Table 5.

PDE models’ applications in PINNs analysis of physiological signals.

Field	Model	Focus	Type of problem	Type of data	Output
Electrophysiology	Eikonal (Sahli et al 2020, Grandits et al 2021, Jiang et al 2024)	Spatial mapping	Forward	In silico data	Activation maps
	State-Space (Jiang et al 2024)	Spatial mapping	Forward	In silico data; In vivo data	ECGI
	Aliev–Panfilov (Herrero et al 2022, Xie and Yao 2022a, 2022b, Chiu et al 2024)	Spatial-temporal evolution	Forward; Inverse; Forward & Inverse	In silico data	Activation maps + ECGI
	Fenton–Karma (Sahli et al 2020, Chiu et al 2024)	Spatial-temporal evolution	Inverse;Forward & Inverse	In silico data	Activation maps
	Mitchell–Schaeffer (Kashtanova et al 2021, Kashtanova et al 2022a)	Spatial-temporal evolution	Forward; Forward & Inverse	In silico data	Activation maps
	Hodgkin–Huxley (Ferrante et al 2022, Yao et al 2023)	Time series prediction	Inverse	In silico data	Neuron action potential
	FitzHugh–Nagumo (Rudi et al 2020, Ferrante et al 2022)	Time series prediction	Inverse	In silico data	Neuron action potential
Muscle Electro- mechanics	Hill-type model (Taneja et al 2022, Zhang et al 2022, Ma et al 2024)	Time series prediction	Forward	In vivo data	Muscle force
	Twitch force model (Li et al 2022)	Time series prediction	Forward	In vivo data	Muscle force
Hemodynamics	Navier–Stokes + Windkessel (Li et al 2024)	Time series prediction	Forward & Inverse	In vivo data	Blood pressure
	Navier–Stokes + continuity (Arzani 2021, Du et al 2023, Moser 2023, Isaev et al 2024b, Sautory and Shadden 2024, Maidu et al 2025)	Spatial mapping	Forward	In silico data	Blood pressure
	Navier–Stokes + Laplace (Kissas et al 2020)	Time series prediction	Forward	In vivo data	Blood pressure
	Burger + KdV (Bhaumik et al 2024)	Spatial-temporal evolution	Forward	In silico data	Blood pressure + velocity
	Linearized Navier–Stokes (Liang et al 2023)	Spatial-temporal evolution	Inverse	In silico data	Blood pressure