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Solving partial differential equations (PDEs) is the canonical approach for understanding the behavior of physical systems.
Artificial neural networks for solving ordinary and partial differential equations
Isaac Lagaris, Aristidis Likas, and Dimitrios I. Fotiadis · 1998
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Traglastuntersuchungen von unbewehrten und bewehrten Betonstrukturen auf der Grundlage eines objektiven Werkstoffgesetzes für Beton
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Numerical implementation of a neural network based material model in finite element analysis
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A marching cubes based failure surface propagation concept for three-dimensional finite elements with non-planar embedded strong discontinuities of higher-order kinematics
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Combinatorial screening for new materials in unconstrained composition space with machine learning
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Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning
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Stein variational gradient descent: A general purpose Bayesian inference algorithm
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Microstructure recognition using convolutional neural networks for prediction of ionic conductivity in ceramics
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A framework for data-driven analysis of materials under uncertainty: Countering the curse of dimensionality
Miguel A. Bessa, R. Bostanabad, Zeliang Liu, A. Hu, Daniel W. Apley, C. Brinson, W. Chen, and Wing Kam Liu · 2017
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Variational Inference: A Review for Statisticians
David M. Blei, Alp Kucukelbir, and Jon D. McAuliffe · 2017
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What uncertainties do we need in Bayesian deep learning for computer vision?
Alex Kendall and Yarin Gal · 2017
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Hybrid constitutive modeling: data-driven learning of corrections to plasticity models
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Material structure-property linkages using three-dimensional convolutional neural networks
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Deep learning approaches for mining structure-property linkages in high contrast composites from simulation datasets
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A multiscale multi-permeability poroplasticity model linked by recursive homogenizations and deep learning
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Bayesian deep convolutional encoder-decoder networks for surrogate modeling and uncertainty quantification
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Solving high-dimensional partial differential equations using deep learning
Jiequn Han, Arnulf Jentzen, Weinan E, and E. Weinan · 2018
A simple baseline for Bayesian uncertainty in deep learning
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Machine learning materials physics: Surrogate optimization and multi-fidelity algorithms predict precipitate morphology in an alternative to phase field dynamics
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Learning constitutive relations from indirect observations using deep neural networks
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System inference for the spatio-temporal evolution of infectious diseases: Michigan in the time of COVID-19
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A unified deep artificial neural network approach to partial differential equations in complex geometries
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The deal.II Library, Version 9.0
G Alzetta, D Arndt, Wolfgang Bangerth, V Boddu, B Brands, D Davydov, R Gassmoeller, T Heister, L Heltai, K Kormann, M Kronbichler, M Maier, J.-P. Pelteret, B Turcksin, and D Wells · 2018
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A Review of the Application of Machine Learning and Data Mining Approaches in Continuum Materials Mechanics
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An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications
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NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations
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Deep Learning of Free Boundary and Stefan Problems
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Weak adversarial networks for high-dimensional partial differential equations
Yaohua Zang, Gang Bao, Xiaojing Ye, and Haomin Zhou · 2020
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Friedrichs Learning: Weak Solutions of Partial Differential Equations via Deep Learning
Fan Chen, Jianguo Huang, Chunmei Wang, and Haizhao Yang · 2020
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D3M: A Deep Domain Decomposition Method for Partial Differential Equations
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Bayesian deep learning with hierarchical prior: Predictions from limited and noisy data
Xihaier Luo and Ahsan Kareem · 2020
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PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parametric PDEs on Irregular Domain
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B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data
Liu Yang, Xuhui Meng, and George Em Karniadakis · 2021
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