Beyond governing-equation residuals: verification and validation of physics-informed neural networks for forward structural-dynamic response prediction

Physics-informed neural networks are increasingly explored for forward structural-dynamic response prediction because governing mechanics can be embedded directly in learning. Satisfying those equations, however, does not establish that a predicted response is numerically reliable or physically credible. Structural dynamics impose further verification and validation (VandV) demands involving derivative-dependent engineering quantities, long-duration responses, frequency and modal behavior, changing operating conditions, and the provenance of the reference used for comparison. Existing PINN reviews identify many of these issues, but they have not provided a study-level audit of how the corresponding evidence is distributed across published forward structural dynamic studies. This Mini Review addresses that gap. Drawing on established computational mechanics VandV practice, we define four evidence dimensions: equation and numerical consistency, structural response verification, dynamic fidelity, and predictive scope with benchmark provenance. Each dimension is resolved into categories with explicit decision rules. These rules are then applied through a full-text review of a delimited study corpus. Each dimension is tied to measurable evidence and to a reporting chain connecting the quantity of interest, the error metric, the reference and its uncertainty, the intended-use tolerance, the observed error, and the resulting VandV conclusion. The resulting evidence map shows that validation coverage remains uneven and that evidence is rarely accumulated across dimensions within individual studies. Worked applications further show that the dimensions complement rather than substitute for one another. Credible forward structural-dynamics PINNs therefore require mechanics-relevant, purpose-specific validation beyond residual minimization or isolated agreement in displacement.