Deep Neural Networks Are Effective At Learning High-Dimensional Hilbert-Valued Functions From Limited Data

Understand

Accurate approximation of scalar-valued functions from sample points is a key task in computational science.

• Recently, machine learning with Deep Neural Networks (DNNs) has emerged as a promising tool for scientific computing, with impressive results achieved on problems where the dimension of the data or problem domain is large.
• This work broadens this perspective, focusing on approximating functions that are Hilbert-valued, i.e.
• take values in a separable, but typically infinite-dimensional, Hilbert space.