Inverse Problems

Many problems in science and engineering are inverse problems. In science, 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 cognitive neuroscience,  one asks how one can detect, classify and recognize the distal origin of signals from their proximal sensory cues, converting well known forward problems in the physical sciences and engineering, e.g.  optics, hydrodynamics and acoustics to inverse problems in psychophysics associated with vision, olfaction, and audition.

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. MahadevanProc. Natl. Acad.  Sci.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]
Optimal control of aging in complex networks E. Sun, T. Michaels, and L. Mahadevan, Proc. Natl. Acad. Sci., 117, 20404-410, 2020. [ONLINE ARTICLE] [DOI] [View PDF] [Download PDF]
Optimal control of plates using incompatible strains G.W. Jones and L. Mahadevan,  Nonlinearity  28, 3153–3174, 2015. [View PDF] [Download PDF]
Optimal intercellular competition in senescence and cancer. Thomas C. T. Michaels and L. Mahadevan, Royal Society. Volume 479, Issu 2276, 30 August 2023. [ONLINE ARTICLE] [DOI] [View PDF] [Download PDF]
Optimal policies for mitigating pandemic costs: a tutorial model. M Serra, S al-Mosleh, S Ganga Prasath, V Raju, S Mantena, J Chandra, S Iams L. MAHADEVAN  Physical Biology. Volume 19, 9 August 2022 . [ONLINE ARTICLE] [DOI] [View PDF] [Download PDF]
Optimal strategies for inhibition of protein aggregation T.C. Michaels, C. Weber and L. Mahadevan, PNAS 116 (29) 14593-14598, 2019. [View PDF] [Download PDF]
Optimal strategies for throwing accurately M. Venkadesan and L. Mahadevan,  Royal Society Open Science  , 4: 170136. 2017. [View PDF] [Download PDF]
Optimal switching between geocentric and egocentric strategies in navigation O. Peleg and L. Mahadevan  Royal Society Open Science  3: 160128, 2016. [View PDF] [Download PDF]
Optimal transport and control of active drops. Suraj Shankar, Vidya Raju and L. Mahadevan,  Proceedings of the National Academy of Sciences. ,119 (35), e2121985119, August 24, 2022 [ONLINE ARTICLE] [DOI] [View PDF] [Download PDF]
Optimal vein density in artificial and real leaves X. Noblin, L. Mahadevan, I. Coomaraswamy, D. Weitz, N. Holbrook and M. Zwieniecki,  Proceedings of the National Academy of Sciences (USA),  105, 9140, 2008. [View PDF] [Download PDF]
Balancing on tightropes and slacklines P. Paoletti and L. Mahadevan,  Journal of the Royal Society - Interface , 9, 2097-2108, 2012. [View PDF] [Download PDF]
Feedback control of protein aggregation. A. J. Dear, T.C. T. Michaels, T. P. J. Knowles, and L. Mahadevan, J. Chem. Phys. 155, 064102 (2021) [DOI] [View PDF] [Download PDF]
Balancing efficiency and homogeneity of biomaterial transport in networks. S. Liese, L. Mahadevan and A. Carlson. Europhysics Letters, Vol. 135 | No. 5 [ONLINE ARTICLE] [DOI] [View PDF] [Download PDF]
Planar controlled gliding, tumbling and descent.
P. Paoletti and L. Mahadevan,  Journal of Fluid Mechanics,  698, 489-516, 2011.  [View PDF] [Download PDF]
Controlled gliding and perching through deep-reinforcement-learning. G.Novati, L. Mahadevan, and P. Koumoutsakos, Physical Review Fluids 4, 093902, 2019. [View PDF] [Download PDF]
Coordinated crawling via reinforcement learning. S. Mishra, W. van Rees, L. MahadevanRoyal Society-Interface, 17: 20200198,  2020. [DOI] [View PDF] [Download PDF]
Models for benthic bipedalism. F. Giardina and L. Mahadevan, Royal Society - Interface 18: 20200701, 2021. [ONLINE ARTICLE] [DOI] [View PDF] [Download PDF]
Intermittent locomotion as an optimal control strategy P. Paoletti and L. Mahadevan,  Proceedings of the Royal Society (A) , 470, 20130535, 2014. [View PDF] [Download PDF]
Organ size control via hydraulically gated oscillations Teresa Ruiz-Herrero, Kévin Alessandri, Basile V. Gurchenkov, Pierre Nassoy and L. Mahadevan,  Development  144, 4422-4427, 2017. [View PDF] [Download PDF]