  We propose a new methodology for pricing options on flow forwards by applying
infinite-dimensional neural networks. We recast the pricing problem as an
optimization problem in a Hilbert space of real-valued function on the positive
real line, which is the state space for the term structure dynamics. This
optimization problem is solved by facilitating a novel feedforward neural
network architecture designed for approximating continuous functions on the
state space. The proposed neural net is built upon the basis of the Hilbert
space. We provide an extensive case study that shows excellent numerical
efficiency, with superior performance over that of a classical neural net
trained on sampling the term structure curves.
