gmtorch: Computing with Gaussian Mixture Uncertainty in PyTorch

Gaussian mixture models (GMMs) can represent multimodal, non-Gaussian uncertainty while retaining analytical structure. Scientific workflows, however, require more than fitting a mixture to observations: uncertain quantities must remain available for subsequent transformations, arithmetic, conditioning, and information combination. We present \textsc{gmtorch}, a \textsc{PyTorch} framework for computing with GMM-represented uncertain scalar and vector quantities. Mixtures may be constructed from parameters or estimated from data; every mixture-valued result remains a complete distribution that can be evaluated, sampled, summarized, conditioned, or used in a subsequent calculation. Marginalization, conditioning, affine maps, sums and differences under independence, and normalized density products are evaluated analytically and can be composed with assumptions made explicit by the selected operations and with component counts tracked. When nonlinear maps leave the finite-GMM family, or exact operations produce impractically many components, the framework provides explicit sample--transform--refit propagation and mixture reduction. Full-covariance computations use Cholesky-based linear algebra and blocked pairwise kernels. Reference checks compare exact operations with independently assembled formulas, and a single-epoch localization example illustrates sequential likelihood-based updating and the resulting growth in mixture components. The contribution is a consistent software realization of established GMM calculus, with exact and approximate steps made explicit.