Finite-speed particle scattering can reconstruct a force field once the particle kinetic energy exceeds the largest potential difference between the domain interior and its boundary, supported by analytic examples and ML experiments.
Two dimensional compact simple Riemannian manifolds are boundary distance rigid
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We prove that knowing the length of geodesics joining points on the boundary of a two-dimensional, compact, simple Riemannian manifold with boundary, we can determine uniquely the Riemannian metric up to the natural obstruction.
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Limits of the inverse scattering problem
Finite-speed particle scattering can reconstruct a force field once the particle kinetic energy exceeds the largest potential difference between the domain interior and its boundary, supported by analytic examples and ML experiments.