FHTW01 | Dr. Simone Pezzuto | Enabling high-dimensional uncertainty quantification

Описание: FHTW01 | Dr. Simone Pezzuto | Enabling high-dimensional uncertainty quantification for cardiac electrophysiology via multifidelity techniques

Speaker: Dr Simone Pezzuto (Università della Svizzera italiana)
Date: 5th Jun 2019 - 17:00 to 17:30
Venue: INI Seminar Room 1
Title: Enabling high-dimensional uncertainty quantification for cardiac electrophysiology via multifidelity techniques
Event: (FHTW01) Uncertainty quantification for cardiac models
Abstract: <span>
 <span>Mathematical
 modeling of the heart, as many other models in biomedical sciences, involves
 a large number of parameters and simplifying approximations. Uncertainties
 for cardiac models are ubiquitous, including anatomy, fiber direction, and
 electric and mechanical properties of the tissue. Hence, both UQ and
 parameter sensitivity naturally arise during modeling, and they shall become
 fundamental in view of clinical applications.<br>
 <br>
 For high-dimensional input uncertainties, e.g., substrate heterogeneity or
 cardiac fibers orientation, and high-dimensional output quantities of
 interest, e.g., the activation map, the method of choice for UQ is the
 classic Monte Carlo (MC) method. MC convergence rate does not suffer from the
 curse of dimensionality, but it is notoriously slow. While sampling a random
 field can be done very efficiently via the pivoted Cholesky decomposition,
 computing the cardiac activation from the bidomain equation is a
 computational demanding task. A single patient-tailored simulation can take
 several CPU-hours even on a large cluster. This makes uncertainty
 quantification (UQ) unfeasible, unless modeling reduction strategies are
 employed.<br>
 <br>
 One such strategy is represented by multifidelity methods [1]. A key ingredient
 of the multifidelity approach is the choice of low-fidelity models. Typical
 strategies are projection-based or data-fit surrogates, which however need to
 be trained anew for each patient and may become inefficient for a large
 dimensionality of the input, as in the case under consideration. Instead, a
 more physics-based approach is to take advantage of the natural hierarchy of
 available models. These include different cellular models for the monodomain
 equation, the time-independent eikonal equation, and the 1D geodesic point
 activation [2,3]. By exploiting statistical correlations in this hierarchy,
 we observed a reduction of the computational cost by at least two orders of
 magnitude, enabling to perform a full analysis within a reasonable time
 frame. Moreover, we incorporate Bayesian techniques, which provide confidence
 intervals and full probability distributions at selected points, thus
 augmenting the information provided by standard frequentist approaches.
 <br>
 <br>
 References:<br>
 [1] Peherstorfer, B., Willcox, K., & Gunzburger, M. (2018). Survey of
 multifidelity methods in uncertainty propagation, inference, and
 optimization. SIAM Review, 60(3), 550-591.<br>
 [2] Quaglino, A., Pezzuto, S., Koutsourelakis, P.S., Auricchio, A., Krause,
 R. (2018). Fast uncertainty quantification of activation sequences in
 patient-specific cardiac electrophysiology meeting clinical time constraints.
 Int J Numer Meth Biomed Engng, e2985.<br>
 [3] Quaglino, A., Pezzuto, S., Krause, R. (2018). Generalized Multifidelity
 Monte Carlo Estimators. Submitted to J Comp Phys. ArXiv: 1807.10521</span></span>

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