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math.AP2022
The Calderón's problem via DeepONets
Javier Castro, Claudio Muñoz, Nicolás Valenzuela
We consider the Dirichlet-to-Neumann operator and the direct and inverse Calderón's mappings appearing in the Inverse Problem of recovering a smooth bounded and positive isotropic…
math.PR2022
The Kolmogorov Infinite Dimensional Equation in a Hilbert space Via Deep Learning Methods
Javier Castro
We consider the nonlinear Kolmogorov equation posed in a Hilbert space , not necessarily of finite dimension. This model was recently studied by Cox et al. [24] in the framework…