A Bayesian multiscale deep learning framework for flows in random media

DOI10.3934/fods.2021016OpenAlexW3174635800MaRDI QIDQ2072635

Nicholas Zabaras, Govinda Anantha Padmanabha

Publication date: 26 January 2022

Published in: Foundations of Data Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.09056

zbMATH Keywords

neural networksmultiscaleBayesianhigh-dimensionalityuncertainty quantificationdeep learning

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Reasoning under uncertainty in the context of artificial intelligence (68T37)

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Uses Software

• FEniCS
• PyTorch
• ImageNet
• Adam
• U-Net
• AlexNet

Cites Work

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• A probabilistic graphical model approach to stochastic multiscale partial differential equations
• Multi-output separable Gaussian process: towards an efficient, fully Bayesian paradigm for uncertainty quantification
• The multiscale restriction smoothed basis method for fractured porous media (F-MSRSB)
• A machine learning approach for efficient uncertainty quantification using multiscale methods
• Bayesian deep convolutional encoder-decoder networks for surrogate modeling and uncertainty quantification
• Multi-scale finite-volume method for elliptic problems in subsurface flow simulation.
• Deep UQ: learning deep neural network surrogate models for high dimensional uncertainty quantification
• Quantifying model form uncertainty in Reynolds-averaged turbulence models with Bayesian deep neural networks
• Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data
• Modeling the dynamics of PDE systems with physics-constrained deep auto-regressive networks
• Deep multiscale model learning
• A multiscale restriction-smoothed basis method for high contrast porous media represented on unstructured grids
• Mixed Multiscale Finite Element Methods for Stochastic Porous Media Flows
• Modelling of Multiscale Structures in Flow Simulations for Petroleum Reservoirs