Table 6.

Summary of the results for PINNs in cardiac electrophysiology.

Article	Objective	Signal characteristics	Error metrics
Sahli et al (2020)	Cardiac activation mapping	In silico data	RMSE
Grandits et al (2021)	Estimate heart conductivity tensor	In silico data; In vivo electroanatomical maps (EAMs)	RMSE
Herrero et al (2022)	Electrophysiological tissue parameters estimation	In silico data; In vitro data	RMSE
Xie and Yao (2022a, 2022b)	Spatiotemporal cardiac electrodynamics modeling	In silico data	RE
Tenderini et al (2022)	Epicardial potentials and activation maps estimation	In silico data	Relative L1-norm error
Kashtanova et al (2022b)	Cardiac electrophysiology dynamics forecasting	In silico data; Ex vivo optical mapping data	MSE
Kashtanova et al (2023)	Cardiac electrophysiology dynamics forecasting	Ex vivo data	MSE
Yao et al (2023)	Ion channels dynamics prediction	In silico data; Real measure membrane potential dataset	RMSE; Pearson coefficient
Nazaret et al (2023)	Heart rate (HR) response prediction	In vivo ECG data	MAE
Xie (2023)	Inverse ECG modeling	In silico data; Body surface potential mapping (BSPM) data	MSE; RE; Correlation coefficient (CC)
Chiu et al (2024)	Drug effects on cardiac electrophysiology	In vitro optimal mapping images	RMSE; RE
Chiu et al (2024)	Cardiac electrophysiology dynamics forecasting with complex geometries and dynamic regimes	In silico data	RMSE
Jiang et al (2024)	Electrocardiographic imaging	In silico data; In vivo data	MSE
Jiang et al (2024)	Cardiac electrophysiology dynamics forecasting	In silico data	MSE
Kuang et al (2024)	Create patient-specific digital twins using non-invasive echocardiography data	In silico pressure-volume data; In vivo echocardiography	MAE
Motiwale et al (2024)	High speed cardiac mechanics simulations	Random in silico data in space	ME

Definitions of RMSE, MSE, MAE, ME and RE can be found in table 2.