We confirm that energy dissipation weighting provides the most accurate approach to determining the effective hydraulic conductivity (Keff) of a binary K grid. Machine learning and deep learning algorithms of varying complexity (decision tree, vanilla CNN, UNET) can infer Keff with extremely high accuracy (R2 > 0.99), even given only the fraction of the grid occupied by the high K medium. Adding information derived from the energy dissipation distribution improved each algorithm. However, all methods failed to infer Keff accurately for outlier cases, all of which were inferred accurately using energy dissipation weighting directly. The UNET architecture could be trained to infer the energy dissipation weighting pattern from an image of the K distribution with high fidelity, although it was less accurate for cases with highly localized structures that controlled flow. Furthermore, the UNET architecture learned to infer the energy dissipation weighting even if it was not trained on this information. However, the weights were represented within the UNET in a way that was not immediately interpretable by a human user. This reiterates the idea that even if ML/DL algorithms are trained to make some hydrologic predictions accurately, they must be designed and trained to provide each user-required output if their results are to be used to improve our understanding of hydrologic systems most effectively.

We demonstrate the application of two simple machine learning tools - regression tree and gradient boosting analyses - to a hydrologic inference problem to address two objectives. The first goal was to infer the flux between a river and the subsurface based on high temporal resolution (5-minute) observations of subsurface pressure and temperature. The second goal was to identify an optimal set of observations to support these inferences. Specifically, we examine how many and what type of observations (pressure and/or temperature) were necessary and at what depths. Using synthetic observations and surface fluxes provided by a fully resolved three-dimensional flow and heat transport model, we found that both machine learning tools could identify the flux well using pressure and temperature measurements collected at three depths, even when considerable noise was added to the synthetic observations. Neither method could provide reasonable flux estimates given only noisy temperature data. A shallow, collocated temperature and pressure observations performed as well as the complete data set. The results show the promise of using machine learning tools to design hydrologic measurement networks - both for determining whether a proposed data set can constrain inversion and for optimizing monitoring networks comprised of multiple measurement types.