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Physics-constrained Deep Learning for High-dimensional Predictive Modeling

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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, which enables medical scientists to monitor and detect abnormal cardiac conditions. However, the high-dimensional sensing data are generally complexly structured with a high level of uncertainty. Realizing the full data potential depends greatly on advanced analytical and predictive methods. Our work presents a physics-constrained deep learning (P-DL) framework for high-dimensional predictive 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 electrocardiogram (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 commonly used in current practice.



Jianxin Xie








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