  Objective: This paper proposes an neural network approach for predicting
heart surface potentials (HSPs) from body surface potentials (BSPs), which
reframes the traditional inverse problem of electrocardiography into a
regression problem through the use of Gaussian 3D (G3D) basis function
decomposition. Methods: HSPs were generated using G3D basis functions and
passed through a boundary element forward model to obtain corresponding BSPs.
The generated BSPs (input) and HSPs (output) were used to train a neural
network, which was then used to predict a variety of synthesized and decomposed
real-world HSPs. Results: Fitted G3D basis function parameters can accurately
reconstruct the real-world left ventricular paced recording with percent root
mean squared error (RMSE) of $1.34 \pm 1.30$%. The basis data trained neural
network was able to predict G3D basis function synthesized data with RMSE of
$8.46 \pm 1.55$%, and G3D representation of real-world data with RMSE of $18.5
\pm 5.25$%. Activation map produced from the predicted time series had a RMSE
of 17.0% and mean absolute difference of $10.3 \pm 10.8$ms when compared to
that produced from the actual left ventricular paced recording. Conclusion: A
Gaussian basis function based data driven model for re-framing the inverse
problem of electrocardiography as a regression problem is successful and
produces promising time series and activation map predictions of real-world
recordings even when only trained using Guassian data. Significance: The HSPs
predicted by the neural network can be used to create activation maps to
identify cardiac dysfunctions during clinical assessment.
