# Optimistic vs Pessimistic Uncertainty Model Unfalsification

## TL;DR

This paper introduces a data-driven method to unfalsify uncertainty models by finding minimal or maximal bounds consistent with observed input-output data, using optimistic and pessimistic approaches.

## Contribution

It develops a novel dual framework for uncertainty unfalsification, including a semi-infinite programming solution for the pessimistic approach.

## Key findings

- The pessimistic approach is formulated as a semi-infinite program.
- The optimistic and pessimistic methods are mathematically dual.
- Both approaches successfully tested on uncertain linear models with simulated data.

## Abstract

We present a novel, input-output data-driven approach to uncertainty model identification. As the true bounds and distributions of system uncertainties ultimately remain unknown, we depart from the goal of identifying the uncertainty model and instead look for minimal concrete statements that can be made based on an uncertain system model and available input-output data. We refer to this as unfalsifying an uncertainty model. Two different unfalsification approaches are taken. The optimistic approach determines the smallest uncertainties that could explain the given data, while the pessimistic approach finds the largest possible uncertainties suggested by the data. The pessimistic problem is revealed to be a semi-infinite program, which is solved using the local reduction algorithm. It is also shown that the optimistic and pessimistic approaches to uncertainty model unfalsification are mathematical duals. Finally, both approaches are tested using an uncertain linear model with data from a simulated nonlinear system.