Related papers: Learning constitutive laws under explicit strain l…
Data-driven methods have changed the way we understand and model materials. However, while providing unmatched flexibility, these methods have limitations such as reduced capacity to extrapolate, overfitting, and violation of physics…
We investigate the integration of Kolmogorov-Arnold Networks (KANs) into hard-constrained recurrent physics-informed architectures (HRPINN) to evaluate the fidelity of learned residual manifolds in oscillatory systems. Motivated by the…
Inferring the mechanical properties of soft tissues from measured deformations is a fundamental challenge in elastography. A rarely examined assumption underlying existing approaches is that the assumed constitutive law correctly describes…
The Kolmogorov-Arnold Theorem (KAT), or more generally, the Kolmogorov Superposition Theorem (KST), establishes that any non-linear multivariate function can be exactly represented as a finite superposition of non-linear univariate…
Kolmogorov-Arnold Networks have recently been introduced as a flexible alternative to multi-layer Perceptron architectures. In this paper, we examine the training dynamics of different KAN architectures and compare them with corresponding…
The mathematical formulation of constitutive models to describe the path-dependent, i.e., inelastic, behavior of materials is a challenging task and has been a focus in mechanics research for several decades. There have been increased…
This work presents a novel framework for physically consistent model error characterization and operator learning for reduced-order models of non-equilibrium chemical kinetics. By leveraging the Bayesian framework, we identify and infer…
Data science has emerged as fourth paradigm of scientific exploration. However many machine learning models operate as black boxes offering limited insight into the reasoning behind their predictions. This lack of transparency is one of the…
We propose a physics-augmented neural network (PANN) framework for finite strain incompressible viscoelasticity within the generalized standard materials theory. The formulation is based on the multiplicative decomposition of the…
Effective molecular representation learning is crucial for advancing molecular property prediction and drug design. Mainstream molecular representation learning approaches are based on Graph Neural Networks (GNNs). However, these approaches…
We propose a neural network framework to preclude the need to define or observe incompletely or inaccurately defined states of a material in order to describe its response. The neural network design is based on the classical Coleman-Gurtin…
In the present work, the applicability of physics-augmented neural network (PANN) constitutive models for complex electro-elastic finite element analysis is demonstrated. For the investigations, PANN models for electro-elastic material…
Catastrophic forgetting remains the central obstacle in continual learning (CL): parameters shared across tasks interfere with one another, and existing regularization methods such as EWC and SI apply uniform penalties without awareness of…
We present a machine learning framework capable of consistently inferring mathematical expressions of hyperelastic energy functionals for incompressible materials from sparse experimental data and physical laws. To achieve this goal, we…
Kolmogorov-Arnold Networks (KANs), whose design is inspired-rather than dictated-by the Kolmogorov superposition theorem, have emerged as a structured alternative to MLPs. This review provides a systematic and comprehensive overview of the…
The research undertakes a comprehensive comparative analysis of Kolmogorov-Arnold Networks (KAN) and Multi-Layer Perceptrons (MLP), highlighting their effectiveness in solving essential computational challenges like nonlinear function…
Deep learning models have revolutionized various domains, with Multi-Layer Perceptrons (MLPs) being a cornerstone for tasks like data regression and image classification. However, a recent study has introduced Kolmogorov-Arnold Networks…
When the system is linear, why should learning be nonlinear? Linear dynamical systems, the analytical backbone of control theory, signal processing and circuit analysis, have exact closed-form solutions via the state transition matrix. Yet…
Classical deep networks are effective because depth enables adaptive geometric deformation of data representations. In quantum neural networks (QNNs), however, depth or state reachability alone does not guarantee this feature-learning…
In this contribution, we present a new Materials Knowledge System framework for microstructure-sensitive predictions of effective stress--strain responses in composite materials. The model is developed for composites with a wide range of…