Uncertainty Quantification of Locally Nonlinear Dynamical Systems using
Neural Networks
- URL: http://arxiv.org/abs/2008.04598v1
- Date: Tue, 11 Aug 2020 09:30:47 GMT
- Title: Uncertainty Quantification of Locally Nonlinear Dynamical Systems using
Neural Networks
- Authors: Subhayan De
- Abstract summary: In structural engineering, often a linear structure contains spatially local nonlinearities with uncertainty present in them.
A standard nonlinear solver for them with sampling-based methods for uncertainty quantification incurs significant computational cost.
In this paper, neural network, a recently popular tool for universal function approximation in the scientific machine learning community is used to estimate the pseudoforce.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Models are often given in terms of differential equations to represent
physical systems. In the presence of uncertainty, accurate prediction of the
behavior of these systems using the models requires understanding the effect of
uncertainty in the response. In uncertainty quantification, statistics such as
mean and variance of the response of these physical systems are sought. To
estimate these statistics sampling-based methods like Monte Carlo often require
many evaluations of the models' governing equations for multiple realizations
of the uncertainty. However, for large complex engineering systems, these
methods become computationally burdensome. In structural engineering, often an
otherwise linear structure contains spatially local nonlinearities with
uncertainty present in them. A standard nonlinear solver for them with
sampling-based methods for uncertainty quantification incurs significant
computational cost for estimating the statistics of the response. To ease this
computational burden of uncertainty quantification of large-scale locally
nonlinear dynamical systems, a method is proposed herein, which decomposes the
response into two parts -- response of a nominal linear system and a corrective
term. This corrective term is the response from a pseudoforce that contains the
nonlinearity and uncertainty information. In this paper, neural network, a
recently popular tool for universal function approximation in the scientific
machine learning community due to the advancement of computational capability
as well as the availability of open-sourced packages like PyTorch and
TensorFlow is used to estimate the pseudoforce. Since only the nonlinear and
uncertain pseudoforce is modeled using the neural networks the same network can
be used to predict a different response of the system and hence no new network
is required to train if the statistic of a different response is sought.
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