  The rapid developments in advanced sensing and imaging bring about a
data-rich environment, facilitating the effective modeling, monitoring, and
control of complex systems. For example, the body-sensor network captures
multi-channel information pertinent to the electrical activity of the heart
(i.e., electrocardiograms (ECG)), which enables medical scientists to monitor
and detect abnormal cardiac conditions. However, the high-dimensional sensing
data are generally complexly structured and realizing the full data potential
depends to a great extent on advanced analytical and predictive methods. This
paper presents a physics-constrained deep learning (P-DL) framework for
high-dimensional inverse ECG modeling. This method integrates the physical laws
of the complex system with the advanced deep learning infrastructure for
effective prediction of the system dynamics. The proposed P-DL approach is
implemented to solve the inverse ECG model and predict the time-varying
distribution of electric potentials in the heart from the ECG data measured by
the body-surface sensor network. Experimental results show that the proposed
P-DL method significantly outperforms existing methods that are commonly used
in current practice.
