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P. 189

Machine learning methods for

robust parameter estimation

Dominik Neumann, Tommaso Mansi
Siemens Healthineers, Princeton, NJ, United States

5.1 Introduction
Individualizing computational models with patient data is a
critical step for clinical applications. The goal consists in estimat-
ing the parameters x of a forward model f such that observable
output variables of the model, denoted y, match clinical observa-
tions z (Fig. 5.1). For instance, when the model f simulates cardiac
electrophysiology (as described in section 1.2), the parameters x
are the electrical conductivities, action potential durations, and
other parameters associated to the cellular model of action po-
tentials. The output y is the electrocardiograms (ECG) and related
parameters, local activation times, etc., which can be measured
using ECG or cardiac mapping devices. Contrary to the forward
model, the inverse model infers the model parameters x from clin-
ical measurements z [377].
A large variety of model personalization algorithms have been
proposed in the last decades. Most methods follow a similar strat-
egy: they iteratively try to ﬁnd the parameter values ˆ x that min-
imize the misﬁt between model output and measurements. In
other words, estimating model parameters is traditionally posed
as an optimization problem, where one seeks to optimize an ob-
jective c deﬁned as the misﬁt between the computed y and mea-
sured z parameters: ˆ x = argmin c (y,z). The estimation is consid-
x
ered successful if a convergence criterion is met, e.g. |c| < ψ where
ψ is a deﬁned threshold. Different optimization techniques have
been proposed, for instance variational techniques, trust region
methods or highly engineered procedures [378,193,379].
Unfortunately, these techniques can suffer from large compu-
tational burden, low robustness and lack of accuracy, due to pa-
rameter ambiguity, data noise and local minima [201,26,82]. The
need for a robust algorithm that works on larger populations [6,
195,380] often leads to more complex methods, which may com-
bine numerous highly engineered optimizers. Typically, the de-

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