Related papers: Learning constitutive laws under explicit strain l…

Traditional constitutive models rely on hand-crafted parametric forms with limited expressivity and generalizability, while neural network-based models can capture complex material behavior but often lack interpretability. To balance these…

A key problem of solid mechanics is the identification of the constitutive law of a material, that is, the relation between strain and stress. Machine learning has lead to considerable advances in this field lately. Here we introduce…

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…

With increasing penetration of distributed energy resources installed behind the meter, there is a growing need for adequate modelling of composite loads to enable accurate power system simulation analysis. Existing measurement based load…

Characterizing crystalline energy landscapes is essential to predicting thermodynamic stability, electronic structure, and functional behavior. While machine learning (ML) enables rapid property predictions, the "black-box" nature of most…

Hybrid constitutive modeling integrates two complementary approaches for describing and predicting a material's mechanical behavior: purely data-driven black-box methods and physically constrained, theory-based models. While black-box…

Symbolic discovery of governing equations is a long-standing goal in scientific machine learning, yet a fundamental trade-off persists between interpretability and scalable learning. Classical symbolic regression methods yield explicit…

Kolmogorov-Arnold Networks (KANs) relocate learnable nonlinearities from nodes to edges, demonstrating remarkable capabilities in scientific machine learning and interpretable modeling. However, current KAN implementations suffer from…

The formulation of rheological constitutive equations -- models that relate internal stresses and deformations in complex fluids -- is a critical step in the engineering of systems involving soft materials. While data-driven models provide…

Understanding and modeling nonlinear dynamical systems is a fundamental challenge across science and engineering. Deep learning has shown remarkable potential for capturing complex system behavior, yet achieving models that are both…

In this paper, we present Convolutional Kolmogorov-Arnold Networks, a novel architecture that integrates the learnable spline-based activation functions of Kolmogorov-Arnold Networks (KANs) into convolutional layers. By replacing…

Kolmogorov-Arnold Networks (KANs) offer a promising path toward interpretable machine learning: their learnable activations can be studied individually, while collectively fitting complex data accurately. In practice, however, trained…

Data-driven constitutive modeling with neural networks has received increased interest in recent years due to its ability to easily incorporate physical and mechanistic constraints and to overcome the challenging and time-consuming task of…

Deep learning methods have been widely used as an end-to-end modeling strategy of electrical energy systems because of their conveniency and powerful pattern recognition capability. However, due to the "closed-box" nature, deep learning…

Reinforcement learning (RL) has been increasingly applied to network control problems, such as load balancing. However, existing RL approaches often suffer from lack of interpretability and difficulty in extracting controller equations. In…

Kolmogorov-Arnold networks (KANs) as an alternative to multi-layer perceptrons (MLPs) are a recent development demonstrating strong potential for data-driven modeling. This work applies KANs as the backbone of a neural ordinary differential…

Constitutive modeling lies at the core of mechanics, allowing us to map strains onto stresses for a material in a given mechanical setting. Historically, researchers relied on phenomenological modeling where simple mathematical…

Machine learning for scientific discovery is increasingly becoming popular because of its ability to extract and recognize the nonlinear characteristics from the data. The black-box nature of deep learning methods poses difficulties in…

While accurate, black-box system identification models lack interpretability of the underlying system dynamics. This paper proposes State-Space Kolmogorov-Arnold Networks (SS-KAN) to address this challenge by integrating Kolmogorov-Arnold…

Kolmogorov-Arnold Networks (KANs) offer an efficient and interpretable alternative to traditional multi-layer perceptron (MLP) architectures due to their finite network topology. However, according to the results of Kolmogorov and…