Related papers: A Neural Operator based Hybrid Microscale Model fo…
Modeling and predicting the dynamics of complex multiscale systems remains a significant challenge due to their inherent nonlinearities and sensitivity to initial conditions, as well as limitations of traditional machine learning methods…
This work proposes a hybrid modeling framework based on recurrent neural networks (RNNs) and the finite element (FE) method to approximate model discrepancies in time dependent, multi-fidelity problems, and use the trained hybrid models to…
Machine Learning tools are nowadays widely applied extensively to the prediction of the properties of molecular materials, using datasets extracted from high-throughput computational models. In several cases of scientific and technological…
Multiscale problems are ubiquitous in physics. Numerical simulations of such problems by solving partial differential equations (PDEs) at high resolution are computationally too expensive for many-query scenarios, such as uncertainty…
Data-driven material models have many advantages over classical numerical approaches, such as the direct utilization of experimental data and the possibility to improve performance of predictions when additional data is available. One…
We propose and study a neural operator framework for learning memory- and material microstructure-dependent constitutive laws for heterogeneous materials. We work in the two-scale setting where homogenization theory provides a systematic…
Complex systems are often decomposed into modular subsystems for engineering tractability. Although various equation based white-box modeling techniques make use of such structure, learning based methods have yet to incorporate these ideas…
In this mini-review we summarize the progress of modeling, simulation and analysis of shock responses of heterogeneous materials in our group in recent years. The basic methodology is as below. We first decompose the problem into different…
Simulating and predicting multiscale problems that couple multiple physics and dynamics across many orders of spatiotemporal scales is a great challenge that has not been investigated systematically by deep neural networks (DNNs). Herein,…
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…
Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing…
Multivariate spatial modeling is key to understanding the behavior of materials downstream in a mining operation. The ore recovery depends on the mineralogical composition, which needs to be properly captured by the model to allow for good…
This paper describes a 2D and 3D simulation engine that quantitatively models the statics, dynamics, and non-linear deformation of heterogeneous soft bodies in a computationally efficient manner. There is a large body of work simulating…
Reduced-order models that accurately abstract high fidelity models and enable faster simulation is vital for real-time, model-based diagnosis applications. In this paper, we outline a novel hybrid modeling approach that combines machine…
The data-driven discovery of partial differential equations (PDEs) consistent with spatiotemporal data is experiencing a rebirth in machine learning research. Training deep neural networks to learn such data-driven partial differential…
We propose a neural physics system for real-time, interactive fluid simulations. Traditional physics-based methods, while accurate, are computationally intensive and suffer from latency issues. Recent machine-learning methods reduce…
Deep Material Network (DMN) has recently emerged as a data-driven surrogate model for heterogeneous materials. Given a particular microstructural morphology, the effective linear and nonlinear behaviors can be successfully approximated by…
The rapid compaction of granular media results in localized heating that can induce chemical reactions, phase transformations, and melting. However, there are numerous mechanisms in play that can be dependent on a variety of microstructural…
Classical multi-scale methods involving two spatial scales face significant challenges when simulating heterogeneous structures with complicated three-scale spatial configurations. This study proposes an innovative higher-order three-scale…
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…