Related papers: A deep learning energy-based method for classical …
We present a method that employs physics-informed deep learning techniques for parametrically solving partial differential equations. The focus is on the steady-state heat equations within heterogeneous solids exhibiting significant phase…
We derive a continuum-level plasticity model for polycrystalline materials in the high energy density regime, based on a single dislocation density and single mobility mechanism, with an evolution model for the dislocation density. The…
A deep learning framework is developed for multiscale characterization of poroelastic media from full waveform data which is known as poroelastography. Special attention is paid to heterogeneous environments whose multiphase properties may…
In this work, we have developed a variational Bayesian inference theory of elasticity, which is accomplished by using a mixed Variational Bayesian inference Finite Element Method (VBI-FEM) that can be used to solve the inverse deformation…
The problem of quasistatic and rate-independent evolution of elastic-plastic-brittle delamination at small strains is considered. Delamination processes for linear elastic bodies glued by an adhesive to each other or to a rigid outer…
In this work, we propose a new deep learning-based scheme for solving high dimensional nonlinear backward stochastic differential equations (BSDEs). The idea is to reformulate the problem as a global optimization, where the local loss…
We introduce a de novo elastography method to learn the elasticity of solids from measured strains. The deep neural network in our new method is supervised by the theory of elasticity and does not require labeled data for training. Results…
This work considers stochastic Galerkin approximations of linear elliptic partial differential equations (PDEs) with stochastic forcing terms and stochastic diffusion coefficients, that cannot be bounded uniformly away from zero and…
Learning the underlying potential energy of stochastic gradient systems from partial and noisy observations is a fundamental problem arising in physics, chemistry, and data-driven modeling. Classical approaches often rely on direct…
This work presents a physics-informed neural network (PINN) based framework to model the strain-rate and temperature dependence of the deformation fields in elastic-viscoplastic solids. To avoid unbalanced back-propagated gradients during…
While much attention of neural network methods is devoted to high-dimensional PDE problems, in this work we consider methods designed to work for elliptic problems on domains $\Omega \subset \mathbb{R} ^d, $ $d=1,2,3$ in association with…
Plasticity is inherent to many engineering materials such as metals. While it can degrade the load-carrying capacity of structures via material yielding, it can also protect structures through plastic energy dissipation. To fully harness…
A physics-informed neural network is presented for poroelastic problems with coupled flow and deformation processes. The governing equilibrium and mass balance equations are discussed and specific derivations for two-dimensional cases are…
Introducing a reduced particle stiffness in discrete element method (DEM) allows for bigger time steps and therefore fewer total iterations in a simulation. Although this approach works well for dry non-adhesive particles, it has been shown…
Euler's elastica constitute an appealing variational image inpainting model. It minimises an energy that involves the total variation as well as the level line curvature. These components are transparent and make it attractive for shape…
Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…
Usage, manipulation, transport, delivery, and mixing of granular or particulate media, comprised of spherical or polyhedral particles, is commonly encountered in industrial sectors of construction (cement and rock fragments), pharmaceutics…
The ability to continuously learn remains elusive for deep learning models. Unlike humans, models cannot accumulate knowledge in their weights when learning new tasks, mainly due to an excess of plasticity and the low incentive to reuse…
The modeling of coupled fluid transport and deformation in a porous medium is essential to predict the various geomechanical process such as CO2 sequestration, hydraulic fracturing, and so on. Current applications of interest, for instance,…
To obtain fast solutions for governing physical equations in solid mechanics, we introduce a method that integrates the core ideas of the finite element method with physics-informed neural networks and concept of neural operators. This…