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.
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