Artificial intelligence (AI) relies on mathematical models that map input data to output labels, necessitating pre-labeled datasets for training. The increasing complexity of AI architectures has escalated data requirements, which pose significant challenges, particularly in physical and environmental systems where data collection is resource-intensive. However, these domains also present the opportunity to integrate underlying physical laws to reduce data demands and model complexity - a paradigm known as Machine Education. Instead of relying solely on data-driven learning, machine education incorporates physical insights into AI models, enabling more efficient solutions with less data.

Two complementary machine education approaches will be presented. First, a hybrid physics-machine learning pipeline for reconstruction of dense physical fields from sparse measurements. It couples Radial Basis Function (RBF) reconstruction with a Neural Network (NN) correction and a Partial Differential Equation (PDE) solver, so that the numerical solver itself is embedded directly in the training loop of the learned component. Notably, the NN is trained without assuming availability of examples of the fully-resolved field. This is made possible by implementing the PDE solver so that it is end-to-end differentiable, allowing gradients to be backpropagated through the solver during training.

Second, a Fourier-based synthetic time series generation technique, which produces signals preserving the mean, variance, and autocorrelation of original datasets, facilitating robust data augmentation when real observations are limited.