Inverse Problems

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.

Related Publications

Biomimetic 4D printing A. S. Gladman, E. A. Matsumoto, R.G. Nuzzo, L. Mahadevan, and J.A. Lewis,  Nature Materials , 15, 413-19, 2016. [View PDF] [Download PDF]
Shape-shifting structured lattices via multimaterial 4D printing. J.W. Boley, W.M. van Rees, C. Lissandrello, M.N. Horenstein, R.L. Truby, A. Kotikian, J.A. Lewis, and L. MahadevanProceedings of the National Academy of Sciences, Oct 2019, 116 (42) 20856-20862, 2019. [ONLINE ARTICLE] [View PDF] [Download PDF]
Programming shape using kirigami tessellations G. P. T. Choi, L. H. Dudte and L. MahadevanNature Materials 18, 999–1004. 2019. [DOI] [View PDF] [Download PDF]
Programming curvature using origami tessellations L.H. Dudte, E. Vouga, T. Tachi and L. Mahadevan,  Nature Materials , 15, 583-88, 2016. [View PDF] [Download PDF]
The branch with the furthest reach Z. Wei, S. Mandre and L. Mahadevan,  Europhysics Letters , 97, 14005, 2012. [View PDF] [Download PDF]
Forward and inverse problems in the mechanics of soft filaments M. Gazzola, L. H. Dudte, A. G. McCormick and L. Mahadevan,  Royal Society Open Science  5: 171628, 2018. [DOI] [View PDF] [Download PDF]
Controlled growth and form of precipitating microsculptures C. N. Kaplan, W. L. Noorduin, L. Li, R. Sadza, L. Folkertsma, J. Aizenberg, L. Mahadevan,  Science  355, 1395-99, 2017. [View PDF] [Download PDF]