PINNs Are Mesh-Free, Not Cost-Free
A lifecycle-accounting note on physics-informed neural networks, solver baselines, and the hidden cost of pretending inference time is the whole workflow.
Physics-informed neural networks are often presented as mesh-free, differentiable alternatives to classical solvers. The uncomfortable question is not whether they can make a persuasive contour plot. They can. The question is whether they improve the complete engineering workflow after accounting for formulation, training, failed runs, tuning, validation, reference data, and reuse.
This post argues for evaluating PINNs through lifecycle cost and validity region rather than trained-model inference alone. Comparing a trained neural surrogate to one solver call is not a comparison. It is accounting theater wearing a GPU badge.
The practical takeaway is to evaluate PINN workflows against strong numerical baselines across the full lifecycle: formulation, training, validation, reuse, and maintenance.