Model inversion via multi-fidelity Bayesian optimization: a new paradigm for parameter estimation in haemodynamics,...

Area of Science:

• Computational Science
• Applied Mathematics
• Optimization

Background:

• Model inversion is computationally intensive, often requiring numerous function evaluations.
• Multi-fidelity data offers a cost-effective way to improve model accuracy.
• Bayesian optimization is effective for global optimization but can be sample-inefficient.

Purpose of the Study:

• To develop a computational framework for efficient model inversion.
• To accurately construct response surfaces in parameter space.
• To efficiently identify global optima with minimal function evaluations.

Main Methods:

• Multi-fidelity information fusion using correlated Gaussian process surrogates.
• Auto-regressive stochastic schemes for surrogate training.
• Bayesian optimization leveraging predictive posterior distributions for adaptive sampling.

Main Results:

• The framework successfully calibrates parameters in blood flow simulations and solves an elliptic partial differential equation.
• Demonstrated effective balancing of exploration-exploitation trade-off using predictive posterior variance.
• Achieved accurate response surface construction and efficient global optimum identification.

Conclusions:

• The proposed framework enables practical model inversion under limited computational budgets.
• Multi-fidelity data fusion significantly enhances the efficiency and accuracy of Bayesian optimization.
• The methodology is broadly applicable to parameter estimation problems in various scientific domains.