An autonomous underwater vehicle navigating without GPS accumulates positioning error at roughly 0.1 to 1 percent of distance traveled — sometimes more. The error compounds because inertial sensors measure acceleration, and position is obtained by double integration. Any bias in the accelerometer, however small, grows quadratically with time. After ten minutes of pure inertial navigation, you may be meters from where you think you are. After an hour, the error can be catastrophic.

PiDR — Physics-Informed Dead Reckoning — addresses this drift by embedding Newtonian mechanics directly into the neural network architecture rather than treating the physics as an implicit pattern for the network to discover. The framework achieves more than 29 percent positioning improvement on real-world datasets from both a mobile robot and an autonomous underwater vehicle. The key design choice is a physics-informed residual component: the network learns to correct the residual between what Newtonian mechanics predicts and what the noisy sensors actually report, rather than learning the entire trajectory from raw data.

This distinction matters because conventional deep-learning approaches to inertial navigation function as black boxes — they can fit training data well but struggle to generalize across platforms, dynamics, and environments. By giving the network the physics for free and asking it only to learn the corrections, PiDR produces a lightweight architecture that transfers between a wheeled robot indoors and a submersible underwater without retraining.

The through-claim extends to any sensing domain where the underlying physics is well understood but sensor noise is not. When you know the equations of motion, forcing the model to rediscover them from data wastes capacity and invites overfitting. Encoding the known physics and learning only the residual error separates what is universal from what is contingent — and the contingent part is always smaller.