Research Projects

Generative Adversarial Networks (GANs), while widely successful in modeling complex data distributions, have not yet been sufficiently leveraged in scientific computing and design. Reasons for this include the lack of flexibility of GANs to represent discrete-valued image data, as well as the lack of control over physical properties of generated samples. We propose a new conditional generative modeling approach (InvNet) that efficiently enables modeling discrete-valued images, while allowing control over their parameterized geometric and statistical properties. We evaluate our approach on several synthetic and real world problems, navigating manifolds of geometric shapes with desired sizes; generation of binary two-phase materials; and the (challenging) problem of generating multi-orientation polycrystalline microstructures.

We explore the space of adversarial examples in terms of semantically valid images. Our approach relies on the use of generative models to simulate the semantic transformations of images.

We integrate classical engineering approaches (i.e., physics models) with machine learning models such as generative models to transform and accelerate such design exploration process.

Our aim is a reliable estimation of a signal or image from its periodic nonlinearities, with a focus on a periodic nonlinear observation model named modulo sensor encountered in high-dynamic range (HDR) imaging.

We leverage the ability of Generative Adversarial Networks (GANs) of learning the real data distribution by using the Generator function as a prior on natural images.

We prove linear convergence of both gradient descent and a new scheme called alternating minimization for training ReLU based 2-layer networks.

We consider the problem of super-resolution for sub-diffraction imaging using our CoPRAM algorithm for sparse phase retrieval.

We consider the problem of recovering a signal from magnitude-only measurements under a structured sparsity prior. The problem is of interest in the fields of nano- and bioimaging systems, astronomical imaging and speech processing.

In this paper, we study the general problem of optimizing a convex function $F(L)$ over the set of $p\times p$ matrices, subject to rank constraints on $L$.

We study the problem of (provably) learning the weights of a two-layer neural network with quadratic activations.

We study the problem of demixing a pair of sparse signals from noisy, nonlinear observations of their superposition.

We consider the problem of unsupervised feature learning via generative models and present efficient algorithms for learning generatice models for sparse coding.