Comparison of representative numerical performance reported in the literature for conventional PDE solvers and the proposed PINN framework
| Method | Source | Relative error (%) | Computational time | Remarks |
|---|---|---|---|---|
| Finite Difference Method (FDM) | LeVeque (2007), Crank (1979), Hundsdorfer et al. (2003) | 0.5–1.2 | Moderate | Simple implementation but mesh-dependent |
| Classical Finite Element Method (FEM) | Frittelli and Sgura (2024), Donea and Huerta (2003), Nie and Thomée (1985) | 0.2–0.5 | Moderate–High | High numerical accuracy with increased computational cost |
| Adaptive Space–Time FEM (STFEM) | Li and Ge (2025) | <0.2 | High | Adaptive mesh refinement further improves numerical accuracy |
| Proposed PINN (Present work) | This study | 0.18 | Fast inference after training | Mesh-free, physics-constrained prediction with simultaneous parameter identification |
| Method | Source | Relative error (%) | Computational time | Remarks |
|---|---|---|---|---|
| Finite Difference Method (FDM) | 0.5–1.2 | Moderate | Simple implementation but mesh-dependent | |
| Classical Finite Element Method (FEM) | 0.2–0.5 | Moderate–High | High numerical accuracy with increased computational cost | |
| Adaptive Space–Time FEM (STFEM) | <0.2 | High | Adaptive mesh refinement further improves numerical accuracy | |
| This study | Mesh-free, physics-constrained prediction with simultaneous parameter identification |
Note(s): The FDM and FEM values represent typical accuracy ranges reported for reaction–diffusion problems rather than direct simulations performed in this study
Sharing content requires targeting cookies to be enabled. Please update your cookie preferences to use this feature.