Leveraging Interpolation Models and Error Bounds for Verifiable
  Scientific Machine Learning
Tyler Chang Andrew Gillette Romit Maulik
Effective verification and validation techniques for modern scientific
machine learning workflows are challenging to devise. Statistical methods are
abundant and easily deployed, but often rely on speculative assumptions about
the data and methods involved. Error bounds for classical interpolation
techniques can provide mathematically rigorous estimates of accuracy, but often
are difficult or impractical to determine computationally. In this work, we
present a best-of-both-worlds approach to verifiable scientific machine
learning by demonstrating that (1) multiple standard interpolation techniques
have informative error bounds that can be computed or estimated efficiently;
(2) comparative performance among distinct interpolants can aid in validation
goals; (3) deploying interpolation methods on latent spaces generated by deep
learning techniques enables some interpretability for black-box models. We
present a detailed case study of our approach for predicting lift-drag ratios
from airfoil images. Code developed for this work is available in a public
Github repository.