Multifidelity data fusion in convolutional encoder/decoder networks
This work addresses regression problems in scientific computing by efficiently combining data of varying fidelity, though it appears incremental as it builds on existing encoder/decoder and multifidelity techniques.
The paper tackles regression accuracy in convolutional neural networks using multifidelity data, demonstrating that encoder/decoder architectures with skip connections require fewer parameters than fully connected networks and can map inputs to outputs of arbitrary dimensionality. Results show accuracy when trained on a mix of few high-fidelity and many low-fidelity data from models like one-dimensional functions and 2D Poisson equation solvers.
We analyze the regression accuracy of convolutional neural networks assembled from encoders, decoders and skip connections and trained with multifidelity data. Besides requiring significantly less trainable parameters than equivalent fully connected networks, encoder, decoder, encoder-decoder or decoder-encoder architectures can learn the mapping between inputs to outputs of arbitrary dimensionality. We demonstrate their accuracy when trained on a few high-fidelity and many low-fidelity data generated from models ranging from one-dimensional functions to Poisson equation solvers in two-dimensions. We finally discuss a number of implementation choices that improve the reliability of the uncertainty estimates generated by Monte Carlo DropBlocks, and compare uncertainty estimates among low-, high- and multifidelity approaches.