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 |