A neural network approach for uncertainty quantification for time-dependent problems with random parameters
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In this work we propose a numerical framework for uncertainty quantification (UQ) for time-dependent problems with neural network surrogates. The new appoach is based on approximating the exact time-integral form of the equation by neural networks, of which the structure is an adaptation of the residual network. The network is trained with data generated by running high-fidelity simulation or by conducting experimental measurements for a very short time. The whole procedure does not require any probability information from the random parameters and can be conducted offline. Once the distribution of the random parameters becomes available a posteriori, one can post-process the neural network surrogate to calculate the statistics of the solution. Several numerical examples are presented to demonstrate the procedure and performance of the proposed method.
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