A Fractal RBF Approach for Enhanced Surrogate Modeling of a Granular Flows
Please login to view abstract download link
Surrogate models have gained significant attention in recent years, especially with the advent of machine learning and the development of neural network-based methods, such as Fourier Neural Operators and Deep Operator Networks, among others. Here we consider surrogates based on Kernel Operator Learning (KOL), which has demonstrated distinct advantages over widely used neural network-based approaches and provides rigorous error analysis. As fractal functions are pivotal in addressing nonlinear and irregular problems, we present a novel KOL method based on the recently developed fractal RBF and demonstrate its effectiveness in such scenarios. To illustrate the effectiveness of the proposed approach, we consider the simulation of a granular flow along a flume as a test scenario. The physics-based model simulating the position of the flow and its velocities has high computational costs. Here we use the kernel-based surrogate models to approximate some key outputs of the model as functions of the granular material density, its internal friction angle, the friction coefficient with the bottom wall, and the slope inclination angle. Our results explore the accuracy and computational efficiency of the fractal RBF surrogate model compared to other kernel-based approaches.