Debris flows are a highly fluid and rapid type of landslide, consisting of water, soil, rocks, and any material entrained during their descent or eroded along their path. These flows typically travel down steep slopes or channels, causing extensive destruction to infrastructure and posing significant risks to human lives. They are fast-moving events that are challenging to predict and to control, with no tools currently available to accurately measure their velocity or discharge. Recent advancements in high-fidelity simulations of extreme events provide a promising approach for their in-depth analysis. However, these novel technologies, while highly useful, are yet too expensive to allow real-time simulations. To address these challenges, our work begins with numerically replicating an experimental benchmark to validate the model, with the ultimate goal of developing a surrogate model capable of predicting the flow behavior almost instantaneously. This involves creating a 2D digital twin of a flume experiment conducted in the laboratory using the Material Point Method (MPM), a technique incorporated into the Kratos Multiphysics code. MPM combines the advantages of both mesh-based and meshless methods. While the material is discretized into Lagrangian particles that carry the material's history, the background grid handles the computation, thus preventing grid distortion. This makes MPM particularly effective for simulating large deformations and an ideal method for modeling debris flows. We design a comprehensive Design of Experiments (DOE) framework, where the input parameters include material characteristics and flume setup variables. The goal is to build a surrogate model capturing the flow's key features and temporal evolution, utilizing fractal radial basis functions (RBFs). The RBFs effectively address nonlinear and irregular problems, making them ideal for modeling the complex physics of debris flows.