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

Abstract

We present a computational framework for model inversion based on multi-fidelity information fusion and Bayesian optimization. The proposed methodology targets the accurate construction of response surfaces in parameter space, and the efficient pursuit to identify global optima while keeping the number of expensive function evaluations at a minimum. We train families of correlated surrogates on available data using Gaussian processes and auto-regressive stochastic schemes, and exploit the resulting predictive posterior distributions within a Bayesian optimization setting. This enables a smart adaptive sampling procedure that uses the predictive posterior variance to balance the exploration versus exploitation trade-off, and is a key enabler for practical computations under limited budgets. The effectiveness of the proposed framework is tested on three parameter estimation problems. The first two involve the calibration of outflow boundary conditions of blood flow simulations in arterial bifurcations using multi-fidelity realizations of one-and three-dimensional models, whereas the last one aims to identify the forcing term that generated a particular solution to an elliptic partial differential equation.

Inverse problems in reduced order models of cardiovascular haemodynamics: aspects of data assimilation and heart rate variability

“…The inverse problem has been addressed in many previous studies, see for example [3][4][5][6][7][8][9][10][11][12][13][14][15][16] and [17,18] for their advantages and disadvantages. A recent Bayesian approach to parameter estimation in cardiovascular models is based on Markov chain Monte Carlo (MCMC) methods with mean or maximum target quantities [19].…”

A probabilistic framework for multidisciplinary design: Application to the hydrostructural optimization of supercavitating hydrofoils

“…The aforementioned workflow can be straightforwardly extended to handle cases involving data that originate from different information sources of variable fidelity. 8,11,18 For simplicity, here, we outline the process corresponding to two levels of fidelity, although this can be generalized to arbitrarily many levels. In a two-level multifidelity setting, we observe data…”

Harnessing Low-Fidelity Data to Accelerate Bayesian Optimization via Posterior Regularization

“…Techniques such as hierarchical partitioning [2], hierarchical modeling [3] and ensemble methods [4], are used to incorporate multiple fidelities/cheap approximations of the BOF. Most relevant to this paper is the line of work on Bayesian optimization with multifidelity data such as the MF-GP-UCB method in [5] and the multi-fidelity BO (MFBO) algorithm in [6]. Research topics that are close to MFBO in concept include multi-information source optimization [7,8], multi-task BO [9], multi-output GP [10,11], meta-learning based BO [12,13].…”

“…The success of the aforementioned methods requires specific assumptions to be satisfied. For instance, MFBO methods in [6,14,15] work under a basic assumption that the relationship between f (x) and f l (x) satisfies f (x) = ρf l (x) + n, where f l (x) denotes an LF approximation of f (x) and n a noise item. Extra operations or assumptions are usually needed to determine the value of the correlation parameter ρ.…”