Axtreme: A Package for Bayesian Surrogate Modeling and Optimization of Extreme Response Calculation

Engineers often need to understand long-term behavior of complex models in stochastic settings, such as when performing Ultimate Limit State (ULS) calculations. Models are expensive to run (in runtime or resources), meaning directly calculating the value of interest is often infeasible. Bayesian surrogate modeling with Design of Experiments (DOE) is one approach to this computational challenge and offers advantages over traditional methods such as environmental contours. However, despite its advantages, the adoption of Bayesian surrogate modeling with DOE in engineering has been limited, due in part to the technical expertise required to implement the methods. To address this, we have developed Axtreme, an open-source Python package extending state-of-the-art Bayesian optimization frameworks for these engineering challenges. Axtreme enables engineers to build accurate surrogate models, compute quantities of interest, and conduct DOE to minimize uncertainty in these calculations efficiently. The package provides a flexible toolkit of ready-to-use functions, helpers, and tutorials, all built on top of robust, industrial-grade frameworks. By reducing the technical barriers to applying Bayesian surrogate modeling and DOE, this package makes advanced uncertainty quantification techniques more accessible, improving decision-making and design efficiency for engineers. In this paper, we introduce the Axtreme package and demonstrate the application on a numerical example.

Keywords: Bayesian surrogate modeling, Gaussian processes, Design of Experiments (DOE), Active learning, Uncertainty quantification.