Related papers: A neural ordinary differential equation framework …

We propose a deep neural network (DNN) as a fast surrogate model for local stress (and in principle strain) calculation in inhomogeneous non-linear material systems. We show that the DNN predicts the local stresses with about 3.8% mean…

The predictive power of neural networks often costs model interpretability. Several techniques have been developed for explaining model outputs in terms of input features; however, it is difficult to translate such interpretations into…

In this article, we present a framework for designing neural networks that remain consistent with the underlying principles of agent-based models. We begin by highlighting the limitations of standard neural differential equations in…

Advancements in artificial intelligence call for a deeper understanding of the fundamental mechanisms underlying deep learning. In this work, we propose a theoretical framework to analyze learning dynamics through the lens of dynamical…

Stress prediction in porous materials and structures is challenging due to the high computational cost associated with direct numerical simulations. Convolutional Neural Network (CNN) based architectures have recently been proposed as…

The inverse problem of supervised reconstruction of depth-variable (time-dependent) parameters in a neural ordinary differential equation (NODE) is considered, that means finding the weights of a residual network with time continuous…

We present an approach to numerical homogenization of the elastic response of microstructures. Our work uses deep neural network representations trained on data obtained from direct numerical simulation (DNS) of martensitic phase…

Parameter estimation in structural dynamics generally involves inferring the values of physical, geometric, or even customized parameters based on first principles or expert knowledge, which is challenging for complex structural systems. In…

In complex systems, information propagation can be defined as diffused or delocalized, weakly localized, and strongly localized. This study investigates the application of graph neural network models to learn the behavior of a linear…

This work addresses the inverse identification of apparent elastic properties of random heterogeneous materials using machine learning based on artificial neural networks. The proposed neural network-based identification method requires the…

We propose a new framework for identifying mechanical properties of heterogeneous materials without a closed-form constitutive equation. Given a full-field measurement of the displacement field, for instance as obtained from digital image…

Using deep learning to analyze mechanical stress distributions has been gaining interest with the demand for fast stress analysis methods. Deep learning approaches have achieved excellent outcomes when utilized to speed up stress…

This study addresses the modelling of elastic bodies, particularly when the relaxed configuration is unknown or non-existent. We adopt the theory of initially stressed materials, incorporating the deformation gradient and stress state of…

In the present work, a machine learning based constitutive model for electro-mechanically coupled material behavior at finite deformations is proposed. Using different sets of invariants as inputs, an internal energy density is formulated…

Machine learning approaches informed by physics have offered new insights into the discovery of constitutive models from data, helping overcome some limitations of traditional constitutive modelling while reducing the cost of otherwise…

Brain activity is intrinsically a neural dynamic process constrained by anatomical space. This leads to significant variations in spatial distribution patterns and correlation patterns of neural activity across variable and heterogeneous…

Stress analysis of heterogeneous media, like composite materials, using Finite Element Analysis (FEA) has become commonplace in design and analysis. However, determining stress distributions in heterogeneous media using FEA can be…

The use of recurrent neural networks to represent the dynamics of unstable systems is difficult due to the need to properly initialize their internal states, which in most of the cases do not have any physical meaning, consequent to the…

This work presents a novel methodology for analysis and control of nonlinear fluid systems using neural networks. The approach is demonstrated on four different study cases being the Lorenz system, a modified version of the…

We propose a new family of neural networks to predict the behaviors of physical systems by learning their underpinning constraints. A neural projection operator lies at the heart of our approach, composed of a lightweight network with an…