Coarse grids, accurate physics: Mitigating discretization error in fast-ion distribution function inference

Solving inverse problems in physics relies on discretized computational models to connect physical parameters to experimental data. Fast-ion distribution function inference typically uses coarse computational grids (e.g., $30 \times 30$ for velocity-space inference or $15\times 15 \times 15$ for orbit-space inference) for computational efficiency, introducing significant discretization errors that are conventionally ignored. This work demonstrates that explicitly modeling the statistics of discretization error through approximation error modeling\textemdash treating the discretization error as a random variable with estimated mean and covariance\textemdash significantly improves inferred distribution accuracy. Applied to synthetic fast-ion D-alpha data for a DIII-D scenario using a TRANSP/NUBEAM simulation of a 65 keV deuterium neutral beam, the approach captures significantly more physical detail, including accurate beam injection features and pitch-angle scattering effects that are lost with conventional approaches. The method easily integrates into existing inference algorithms by augmenting the measurement covariance matrix with the estimated discretization error covariance. We recommend that practitioners incorporate this approximation error modeling approach in all fast-ion distribution function inference applications.

Work supported by US DOE under DE-SC0020337, DE-FG02-06ER54867 and DE-FC02-04ER54698.