Numerical simulations of fracture provide a cost- and time-effective alternative to laboratory experiments. Recent advances in the development of higher-order models for phase-field fracture, combined with higher-order isogeometric analysis (IGA) discretizations, have shown significant reduction of computational costs to perform numerical simulation of brittle fracture [1,2,3]. However, the predictions produced by the numerical model depend on stochastic material parameters (e.g., fracture toughness) as well as model-induced parameters (e.g., the characteristic length). In this talk, we focus on uncertainty quantification (UQ) for phase-field fracture. As a forward model, we use the fourth-order AT-1 model from [3], discretized over higher-order (adaptive) spline discretizations [4]. Using this model, we aim to quantify the uncertainty of global quantities of interest like the critical load with respect to the fracture toughness and the characteristic length, through the construction of common surrogate models like sparse grids or Gaussian processes. [1] Michael J. Borden, Thomas J.R. Hughes, Chad M. Landis, and Clemens V. Verhoosel, "A Higher-Order Phase-Field Model for Brittle Fracture: Formulation and Analysis within the Isogeometric Analysis Framework.", Computer Methods in Applied Mechanics and Engineering 273: 100–118, 2014. [2] Luigi Greco, Alessia Patton, Matteo Negri, Alessandro Marengo, Umberto Perego, and Alessandro Reali. "Higher Order Phase-Field Modeling of Brittle Fracture via Isogeometric Analysis". Engineering with Computers: 1–20, 2024. [3] Luigi Greco, Eleonora Maggiorelli, Matteo Negri, Alessia Patton, and Alessandro Reali. "AT1 Fourth-Order Isogeometric Phase-Field Modeling of Brittle Fracture". arXiv preprint arXiv:2501.16968, 2025. [4] Hugo M. Verhelst, Luigi Greco and Alessandro Reali. "Adaptive Isogeometric Analysis of Phase-Field Fracture". Submitted.