Deep learning architectures for nonlinear operator functions and nonlinear inverse problems

Understand

We develop a theoretical analysis for special neural network architectures, termed operator recurrent neural networks, for approximating nonlinear functions whose inputs are linear operators.

• Such functions commonly arise in solution algorithms for inverse boundary value problems.
• Traditional neural networks treat input data as vectors, and thus they do not effectively capture the multiplicative structure associated with the linear operators that correspond to the data in such inverse problems.
• We therefore introduce a new family that resembles a standard neural network architecture, but where the input data acts multiplicatively on vectors.