Related papers: Polyconvex Physics-Augmented Neural Network Consti…

We introduce copresheaf topological neural networks (CTNNs), a powerful unifying framework that encapsulates a wide spectrum of deep learning architectures, designed to operate on structured data, including images, point clouds, graphs,…

We present a PDE-based framework that generalizes Group equivariant Convolutional Neural Networks (G-CNNs). In this framework, a network layer is seen as a set of PDE-solvers where geometrically meaningful PDE-coefficients become the…

We show that deep convolutional neural networks (CNN) can massively outperform traditional densely-connected neural networks (both deep or shallow) in predicting eigenvalue problems in mechanics. In this sense, we strike out in a new…

The aim of this study is three-fold: (i) to present a general higher-order shell theory to analyze large deformations of thin or thick shell structures made of general compressible hyperelastic materials; (ii) to utilize the orthonormal or…

Physics-based simulations are often used to model and understand complex physical systems and processes in domains like fluid dynamics. Such simulations, although used frequently, have many limitations which could arise either due to the…

Traditional algorithms for compressive sensing recovery are computationally expensive and are ineffective at low measurement rates. In this work, we propose a data driven non-iterative algorithm to overcome the shortcomings of earlier…

We applied physics-informed neural networks to solve the constitutive relations for nonlinear, path-dependent material behavior. As a result, the trained network not only satisfies all thermodynamic constraints but also instantly provides…

Elasticity images map biomechanical properties of soft tissues to aid in the detection and diagnosis of pathological states. In particular, quasi-static ultrasonic (US) elastography techniques use force-displacement measurements acquired…

A variety of modeling techniques have been developed in the past decade to reduce the computational expense and improve the accuracy of modeling. In this study, a new framework of modeling is suggested. Compared with other popular methods,…

Graph Neural Networks (GNNs) with equivariant properties have emerged as powerful tools for modeling complex dynamics of multi-object physical systems. However, their generalization ability is limited by the inadequate consideration of…

Normalization techniques have become a basic component in modern convolutional neural networks (ConvNets). In particular, many recent works demonstrate that promoting the orthogonality of the weights helps train deep models and improve…

Physics Informed Neural Networks offer a mesh free framework for solving PDEs but are highly sensitive to loss weight selection. We propose two dimensional analysis based weighting schemes, one based on quantifiable terms, and another also…

Data-driven constitutive modeling is an emerging field in computational solid mechanics with the prospect of significantly relieving the computational costs of hierarchical computational methods. Traditionally, these surrogates have been…

In comparison to classical shallow representation learning techniques, deep neural networks have achieved superior performance in nearly every application benchmark. But despite their clear empirical advantages, it is still not well…

A key problem of solid mechanics is the identification of the constitutive law of a material, that is, the relation between strain and stress. Machine learning has lead to considerable advances in this field lately. Here we introduce…

Deep convolutional networks provide state of the art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and non-linearities.…

Learning to reason about relations and dynamics over multiple interacting objects is a challenging topic in machine learning. The challenges mainly stem from that the interacting systems are exponentially-compositional, symmetrical, and…

For the formulation of machine learning-based material models, the usage of invariants of deformation tensors is attractive, since this can a priori guarantee objectivity and material symmetry. In this work, we consider incompressible,…

The theory of evolving natural configurations is an effective technique to model dissipative processes. In this paper, we use this theory to revisit nonlinear constitutive models of viscoelastic solids. Particularly, a Maxwell and a…

Accuracy in neural PDE solvers often breaks down not because of limited expressivity, but due to poor optimisation caused by ill-conditioning, especially in multi-fidelity and stiff problems. We study this issue in Physics-Informed Extreme…