Related papers: Learning constitutive laws under explicit strain l…
Time series classification is a relevant step supporting decision-making processes in various domains, and deep neural models have shown promising performance in this respect. Despite significant advancements in deep learning, the…
Probabilistic representations, such as Bayesian and Markov networks, are fundamental to much of statistical machine learning. Thus, learning probabilistic representations directly from data is a deep challenge, the main computational…
This work presents a three-dimensional constitutive model for shape memory alloys considering the TRansformation-Induced Plasticity (TRIP) as well as the Two-Way Shape Memory Effect (TWSME) through a large deformation framework. The…
The Kolmogorov-Arnold Network (KAN) has emerged as a promising neural network architecture for small-scale AI+Science applications. However, it suffers from inflexibility in modeling ridge functions, which is widely used in representing the…
Kolmogorov-Arnold Networks (KANs) have emerged as a promising alternative to traditional Multi-Layer Perceptrons (MLPs), offering enhanced interpretability and a solid mathematical foundation. However, their parameter efficiency remains a…
The Kolmogorov-Arnold representation theorem offers a theoretical alternative to Multi-Layer Perceptrons (MLPs) by placing learnable univariate functions on edges rather than nodes. While recent implementations such as Kolmogorov-Arnold…
We propose and study a neural operator framework for learning memory- and material microstructure-dependent constitutive laws for heterogeneous materials. We work in the two-scale setting where homogenization theory provides a systematic…
Robot locomotion learning using reinforcement learning suffers from training sample inefficiency and exhibits the non-understandable/black-box nature. Thus, this work presents a novel SME-AGOL to address such problems. Firstly, Sequential…
Kolmogorov-Arnold Networks (KANs) shift neural computation from linear layers to learnable nonlinear edge functions, but implementing these nonlinearities efficiently in hardware remains an open challenge. Here we introduce a physical…
The discovery of constitutive models for hyperelastic materials is essential yet challenging due to their nonlinear behavior and the limited availability of experimental data. Traditional methods typically require extensive stress-strain or…
Although Kolmogorov-Arnold-based interpretable networks (KANs) possess strong theoretical expressiveness, they suffer from severe parameter explosion and limited ability to capture high-frequency features in high-dimensional tasks. To…
Kolmogorov-Arnold Networks (KANs) offer a promising framework for approximating complex nonlinear functions, yet the original B-spline formulation suffers from significant computational overhead due to De Boor algorithm. While recent…
Highly compressible solids, such as foams, exhibit complex responses, including pronounced tension-compression asymmetry. Capturing such behaviors within unified hyperelastic frameworks remains challenging. Invariant-based hyperelastic…
We introduce Sprecher Networks (SNs), a family of trainable architectures derived from David Sprecher's 1965 constructive form of the Kolmogorov-Arnold representation. Each SN block implements a "sum of shifted univariate functions" using…
Accurately modeling the mechanical behavior of materials is crucial for numerous engineering applications. The quality of these models depends directly on the accuracy of the constitutive law that defines the stress-strain relation.…
This paper explores alternative formulations of the Kolmogorov Superposition Theorem (KST) as a foundation for neural network design. The original KST formulation, while mathematically elegant, presents practical challenges due to its…
Hypergraph representation learning has garnered increasing attention across various domains due to its capability to model high-order relationships. Traditional methods often rely on hypergraph neural networks (HNNs) employing message…
The accuracy and fidelity of deformation simulations are highly dependent upon the underlying constitutive material model. Commonly used linear or nonlinear constitutive material models only cover a tiny part of possible material behavior.…
Mechanical densification of granular bodies is a process in which a loose material becomes increasingly cohesive as the applied pressure increases. A constitutive description of this process faces the formidable problem that granular and…
Modern machine learning, grounded in the Universal Approximation Theorem, has achieved significant success in the study of phase transitions in both equilibrium and non-equilibrium systems. However, identifying the critical points of…