Multitask and Multifidelity Convolutional Encoder-Decoder Networks

We present a unified framework for segmentation and regression tasks with convolutional encoder-decoder networks, using, as a motivation, the problem of estimating the relative pressures from velocity fields acquired through Magnetic Resonance Imaging (MRI). First, we characterize the properties of the noise generated from undersampled 4D flow MRI Fourier space data. Next, we propose several convolutional neural network architectures for jointly segmenting the fluid region and predicting the relative pressure within that region, combining commonly adopted loss function formulations with physics-informed regularization. Finally, we extend these architectures to fuse multifidelity data for various regression tasks and perform uncertainty quantification through Monte Carlo DropBlocks. For the multifidelity fusion, we consider data regimes with varying input and output dimensionality.