Related papers: Learning hyperelastic anisotropy from data via a t…

We introduce a data-driven framework to automatically identify interpretable and physically meaningful hyperelastic constitutive models from sparse data. Leveraging symbolic regression, an algorithm based on genetic programming, our…

We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…

Originating from condensed matter physics, tensor networks are compact representations of high-dimensional tensors. In this paper, the prowess of tensor networks is demonstrated on the particular task of one-class anomaly detection. We…

Traditional computational methods, such as the finite element analysis, have provided valuable insights into uncovering the underlying mechanisms of brain physical behaviors. However, precise predictions of brain physics require effective…

Artificial and biological agents cannon learn given completely random and unstructured data. The structure of data is encoded in the metric relationships between data points. In the context of neural networks, neuronal activity within a…

Anomaly detection is fundamental yet, challenging problem with practical applications in industry. The current approaches neglect the higher-order dependencies within the networks of interconnected sensors in the high-dimensional time…

Given observations of a physical system, identifying the underlying non-linear governing equation is a fundamental task, necessary both for gaining understanding and generating deterministic future predictions. Of most practical relevance…

This work investigates different sufficient and necessary criteria for hyperelastic, isotropic polyconvex material models, focusing on neural network implementations for compressible and incompressible materials. Furthermore, the…

Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…

We study inverse problems in anisotropic elasticity using tools from algebraic geometry. The singularities of solutions to the elastic wave equation in dimension $n$ with an anisotropic stiffness tensor have propagation kinematics captured…

A novel machine learning algorithm is presented, serving as a data-driven turbulence modeling tool for Reynolds Averaged Navier-Stokes (RANS) simulations. This machine learning algorithm, called the Tensor Basis Random Forest (TBRF), is…

Anisotropy in crystals plays a pivotal role in many technological applications. For example, anisotropic electronic and thermal transport are thought to be beneficial for thermoelectric applications, while anisotropic mechanical properties…

Anomaly detection (AD) is increasingly recognized as a key component for ensuring the resilience of future communication systems. While deep learning has shown state-of-the-art AD performance, its application in critical systems is hindered…

In this paper, we introduce tensor involved peridynamics, a unified framework for simulating both isotropic and anisotropic materials. While traditional peridynamics models effectively simulate isotropic materials, they face challenges with…

We present a machine learning framework to train and validate neural networks to predict the anisotropic elastic response of the monoclinic organic molecular crystal $\beta$-HMX in the geometrical nonlinear regime. A filtered molecular…

Here we assess the applicability of graph neural networks (GNNs) for predicting the grain-scale elastic response of polycrystalline metallic alloys. Using GNN surrogate models, grain-averaged stresses during uniaxial elastic tension in Low…

An artificial neural-network-based subgrid-scale model using the resolved stress, which is capable of predicting untrained decaying isotropic turbulence, is developed. Providing the grid-scale strain-rate tensor alone as input leads the…

Polyconvexity is one of the known conditions which guarantee existence of solutions of boundary value problems in finite elasticity. In this work we propose a framework for development of polyconvex strain energy functions for hyperelastic…

Fiber-reinforced soft biological tissues are typically modeled as hyperelastic, anisotropic, and nearly incompressible materials. To enforce incompressibility a multiplicative split of the deformation gradient into a volumetric and an…

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…