Related papers: A Kolmogorov-Arnold Surrogate Model for Chemical E…

Multilayer Perceptron (MLP), as a simple yet powerful model, continues to be widely used in classification and regression tasks. However, traditional MLPs often struggle to efficiently capture nonlinear relationships in load data when…

High-fidelity numerical simulation of subsurface flow is computationally intensive, especially for many-query tasks such as uncertainty quantification and data assimilation. Deep learning (DL) surrogates can significantly accelerate forward…

Many engineering applications rely on the evaluation of expensive, non-linear high-dimensional functions. In this paper, we propose the RONAALP algorithm (Reduced Order Nonlinear Approximation with Active Learning Procedure) to…

We create an data-efficient and accurate surrogate model for structure-property linkages of spinodoid metamaterials with only 75 data points -- far fewer than the several thousands used in prior works -- and demonstrate its use in…

The ubiquity of fluids in the physical world explains the need to accurately simulate their dynamics for many scientific and engineering applications. Traditionally, well established but resource intensive CFD solvers provide such…

Traditional physics-based models of geophysical flows, such as debris flows and landslides that pose significant risks to human lives and infrastructure are computationally expensive, limiting their utility for large-scale parameter sweeps,…

The development of next-generation structural materials for harsh environments requires rapid assessment of mechanical performance and its dependence on microstructure. While full-field crystal plasticity (CP) models provide detailed…

Assessing the safety and environmental impacts of subsurface resource exploitation and management is critical and requires robust geomechanical modeling. However, uncertainties stemming from model assumptions, intrinsic variability of…

Reliability-based design optimization (RBDO) is an active field of research with an ever increasing number of contributions. Numerous methods have been proposed for the solution of RBDO, a complex problem that combines optimization and…

Simulating 2D flow in fractured crystalline rock requires 2D stochastic discrete-fracture matrix (DFM) models. To obtain the simulation statistics of interest at an affordable computational cost, we aim to use the multilevel Monte Carlo…

Simulations of Al thin film sputter depositions rely on accurate plasma and surface interaction models. Establishing the latter commonly requires a higher level of abstraction and means to dismiss the fundamental atomic fidelity. Previous…

Algorithmic speedup of training common neural architectures is made difficult by the lack of structure guaranteed by the function compositions inherent to such networks. In contrast to multilayer perceptrons (MLPs), Kolmogorov-Arnold…

Direct numerical simulation of hierarchical materials via homogenization-based concurrent multiscale models poses critical challenges for 3D large scale engineering applications, as the computation of highly nonlinear and path-dependent…

Surrogate models provide compact relations between user-defined input parameters and output quantities of interest, enabling the efficient evaluation of complex parametric systems in many-query settings. Such capabilities are essential in a…

The field of scientific machine learning, which originally utilized multilayer perceptrons (MLPs), is increasingly adopting Kolmogorov-Arnold Networks (KANs) for data encoding. This shift is driven by the limitations of MLPs, including poor…

Kolmogorov-Arnold Networks (KANs) uniquely combine high accuracy with interpretability, making them valuable for scientific modeling. However, it is unclear a priori how deep a network needs to be for any given task, and deeper KANs can be…

This contribution proposes novel data-driven surrogate modeling approaches for parameterized parabolic PDEs, where the parameter dependence can be split into two parts with different decay behavior of the Kolmogorov $N$-width. Such problems…

In multi-objective design tasks, the computational cost increases rapidly when high-fidelity simulations are used to evaluate objective functions. Surrogate models help mitigate this cost by approximating the simulation output, simplifying…

This systematic review explores the theoretical foundations, evolution, applications, and future potential of Kolmogorov-Arnold Networks (KAN), a neural network model inspired by the Kolmogorov-Arnold representation theorem. KANs…

Kolmogorov-Arnold Networks (KANs) were proposed as an alternative to traditional neural network architectures based on multilayer perceptrons (MLP-NNs). The potential advantages of KANs over MLP-NNs, including significantly enhanced…