Parameter Estimation and Modeling in Dynamic Systems

Parameter estimation and modelling in dynamic systems underpin the quantitative description, analysis and control of processes that evolve over time. Such systems span chemical reactors, biological cultures, environmental processes and engineered devices. A mathematical model typically comprises ordinary or partial differential equations whose structure is derived from first principles, such as mass and energy balances, or from phenomenological relationships. Parameters within these models—rate constants, transfer coefficients, interaction strengths—are seldom known a priori and must be inferred from experimental or operational data. Accurate estimation is challenged by measurement noise, limited observability, structural uncertainty and correlations among parameters. To address these challenges, a rich toolkit has emerged, combining classical optimisation techniques, sensitivity and identifiability analyses, Bayesian inference, regularisation and hybrid data‐driven methods. Robust parameterisation supports reliable prediction, uncertainty quantification and real‐time control, enabling the deployment of digital twins, optimised experimental design and adaptive process management across disciplines.

Research from Nature Portfolio

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Research from all publishers

Recent advances from other sources illustrate the blend of first-principles and data-based strategies, rigorous identifiability frameworks and computational improvements. Hybrid AI modelling techniques for pilot-scale bubble column aeration have combined species conservation balances with machine-learning components for mass-transfer coefficients, highlighting trade-offs between interpretability and accuracy and introducing symbolic regression to yield transparent, high-performance models. A framework for model reliability and estimability analysis applied to crystallisation with multi-impurity, multi-dimensional population balance models has demonstrated systematic orthogonalisation and global‐sensitivity methods to select an optimal subset of parameters, ensuring reliable prediction despite noisy and correlated data. In dynamic multistage processes such as reactive distillation columns, a multiple-shooting approach integrated with sensitivity analysis segments the operating trajectory and preselects the most influential parameters per segment, reducing computational burden and improving convergence to global optima.

Parameter Estimation and Modeling in Dynamic Systems publication trend

The graph below shows the total number of articles in parameter estimation and modeling in dynamic systems across all publications each year (not limited to Nature Index journals).

Technical terms

Dynamic system: A mathematical representation of a process whose state evolves over time according to differential or difference equations.

Parameter estimation: The procedure of calibrating model parameters so that simulated outputs align with observed data.

Identifiability: The property determining whether unique parameter values can be recovered from available measurements.

Sensitivity analysis: The quantification of how variations in parameters influence model outputs.

Bayesian estimation: An inference framework that combines prior information with data likelihood to obtain parameter probability distributions.

Multiple shooting: A numerical technique that divides a time horizon into segments to improve stability and convergence in parameter fitting for dynamic models.

References

1. Hybrid AI modeling techniques for pilot scale bubble column aeration: A comparative study. Computers & Chemical Engineering (2024).
2. A framework for model reliability and estimability analysis of crystallization processes with multi-impurity multi-dimensional population balance models. Computers & Chemical Engineering (2019).
3. Parameter Estimation for Multistage Processes: A Multiple Shooting Approach Integrated with Sensitivity Analysis. Industrial & Engineering Chemistry Research (2024).