Table 4.

PDE models’ properties in PINNs analysis of physiological signals.

Field	Model	No. of PDE/ODE	No. of Vars	Domain Dimension	Boundary conditions
Electrophysiology	Eikonal (Sahli et al 2020, Grandits et al 2021, Jiang et al 2024)	1 PDE	2 & 3	2D & 3D	N/A
	State-Space (Jiang et al 2024)	Neural ODEs	64	3D	N/A
	Aliev–Panfilov (Herrero et al 2022, Xie and Yao 2022a, 2022b, Chiu et al 2024)	1 ODE + 1 PDE	4	1-D & 2D & 3D	Neumman
	Fenton–Karma (Sahli et al 2020, Chiu et al 2024)	2 ODEs + 1 PDE	4	2D & 3D	Neumman
	Mitchell–Schaeffer (Kashtanova et al 2021, Kashtanova et al 2022a)	2 ODEs	3 & 4	2D & 3D	N/A
	Hodgkin–Huxley (Ferrante et al 2022, Yao et al 2023)	4 ODEs	5	1-D	N/A
	FitzHugh–Nagumo (Rudi et al 2020, Ferrante et al 2022)	2 ODEs	3	1-D	N/A
Muscle Electro- mechanics	Hill-type model (Taneja et al 2022, Zhang et al 2022, Ma et al 2024)	2 ODEs	3	1-D	N/A
	Twitch force model (Li et al 2022)	1 ODE	no. of MUs	1-D	N/A
Hemodynamics	Navier–Stokes + Windkessel (Li et al 2024)	2 PDEs	3	1-D	Windkessel
	Navier–Stokes + continuity (Arzani 2021, Du et al 2023, Moser 2023, Isaev et al 2024b, Sautory and Shadden 2024, Maidu et al 2025)	3 PDEs	8	1-D & 2D & 3D	Dirichlet & Neumman
	Navier–Stokes + Laplace (Kissas et al 2020)	2 PDEs	5	4D	Windkessel
	Burger + KdV (Bhaumik et al 2024)	2 PDEs	3	1-D	Neumman
	Linearized Navier–Stokes (Liang et al 2023)	2 PDEs	4	1-D	Dirichlet

‘N/A’ indicates that either no boundary condition is applied in the model or the paper does not explicitly provide information about the boundary condition.