
A comprehensive deep learningbased approach to reduced order modeling of nonlinear timedependent parametrized PDEs
Traditional reduced order modeling techniques such as the reduced basis ...
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A Deep Neural Network Surrogate for HighDimensional Random Partial Differential Equations
Developing efficient numerical algorithms for high dimensional random Pa...
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L1based reduced over collocation and hyper reduction for steady state and timedependent nonlinear equations
The task of repeatedly solving parametrized partial differential equatio...
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Variancebased sensitivity analysis for timedependent processes
The global sensitivity analysis of timedependent processes requires his...
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Model order reduction for parametric high dimensional models in the analysis of financial risk
This paper presents a model order reduction (MOR) approach for high dime...
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Onthefly construction of surrogate constitutive models for concurrent multiscale mechanical analysis through probabilistic machine learning
Concurrent multiscale finite element analysis (FE2) is a powerful approa...
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Integration of adversarial autoencoders with residual dense convolutional networks for inversion of solute transport in nonGaussian conductivity fields
Characterization of a nonGaussian channelized conductivity field in sub...
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Nonintrusive surrogate modeling for parametrized timedependent PDEs using convolutional autoencoders
This work presents a nonintrusive surrogate modeling scheme based on machine learning technology for predictive modeling of complex systems, described by parametrized timedependent PDEs. For these problems, typical finite element approaches involve the spatiotemporal discretization of the PDE and the solution of the corresponding linear system of equations at each time step. Instead, the proposed method utilizes a convolutional autoencoder in conjunction with a feed forward neural network to establish a lowcost and accurate mapping from the problem's parametric space to its solution space. For this purpose, time history response data are collected by solving the highfidelity model via FEM for a reduced set of parameter values. Then, by applying the convolutional autoencoder to this data set, a lowdimensional representation of the highdimensional solution matrices is provided by the encoder, while the reconstruction map is obtained by the decoder. Using the latent representation given by the encoder, a feedforward neural network is efficiently trained to map points from the problem's parametric space to the compressed version of the respective solution matrices. This way, the encoded response of the system at new parameter values is given by the neural network, while the entire response is delivered by the decoder. This approach effectively bypasses the need to serially formulate and solve the system's governing equations at each time increment, thus resulting in a significant cost reduction and rendering the method ideal for problems requiring repeated model evaluations or 'realtime' computations. The elaborated methodology is demonstrated on the stochastic analysis of timedependent PDEs solved with the Monte Carlo method, however, it can be straightforwardly applied to other similartype problems, such as sensitivity analysis, design optimization, etc.
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