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Multiscale inverse problem, from Schroedinger to Newton to Boltzmann

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FKTW05 - Frontiers in numerical analysis of kinetic equations

Inverse problems are ubiquitous. People probe the media with sources and measure the outputs. At the scale of quantum, classical, statistical and fluid, these are inverse Schroedinger, inverse Newton’s second law, inverse Boltzmann problem, and inverse diffusion respectively. The universe, however, should have a universal mathematical description, as Hilbert proposed in 1900. In this talk, we initiate a line of research that connects inverse Schroedinger, to inverse Newton, to inverse Boltzmann, and finally to inverse diffusion. We will argue these are the same problem merely represented at different scales. The connections open the door to developing fast solvers for solving ill-posed inverse problems.

This talk is part of the Isaac Newton Institute Seminar Series series.

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