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.

验证和验证现代科学机器学习工作流程的有效技术是很具挑战性的。本研究通过展示（1）多个标准插值技术具有信息丰富的误差界限，可以进行高效计算或估计；（2）不同插值器之间的比较性能有助于验证目标；（3）在深度学习技术生成的潜在空间上部署插值方法，使得黑匣子模型具有一定的可解释性。我们提供了一个详细的案例研究，用于从飞翼图像预测升阻比。本研究的代码可在公共 Github 存储库中获取。