Chemistry and materials research increasingly blends scientific insight with data-driven methods. The hierarchy of integration between them provides a framework for the use of data science. At level one, machine learning can be used to replace computationally expensive calculations within the overall workflow. Examples included the determination of molecular forces needed to integrate molecular dynamics, and the determination of multidimensional non-recrossing dividing surfaces to calculate transition state theory rates. At level two, data science can be used to predict overall properties without

reference to any intermediate quantities. Examples include our recent determination of nanoparticle features to their effects on organismal viability through the use of ensemble methods suited to small datasets. At level three, the learning model is engineered to reflect the system itself.

For example, we can predict electronic band gaps using nested autoencoders that capture features and labels across multiple length scales at once. At level four, physics-based theory and simulation are coupled seamlessly with data-science workflows in closed loops. While deeper integration feels natural to chemists, it can seem at odds with data-science practices that ``let the data speak'' without prior assumptions. Through the integration hierarchy, we show how to best reconcile domain science within data science approaches to accelerate reliable molecular and materials discovery.