154 research outputs found
A machine learning approach for efficient uncertainty quantification using multiscale methods
Several multiscale methods account for sub-grid scale features using coarse
scale basis functions. For example, in the Multiscale Finite Volume method the
coarse scale basis functions are obtained by solving a set of local problems
over dual-grid cells. We introduce a data-driven approach for the estimation of
these coarse scale basis functions. Specifically, we employ a neural network
predictor fitted using a set of solution samples from which it learns to
generate subsequent basis functions at a lower computational cost than solving
the local problems. The computational advantage of this approach is realized
for uncertainty quantification tasks where a large number of realizations has
to be evaluated. We attribute the ability to learn these basis functions to the
modularity of the local problems and the redundancy of the permeability patches
between samples. The proposed method is evaluated on elliptic problems yielding
very promising results.Comment: Journal of Computational Physics (2017
Parametrization of stochastic inputs using generative adversarial networks with application in geology
We investigate artificial neural networks as a parametrization tool for
stochastic inputs in numerical simulations. We address parametrization from the
point of view of emulating the data generating process, instead of explicitly
constructing a parametric form to preserve predefined statistics of the data.
This is done by training a neural network to generate samples from the data
distribution using a recent deep learning technique called generative
adversarial networks. By emulating the data generating process, the relevant
statistics of the data are replicated. The method is assessed in subsurface
flow problems, where effective parametrization of underground properties such
as permeability is important due to the high dimensionality and presence of
high spatial correlations. We experiment with realizations of binary
channelized subsurface permeability and perform uncertainty quantification and
parameter estimation. Results show that the parametrization using generative
adversarial networks is very effective in preserving visual realism as well as
high order statistics of the flow responses, while achieving a dimensionality
reduction of two orders of magnitude
Regression-based sparse polynomial chaos for uncertainty quantification of subsurface flow models
Surrogate-modelling techniques including Polynomial Chaos Expansion (PCE) is
commonly used for statistical estimation (aka. Uncertainty Quantification) of
quantities of interests obtained from expensive computational models. PCE is a
data-driven regression-based technique that relies on spectral polynomials as
basis-functions. In this technique, the outputs of few numerical simulations
are used to estimate the PCE coefficients within a regression framework
combined with regularization techniques where the regularization parameters are
estimated using standard cross-validation as applied in supervised machine
learning methods.
In the present work, we introduce an efficient method for estimating the PCE
coefficients combining Elastic Net regularization with a data-driven feature
ranking approach. Our goal is to increase the probability of identifying the
most significant PCE components by assigning each of the PCE coefficients a
numerical value reflecting the magnitude of the coefficient and its stability
with respect to perturbations in the input data. In our evaluations, the
proposed approach has shown high convergence rate for high-dimensional
problems, where standard feature ranking might be challenging due to the curse
of dimensionality.
The presented method is implemented within a standard machine learning
library (Scikit-learn) allowing for easy experimentation with various solvers
and regularization techniques (e.g. Tikhonov, LASSO, LARS, Elastic Net) and
enabling automatic cross-validation techniques using a widely used and well
tested implementation. We present a set of numerical tests on standard
analytical functions, a two-phase subsurface flow model and a simulation
dataset for CO2 sequestration in a saline aquifer. For all test cases, the
proposed approach resulted in a significant increase in PCE convergence rates.Comment: 28 pages, 7 figures, published in Journal of Computational Physics
(2019
Generating Infinite-Resolution Texture using GANs with Patch-by-Patch Paradigm
In this paper, we introduce a novel approach for generating texture images of
infinite resolutions using Generative Adversarial Networks (GANs) based on a
patch-by-patch paradigm. Existing texture synthesis techniques often rely on
generating a large-scale texture using a one-forward pass to the generating
model, this limits the scalability and flexibility of the generated images. In
contrast, the proposed approach trains GANs models on a single texture image to
generate relatively small patches that are locally correlated and can be
seamlessly concatenated to form a larger image while using a constant GPU
memory footprint. Our method learns the local texture structure and is able to
generate arbitrary-size textures, while also maintaining coherence and
diversity. The proposed method relies on local padding in the generator to
ensure consistency between patches and utilizes spatial stochastic modulation
to allow for local variations and diversity within the large-scale image.
Experimental results demonstrate superior scalability compared to existing
approaches while maintaining visual coherence of generated textures
Reduced order modeling of subsurface multiphase flow models using deep residual recurrent neural networks
We present a reduced order modeling (ROM) technique for subsurface
multi-phase flow problems building on the recently introduced deep residual
recurrent neural network (DR-RNN) [1]. DR-RNN is a physics aware recurrent
neural network for modeling the evolution of dynamical systems. The DR-RNN
architecture is inspired by iterative update techniques of line search methods
where a fixed number of layers are stacked together to minimize the residual
(or reduced residual) of the physical model under consideration. In this
manuscript, we combine DR-RNN with proper orthogonal decomposition (POD) and
discrete empirical interpolation method (DEIM) to reduce the computational
complexity associated with high-fidelity numerical simulations. In the
presented formulation, POD is used to construct an optimal set of reduced basis
functions and DEIM is employed to evaluate the nonlinear terms independent of
the full-order model size.
We demonstrate the proposed reduced model on two uncertainty quantification
test cases using Monte-Carlo simulation of subsurface flow with random
permeability field. The obtained results demonstrate that DR-RNN combined with
POD-DEIM provides an accurate and stable reduced model with a fixed
computational budget that is much less than the computational cost of standard
POD-Galerkin reduced model combined with DEIM for nonlinear dynamical systems
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