Physics-guided machine learning for sim-to-real calibration of NV diamond magnetometers

NV-diamond magnetometers are attractive because they can measure magnetic fields in unshielded environments, but they are hard to deploy outside the lab. The main bottleneck is calibration: real ODMR spectra are noisy, distorted by hardware non-idealities, and often do not match clean simulated data. Standard machine learning also struggles here because it needs lots of labeled data and tends to fail when synthetic training data do not look like real measurements.

The paper proposes a physics-guided hybrid machine learning framework for decoding ODMR spectra. Instead of treating the spectrum as just a generic input array, the model builds in the Zeeman relation that links resonance splitting to the magnetic field. That physical constraint is used during training to narrow the search space and stabilize learning.

To address the sim-to-real gap, the authors also use a hybrid data strategy. They start from a small number of real experimental spectra, fit baseline physical parameters, and then generate a much larger synthetic dataset that includes realistic non-idealities such as noise and asymmetry. This lets the network train on data that are closer to the experimental domain than idealized simulations alone.

On synthetic validation data, the physics-guided model converges much more reliably than a purely statistical neural network. The reported average error drops from 0.189 G for the stochastic baseline to 0.00142 G for the physics-guided model, and to 0.00051 G for the ensemble version. The authors summarize this as a 372-fold precision improvement over the baseline.

The hybrid model is then tested on 20 raw experimental ODMR spectra that were excluded from training. It predicts the longitudinal magnetic field with tight clustering around the ideal parity line, showing that the model can generalize to uncalibrated experimental data rather than only to clean simulations.