A Probabilistic Approach to Robust Optimal Experiment Design with Chance Constraints

TL;DR

This paper introduces a probabilistic robust optimal experiment design method for nonlinear systems, incorporating chance constraints and polynomial chaos for uncertainty propagation, demonstrated on a biological signaling pathway.

Contribution

It develops a novel robust OED framework that handles probabilistic uncertainties and constraints systematically using polynomial chaos expansion.

Findings

Effective handling of probabilistic uncertainties in experiment design.

Successful application to biological signaling pathway modeling.

Enhanced constraint satisfaction under uncertainty.

Abstract

Accurate estimation of parameters is paramount in developing high-fidelity models for complex dynamical systems. Model-based optimal experiment design (OED) approaches enable systematic design of dynamic experiments to generate input-output data sets with high information content for parameter estimation. Standard OED approaches however face two challenges: (i) experiment design under incomplete system information due to unknown true parameters, which usually requires many iterations of OED; (ii) incapability of systematically accounting for the inherent uncertainties of complex systems, which can lead to diminished effectiveness of the designed optimal excitation signal as well as violation of system constraints. This paper presents a robust OED approach for nonlinear systems with arbitrarily-shaped time-invariant probabilistic uncertainties. Polynomial chaos is used for efficient uncertainty propagation. The distinct feature of the robust OED approach is the inclusion of chance constraints to ensure constraint satisfaction in a stochastic setting. The presented approach is demonstrated by optimal experimental design for the JAK-STAT5 signaling pathway that regulates various cellular processes in a biological cell.