Many problems in science and engineering are inverse problems. For example, an experimental result that requires an explanation asks the question – given the data, what is the theory/model that provides it? In engineering, a given function (in a product/software …. ) requires a design that provides the function. In perception, vision, olfaction, and audition are inverse problems associated with optics, hydrodynamics and acoustics – for in each case, one asks how one can detect, classify and recognize the distal origin of signals from their proximal sensory cues.
Inverse problems are often defined by a goal to be achieved subject to some constraints (such as adherence to physical law, robustness to noise, symmetry), and are usually not well-posed, i.e. they can lead to multiple answers. Our interests in this area span both methodological and practical aspects. In methodology, a recent interest is in statistical-geometric inverse problems from perceptual psychology and cognition. And from a practical perspective, we have worked on a diverse range of applications that include structural optimization, strategies for 3d and 4d printing, optimal drug treatment protocols for protein misfolding diseases, efficient locomotion etc.