating Predictions of Unobserved Quantities

TL;DR

This paper proposes a validation framework for computational models to reliably predict unobserved quantities, especially in extrapolative scenarios, by incorporating uncertainty quantification and testing with a nonlinear oscillator example.

Contribution

It introduces a comprehensive validation and predictive assessment process that accounts for known sources of error in models, enhancing the reliability of extrapolative predictions.

Findings

Validated the methodology on a nonlinear oscillator example.

Demonstrated improved confidence in unobserved QoI predictions.

Provided a structured approach for model validation beyond observed data.

Abstract

The ultimate purpose of most computational models is to make predictions, commonly in support of some decision-making process (e.g., for design or operation of some system). The quantities that need to be predicted (the quantities of interest or QoIs) are generally not experimentally observable before the prediction, since otherwise no prediction would be needed. Assessing the validity of such extrapolative predictions, which is critical to informed decision-making, is challenging. In classical approaches to validation, model outputs for observed quantities are compared to observations to determine if they are consistent. By itself, this consistency only ensures that the model can predict the observed quantities under the conditions of the observations. This limitation dramatically reduces the utility of the validation effort for decision making because it implies nothing about predictions of unobserved QoIs or for scenarios outside of the range of observations. However, there is no agreement in the scientific community today regarding best practices for validation of extrapolative predictions made using computational models. The purpose of this paper is to propose and explore a validation and predictive assessment process that supports extrapolative predictions for models with known sources of error. The process includes stochastic modeling, calibration, validation, and predictive assessment phases where representations of known sources of uncertainty and error are built, informed, and tested. The proposed methodology is applied to an illustrative extrapolation problem involving a misspecified nonlinear oscillator.