Derivate Informed Neural Operator: An Efficient Framework for High-Dimensional Parametric Derivative Learning. (arXiv:2206.10745v1 [math.NA])

Web: http://arxiv.org/abs/2206.10745

Neural operators have gained significant attention recently due to their
ability to approximate high-dimensional parametric maps between function
spaces. At present, only parametric function approximation has been addressed
in the neural operator literature. In this work we investigate incorporating
parametric derivative information in neural operator training; this information
can improve function approximations, additionally it can be used to improve the
approximation of the derivative with respect to the parameter, which is often
the key to scalable solution of high-dimensional outer-loop …

arxiv framework learning math neural parametric