These notes were compiled as lecture notes for a course developed and taught at the University of the Southern California. They should be accessible to a typical engineering graduate student with a st...

Residual representation learning simplifies the optimization problem of learning complex functions and has been widely used by traditional convolutional neural networks. However, it has not been appli...

Deep neural networks and the ENO procedure are both efficient frameworks for approximating rough functions. We prove that at any order, the ENO interpolation procedure can be cast as a deep ReLU neura...

Deep Neural Networks, often owing to the overparameterization, are shown to be capable of exactly memorizing even randomly labelled data. Empirical studies have also shown that none of the standard re...

Evidential deep learning, built upon belief theory and subjective logic, offers a principled and computationally efficient way to turn a deterministic neural network uncertainty-aware. The resultant e...

We consider the generic deep image enhancement problem where an input image is transformed into a perceptually better-looking image. Recent methods for image enhancement consider the problem by perfor...

Inverse problems are ubiquitous in nature, arising in almost all areas of science and engineering ranging from geophysics and climate science to astrophysics and biomechanics. One of the central chall...

Many large scale problems in computational fluid dynamics such as uncertainty quantification, Bayesian inversion, data assimilation and PDE constrained optimization are considered very challenging com...

Recently, there is a vast interest in developing image feature learning methods that are independent of the training data, such as deep image prior, InGAN, SinGAN, and DCIL. These methods are unsuperv...

In this paper, we propose a new approach for facial expression recognition using deep covariance descriptors. The solution is based on the idea of encoding local and global Deep Convolutional Neural N...