For high-dimensio nal input uncertainties\, e.g.\, substrate heterog eneity or cardiac fibers orientation\, and high- dimensional output quantities of interest\, e.g. \, the activation map\, the method of choice for U Q is the classic Monte Carlo (MC) method. MC con vergence rate does not suffer from the curse of dimensionality\, but it is notoriously slow. While sampling a random field can be done very effici ently via the pivoted Cholesky decomposition\, c omputing the cardiac activation from the bidomain equation is a computational demanding task. A si ngle patient-tailored simulation can take severa l CPU-hours even on a large cluster. This makes un certainty quantification (UQ) unfeasible\, unles s modeling reduction strategies are employed.

One such strategy is represented by multifidelity methods [1]. A key ingredient of the multifidelity approach is the choice of low-fi delity models. Typical strategies are projection -based or data-fit surrogates\, which however need to be trained anew for each patient and may bec ome inefficient for a large dimensionality of th e input\, as in the case under consideration. Inst ead\, a more physics-based approach is to take a dvantage of the natural hierarchy of available m odels. These include different cellular models for the monodomain equation\, the time-independent eikonal equation\, and the 1D geodesic point act ivation [2\,3]. By exploiting statistical correlat ions in this hierarchy\, we observed a reduction of the computational cost by at least two orders of magnitude\, enabling to perform a full analys is within a reasonable time frame. Moreover\, we incorporate Bayesian techniques\, which provide c onfidence intervals and full probability distrib utions at selected points\, thus augmenting the information provided by standard frequentist appro aches.

References:

[1] Peherstorfer\, B.\, Willcox\, K.\, &\; Gunzbur ger\, M. (2018). Survey of multifidelity methods in uncertainty propagation\, inference\, and op timization. SIAM Review\, 60(3)\, 550-591.

[2] Quaglino\, A.\, Pezzuto\, S.\, Koutsourelakis \, P.S.\, Auricchio\, A.\, Krause\, R. (2018). F ast uncertainty quantification of activation seque nces in patient-specific cardiac electrophysiolo gy meeting clinical time constraints. Int J Nume r Meth Biomed Engng\, e2985.

[3] Quaglino\ , A.\, Pezzuto\, S.\, Krause\, R. (2018). Generali zed Multifidelity Monte Carlo Estimators. Submit ted to J Comp Phys. ArXiv: 1807.10521 LOCATION:Seminar Room 1\, Newton Institute CONTACT:info@newton.ac.uk END:VEVENT END:VCALENDAR