We use the maximum-entropy variational technique to infer solutions to second-order partial differential equations. We restrict ourselves to problems with Dirichlet boundary conditions. First, we construct a basis of moment functions in terms of which we set up the constraints for a maximum entropy inversion for the inference of solutions to elliptic equations. Then we extend the scheme to the inference of time dependence in evolution equations. This extension is done by solving a small system of first-order initial-value differential equations for the moments of the solution vector. [References: 24]
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