Sam Siavoshian

Constrained Diffusion for Orbital Monte Carlo

Constrained Diffusion for Data-Scarce Orbital Monte Carlo in Constellation Tasking

Second author, with Johns Hopkins. Preprint on arXiv:2610.09323, DOI 10.48550/arXiv.2610.09323. Under review, IEEE Aerospace Conference 2027. PDF. Other papers.

Heatmap of shifted-blind trajectory MMD by force tier and generator. Degree-8 gravity with drag is the hardest tier for every model.
Figure 4. Shifted-blind trajectory MMD by force tier and generator. Degree-8 gravity with drag is the hardest tier for every model. No cell passes its permutation equality test.

Abstract

Constellation Monte Carlo results depend on the orbital population used to evaluate a tasking policy. With scarce reference trajectories, replay limits geometric diversity, while independent orbital-element jitter can violate physical constraints. We study constrained diffusion for orbital-population augmentation. A force-conditioned diffusion model learns a 13-dimensional orbital prior, recovering semimajor axis from perigee altitude and eccentricity; Basilisk propagates each sample under one of five force-model tiers. Using 800 reference trajectories, we compare diffusion with jittered bootstrap, per-tier Gaussian mixtures, and a conditional variational autoencoder, and evaluate distributional fidelity, support shift, classical astrodynamics diagnostics, and 4,000 paired GoDSAT-compatible campaigns. The largest diffusion model achieves held-out trajectory MMD of 0.0171 ± 0.0239, similar to bootstrap (0.0170) and the mixture (0.0198), but samples farther from training priors (median nearest-training distance 2.7 versus 0.10 standardized units). All generators fail to match the shifted-blind population (classifier AUC 0.991–0.998). Endpoint-conditioned samples satisfy Lambert boundaries but have greater interior error than the matched Lambert reference (29.2 versus 5.7 km mean RMSE). Residual diffusion improves selected sparse forecasts and catalog-mode recall but does not outperform classical estimators on custody ranking. In a fixed 16-satellite configuration, diffusion yields similar mean custody to replay and bootstrap, while the force-tier mixture shifts custody by about 5.5 percentage points. Constrained diffusion supports local, in-support augmentation but cannot replace orbital dynamics or serve as an operational posterior. Orbital-population construction is a consequential source of uncertainty in constellation analysis.

Cite

APA

Ramadan, O., Siavoshian, S., Saeed, A. K., Johnson, B. A., Diab, A. M. E.-A., & Rodriguez, B. M. (2026). Constrained diffusion for data-scarce orbital Monte Carlo in constellation tasking (arXiv:2610.09323). arXiv. https://doi.org/10.48550/arXiv.2610.09323

BibTeX
@misc{ramadan2026constrained,
  title         = {Constrained Diffusion for Data-Scarce Orbital {Monte Carlo} in Constellation Tasking},
  author        = {Ramadan, Omar and Siavoshian, Sam and Saeed, Amir Kashif and Johnson, Benjamin A. and Diab, Amin Mohamed El-Amin and Rodriguez, Benjamin M.},
  year          = {2026},
  eprint        = {2610.09323},
  archivePrefix = {arXiv},
  primaryClass  = {astro-ph.IM},
  doi           = {10.48550/arXiv.2610.09323},
  url           = {https://arxiv.org/abs/2610.09323}
}