ParetoEnsembles.jl: A Julia Package for Multiobjective Parameter Estimation Using Pareto Optimal Ensemble Techniques
2026-03-31 • Mathematical Software
Mathematical Software
AI summaryⓘ
The authors present ParetoEnsembles.jl, a free Julia software tool that helps find many good sets of parameters for complex models instead of just one best set. Their method uses a technique called Pareto Optimal Ensemble Techniques (POETs), which efficiently explores trade-offs between multiple goals without needing gradient information. They improved the algorithm's speed and accuracy and tested it on biological models, showing it can predict important results well even if some parameters are uncertain. Their work aims to make it easier for scientists to understand uncertainties in mathematical models.
Pareto optimalitysimulated annealingparameter estimationmechanistic modelingensemble methodsJulia programming languagemulti-objective optimizationmodel uncertaintyparameter identifiabilitycell-free gene expression
Authors
Jeffrey D. Varner
Abstract
Mathematical models of natural and man-made systems often have many adjustable parameters that must be estimated from multiple, potentially conflicting datasets. Rather than reporting a single best-fit parameter vector, it is often more informative to generate an ensemble of parameter sets that collectively map out the trade-offs among competing objectives. This paper presents ParetoEnsembles.jl, an open-source Julia package that generates such ensembles using Pareto Optimal Ensemble Techniques (POETs), a simulated-annealing-based algorithm that requires no gradient information. The implementation corrects the original dominance relation from weak to strict Pareto dominance, reduces the per-iteration ranking cost from $O(n^2 m)$ to $O(nm)$ through an incremental update scheme, and adds multi-chain parallel execution for improved front coverage. We demonstrate the package on a cell-free gene expression model fitted to experimental data and a blood coagulation cascade model with ten estimated rate constants and three objectives. A controlled synthetic-data study reveals parameter identifiability structure, with individual rate constants off by several-fold yet model predictions accurate to 7%. A five-replicate coverage analysis confirms that timing features are reliably covered while peak amplitude is systematically overconfident. Validation against published experimental thrombin generation data demonstrates that the ensemble predicts held-out conditions to within 10% despite inherent model approximation error. By making ensemble generation lightweight and accessible, ParetoEnsembles.jl aims to lower the barrier to routine uncertainty characterization in mechanistic modeling.