A physics-informed neural network that solves the groundwater diffusion PDE by automatic differentiation and inverts it to recover unreported well pumping rates from sparse sensor data. Validated the forward solver to 0.91% relative L2 error against the analytical Theis solution, and recovered spatially varying depletion rates at 5.15% error on synthetic benchmarks. Held-out spatial validation on unseen Ogallala aquifer wells exposed overfitting; the published model card reports the true 38.3% holdout error and the model's intended-use limits honestly rather than only the best-case numbers. Served behind a FastAPI inference API with a Next.js and Leaflet frontend, containerized with Docker Compose.