How do neurons in the brain represent external stimuli in a manner that enables an organism to achieve its goals? The search for answers to this question, which pervades most of modern neuroscience research, requires the solution to inverse problems, namely algorithms for mapping data, such as recordings of neural activity in the brain, to latent variables which, in the neuroscience setting, quantify the effects of stimuli on neural activity. Inverse problems abound in science and engineering, ranging from image reconstruction problems (e.g., in MRI) to mask-design problems in computational lithography and source separation problems in radar, astrophysics, seismology, and neuroscience, to name a few examples. 

Physical/statistical models often constrain the latent variables and how they relate to the data we acquire. In recent years, deep learning algorithms, largely myopic of these constraints, have become a popular method for solving inverse problems. My research demonstrates, both in theory and in practice, how to incorporate physical/statistical constraints in the design of deep learning algorithms for solving inverse problems. My research also shows that deep learning algorithms designed in this fashion make powerful interpretable tools for elucidating the principles of neural computation; and for solving a wide range of inverse problems in imaging, physics, and beyond, particularly in the data-scarce regimes typical in engineering and science.

Biological intelligence has developed an uncanny ability to perform tasks such as object recognition and navigation, which require solutions, in dynamic settings, to inverse problems involving stimuli from multiple senses. I hypothesize that biological agents rely on highly-distributed computations to solve dynamic, multi-sensory inverse problems. In the future, I plan to develop models, theories, and experiments to test this hypothesis and artificial agents with this capability.