A stabilized FEM with POD and autoencoder compression plus a learned solution operator reconstructs PDE solutions in unique continuation problems, with a first-order H1 error estimate in the linear case and numerical demonstrations for nonlinear cases.
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Stabilizing and Solving Unique Continuation Problems by Parameterizing Data and Learning Finite Element Solution Operators
A stabilized FEM with POD and autoencoder compression plus a learned solution operator reconstructs PDE solutions in unique continuation problems, with a first-order H1 error estimate in the linear case and numerical demonstrations for nonlinear cases.