PDE-constrained structural correction: A physics-informed mechanism for mismatched ODEs in coupled systems

Coupled partial differential equation–ordinary differential equation (PDE–ODE) systems arise in many physical, biological, and engineering applications, where parameter mismatches in the ODE subsystem can substantially degrade state reconstruction. This work investigates whether accurate PDE constraints can structurally correct mismatched ODE dynamics during joint optimization. We develop a PDE-constrained physics-informed neural network (PINN) framework with a multi-component loss that enables systematic control of the relative influence of PDE and ODE constraints. Theoretical analysis shows that minimization of the PDE residual can provide a global regularization effect through the coupling between the PDE and ODE states. Numerical experiments and ablation studies further demonstrate that dense PDE constraints generate a strong optimization signal that can counteract the influence of a mismatched ODE model and guide the inferred ODE trajectory toward the ground truth. For the three tested parameter offsets ( 𝛿 ⁢ 𝜇 = 0 . 1 –0.3, corresponding to relative deviations of 12.5%–37.5%), the proposed framework reduces the state reconstruction error by an average of 48.6% compared with direct integration of the mismatched ODE. These results indicate that partially accurate physical knowledge can compensate for model mismatch in coupled systems and provide a useful perspective for inverse problems and system identification.