POETs

POETs estimates parameter and model ensembles using constrained multiobjective optimization to quantify uncertainty and improve robustness of deterministic mathematical models.

Key Features:

• Multiobjective optimization: Implements a Pareto Optimal Ensemble Technique that integrates simulated annealing with Pareto optimality to identify ensembles on or near the tradeoff surface between competing training objectives.
• Implementation: Developed in the Julia programming language.
• Computational efficiency: Identifies optimal or near-optimal solutions approximately six times faster than a corresponding Octave implementation on evaluated test functions.
• Problem versatility: Handles mixed binary and continuous variable problems, bilevel optimization, and constrained scenarios without modifications to the core algorithm.
• Ensemble selection and uncertainty quantification: Selects parameter ensembles based on simulation error and criteria such as diversity or steady-state performance and uses ensemble simulation to estimate confidence intervals for model variables.
• Handling conflicting objectives: Generates parameter ensembles that balance conflicting training objectives and can reconcile tradeoffs across multiple datasets.

Scientific Applications:

• Multiobjective benchmark problems: Applied to suites of multiobjective test functions with parameter bounds and system constraints to identify Pareto-optimal ensembles.
• Biochemical model calibration: Demonstrated on a proof-of-concept biochemical model with four conflicting training objectives, producing ensembles that matched the mean of training data while performing well on individual objectives.
• Uncertainty quantification in deterministic models: Used to estimate confidence intervals and robustly constrain predictions when parameters are poorly constrained.

Methodology:

Integrates simulated annealing with Pareto optimality for constrained multiobjective optimization, selects ensembles based on simulation error and metrics such as diversity or steady-state performance, and simulates ensembles to estimate confidence intervals for model variables.