Related papers: Physics-based Machine Learning for Computational F…

Modeling fracture is computationally expensive even in computational simulations of two-dimensional problems. Hence, scaling up the available approaches to be directly applied to large components or systems crucial for real applications…

Direct observations of earthquake nucleation and propagation are few and yet the next decade will likely see an unprecedented increase in indirect, surface observations that must be integrated into modeling efforts. Machine learning (ML)…

Notched components are commonly used in engineering structures, where stress concentration may easily lead to crack initiation and development. The main goal of this work is to develop a simple numerical method to predict the structural…

An image-based deep learning framework is developed in this paper to predict damage and failure in microstructure-dependent composite materials. The work is motivated by the complexity and computational cost of high-fidelity simulations of…

Accurately modeling the mechanical behavior of materials is crucial for numerous engineering applications. The quality of these models depends directly on the accuracy of the constitutive law that defines the stress-strain relation.…

Modeling complex physical dynamics is a fundamental task in science and engineering. Traditional physics-based models are sample efficient, and interpretable but often rely on rigid assumptions. Furthermore, direct numerical approximation…

We present a new data-driven paradigm for variational brittle fracture mechanics. The fracture-related material modeling assumptions are removed and the governing equations stemming from variational principles are combined with a set of…

Physics-informed machine learning (PIML) is an emerging framework that integrates physical knowledge into machine learning models. This physical prior often takes the form of a partial differential equation (PDE) system that the regression…

Direct numerical simulation of hierarchical materials via homogenization-based concurrent multiscale models poses critical challenges for 3D large scale engineering applications, as the computation of highly nonlinear and path-dependent…

In this work we aim to develop a unified mathematical framework and a reliable computational approach to model the brittle fracture in heterogeneous materials with variability in material microstructures, and to provide statistic metrics…

Existing point cloud representation learning methods primarily rely on data-driven strategies to extract geometric information from large amounts of scattered data. However, most methods focus solely on the spatial distribution features of…

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…

Given (small amounts of) time-series' data from a high-dimensional, fine-grained, multiscale dynamical system, we propose a generative framework for learning an effective, lower-dimensional, coarse-grained dynamical model that is predictive…

We present the application of a class of deep learning, known as Physics Informed Neural Networks (PINN), to learning and discovery in solid mechanics. We explain how to incorporate the momentum balance and constitutive relations into PINN,…

The intersection of physics and machine learning has given rise to the physics-enhanced machine learning (PEML) paradigm, aiming to improve the capabilities and reduce the individual shortcomings of data- or physics-only methods. In this…

The use of machine learning in fluid dynamics is becoming more common to expedite the computation when solving forward and inverse problems of partial differential equations. Yet, a notable challenge with existing convolutional neural…

Weather forecasting is essential but remains computationally intensive and physically incomplete in traditional numerical weather prediction (NWP) methods. Deep learning (DL) models offer efficiency and accuracy but often ignore physical…

Finite element methods (FEM) are popular approaches for simulation of soft tissues with elastic or viscoelastic behavior. However, their usage in real-time applications, such as in virtual reality surgical training, is limited by…

We propose a data-driven constitutive framework for anisotropic damage mechanics based on the second-order damage tensor approach for both compressible and incompressible materials. The formulation is thermodynamically consistent and…

Since the turn of the millennium, capitalizing on modern advances in mathematics and computation, a slew of computational models have been proposed in the literature with the objective of describing the nucleation and propagation of…