Data science models, although successful in a number of commercial domains, have had limited applicability in scientific problems involving complex physical phenomena. Theory-guided data science (TGDS) is an emerging paradigm that aims to leverage the wealth of scientific knowledge for improving the effectiveness of data science models in enabling scientific discovery. The overarching vision of TGDS is to introduce scientific consistency as an essential component for learning generalizable models. Further, by producing scientifically interpretable models, TGDS aims to advance our scientific understanding by discovering novel domain insights. Indeed, the paradigm of TGDS has started to gain prominence in a number of scientific disciplines such as turbulence modeling, material discovery, quantum chemistry, bio-medical science, bio-marker discovery, climate science, and hydrology. In this paper, we formally conceptualize the paradigm of TGDS and present a taxonomy of research themes in TGDS. We describe several approaches for integrating domain knowledge in different research themes using illustrative examples from different disciplines. We also highlight some of the promising avenues of novel research for realizing the full potential of theory-guided data science.

The rapid growth of data in water resources has created new opportunities to accelerate knowledge discovery with the use of advanced deep learning tools. Hybrid models that integrate theory with state‐of‐the art empirical techniques have the potential to improve predictions while remaining true to physical laws. This paper evaluates the Process‐Guided Deep Learning (PGDL) hybrid modeling framework with a use‐case of predicting depth‐specific lake water temperatures. The PGDL model has three primary components: a deep learning model with temporal awareness (long short‐term memory recurrence), theory‐based feedback (model penalties for violating conversation of energy), and model pretraining to initialize the network with synthetic data (water temperature predictions from a process‐based model). In situ water temperatures were used to train the PGDL model, a deep learning (DL) model, and a process‐based (PB) model. Model performance was evaluated in various conditions, including when training data were sparse and when predictions were made outside of the range in the training data set. The PGDL model performance (as measured by root‐mean‐square error (RMSE)) was superior to DL and PB for two detailed study lakes, but only when pretraining data included greater variability than the training period. The PGDL model also performed well when extended to 68 lakes, with a median RMSE of 1.65 °C during the test period (DL: 1.78 °C, PB: 2.03 °C; in a small number of lakes PB or DL models were more accurate). This case‐study demonstrates that integrating scientific knowledge into deep learning tools shows promise for improving predictions of many important environmental variables.

Geosciences is a field of great societal relevance that requires solutions to several urgent problems facing our humanity and the planet. As geosciences enters the era of big data, machine learning (ML)-that has been widely successful in commercial domains-offers immense potential to contribute to problems in geosciences. However, problems in geosciences have several unique challenges that are seldom found in traditional applications, requiring novel problem formulations and methodologies in machine learning. This article introduces researchers in the machine learning (ML) community to these challenges offered by geoscience problems and the opportunities that exist for advancing both machine learning and geosciences. We first highlight typical sources of geoscience data and describe their properties that make it challenging to use traditional machine learning techniques. We then describe some of the common categories of geoscience problems where machine learning can play a role, and discuss some of the existing efforts and promising directions for methodological development in machine learning. We conclude by discussing some of the emerging research themes in machine learning that are applicable across all problems in the geosciences, and the importance of a deep collaboration between machine learning and geosciences for synergistic advancements in both disciplines.

Aim Functional traits of organisms are key to understanding and predicting biodiversity and ecological change, which motivates continuous collection of traits and their integration into global databases. Such trait matrices are inherently sparse, severely limiting their usefulness for further analyses. On the other hand, traits are characterized by the phylogenetic trait signal, trait-trait correlations and environmental constraints, all of which provide information that could be used to statistically fill gaps. We propose the application of probabilistic models which, for the first time, utilize all three characteristics to fill gaps in trait databases and predict trait values at larger spatial scales.Innovation For this purpose we introduce BHPMF, a hierarchical Bayesian extension of probabilistic matrix factorization (PMF). PMF is a machine learning technique which exploits the correlation structure of sparse matrices to impute missing entries. BHPMF additionally utilizes the taxonomic hierarchy for trait prediction and provides uncertainty estimates for each imputation. In combination with multiple regression against environmental information, BHPMF allows for extrapolation from point measurements to larger spatial scales. We demonstrate the applicability of BHPMF in ecological contexts, using different plant functional trait datasets, also comparing results to taking the species mean and PMF.Main conclusions Sensitivity analyses validate the robustness and accuracy of BHPMF: our method captures the correlation structure of the trait matrix as well as the phylogenetic trait signal -also for extremely sparse trait matrices -and provides a robust measure of confidence in prediction accuracy for each missing entry. The combination of BHPMF with environmental constraints provides a promising concept to extrapolate traits beyond sampled regions, accounting for intraspecific trait variability. We conclude that BHPMF and its derivatives have a high potential to support future trait-based research in macroecology and functional biogeography.