Related papers: Learning constitutive laws under explicit strain l…

The constitutive behavior of polymeric materials is often modeled by finite linear viscoelastic (FLV) or quasi-linear viscoelastic (QLV) models. These popular models are simplifications that typically cannot accurately capture the nonlinear…

Small-angle scattering (SAS) techniques are indispensable tools for probing the structure of soft materials. However, traditional analytical models often face limitations in structural inversion for complex systems, primarily due to the…

In solid mechanics, Data-driven approaches are widely considered as the new paradigm that can overcome the classic problems of constitutive models such as limiting hypothesis, complexity, and high dependence on training data. However,…

Uncovering physical laws from experimental data is a fundamental goal of theoretical physics. In this work, we apply the spline-based, interpretable Kolmogorov-Arnold Network (KAN) to explore the algebraic structure underlying the baryon…

The major challenge in determining a hyperelastic model for a given material is the choice of invariants and the selection how the strain energy function depends functionally on these invariants. Here we introduce a new data-driven…

Kolmogorov-Arnold Networks (KAN) is a groundbreaking model recently proposed by the MIT team, representing a revolutionary approach with the potential to be a game-changer in the field. This innovative concept has rapidly garnered worldwide…

Despite their impressive performance, contemporary neural networks often lack structural safeguards that promote stable learning and interpretable behavior. In this work, we introduce a reformulation of layer-level transformations that…

Kolmogorov-Arnold Networks (KANs) are a recently introduced neural architecture that replace fixed nonlinearities with trainable activation functions, offering enhanced flexibility and interpretability. While KANs have been applied…

The development of accurate constitutive models for materials that undergo path-dependent processes continues to be a complex challenge in computational solid mechanics. Challenges arise both in considering the appropriate model assumptions…

Nuclear mass prediction is one of the core issues in nuclear physics research, yet it faces the challenge of small-sample datasets with high complexity. This study introduces the Kolmogorov-Arnold Network (KAN) into the refinement of…

An extendable, efficient and explainable Machine Learning approach is proposed to represent cyclic plasticity and replace conventional material models based on the Radial Return Mapping algorithm. High accuracy and stability by means of a…

Constitutive and closure models play important roles in computational mechanics and computational physics in general. Classical constitutive models for solid and fluid materials are typically local, algebraic equations or flow rules…

We develop a new neural network architecture that strictly enforces constitutive constraints such as polyconvexity, frame-indifference, and the symmetry of the stress and material stiffness. Additionally, we show that the accuracy of the…

This paper introduces Stress-Aware Learning, a resilient neural training paradigm in which deep neural networks dynamically adjust their optimization behavior - whether under stable training regimes or in settings with uncertain dynamics -…

Constitutive models play a crucial role in materials science as they describe the behavior of the materials in mathematical forms. Over the last few decades, the rapid development of manufacturing technologies have led to the discovery of…

Kolmogorov-Arnold Networks (KANs) have recently demonstrated promising potential in scientific machine learning, partly due to their capacity for grid adaptation during training. However, existing adaptation strategies rely solely on input…

Tabular data analysis presents unique challenges that arise from heterogeneous feature types, missing values, and complex feature interactions. While traditional machine learning methods like gradient boosting often outperform deep…

By utilising their adaptive activation functions, Kolmogorov-Arnold Networks (KANs) can be applied in a novel way for the diverse machine learning tasks, including cyber threat detection. KANs substitute conventional linear weights with…

Inspired by the Kolmogorov-Arnold representation theorem, we propose Kolmogorov-Arnold Networks (KANs) as promising alternatives to Multi-Layer Perceptrons (MLPs). While MLPs have fixed activation functions on nodes ("neurons"), KANs have…

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…