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 autonomous identification of time-steps where the behavior of a time-series significantly deviates from a predefined model, or time-series change point detection, is an active field of research with notable applications in finance, health, and advertising. One family of time-series change detection algorithms, referred to as “model-based methods”, although useful for many applications, performs poor when the data are noisy and have outliers. We introduce a new framework that enables existing model-based methods to be more robust to these data challenges. We demonstrate the effectiveness of our approach on remote sensing and mobile health data. Our method introduces two new concepts: (i) a random sampling procedure allows us to overcome outliers, and (ii) a matrix-based representation of anomaly scores provides a flexible and intuitive way to identify multiple types of changes and test their significance. We show that our method performs better than several baseline methods, including application-specific algorithms, and provide all data and open-source code.

Mesoscale ocean eddies are a critical component of the Earth System as they dominate the ocean's kinetic energy and impact the global distribution of oceanic heat, salinity, momentum, and nutrients. Therefore, accurately representing these dynamic features is critical for our planet's sustainability. The majority of methods that identify eddies from satellite observations analyze the data in a frame-by-frame basis despite the fact that eddies are dynamic objects that propagate across space and time. We introduce the notion of spatio-temporal consistency to identify eddies in a continuous spatio-temporal field, to simultaneously ensure that the features detected are both spatially and temporally consistent. Our spatio-temporal consistency approach allows us to remove most of the expert criteria used in traditional methods to reduce false negatives. The removal of arbitrary heuristics enables us to render more complete eddy dynamics by identifying smaller and longer lived eddies compared to existing methods.

Mesoscale ocean eddies transport heat, salt, energy, and nutrients across oceans. As a result, accurately identifying and tracking such phenomena are crucial for understanding ocean dynamics and marine ecosystem sustainability. Traditionally, ocean eddies are monitored through two phases: identification and tracking. A major challenge for such an approach is that the tracking phase is dependent on the performance of the identification scheme, which can be susceptible to noise and sampling errors. In this paper, we focus on tracking, and introduce the concept of multiple hypothesis assignment (MHA), which extends traditional multiple hypothesis tracking for cases where the features tracked are noisy or uncertain. Under this scheme, features are assigned to multiple potential tracks, and the final assignment is deferred until more data are available to make a relatively unambiguous decision. Unlike the most widely used methods in the eddy tracking literature, MHA uses contextual spatio-temporal information to take corrective measures autonomously on the detection step a pos- teriori and performs significantly better in the presence of noise. This study is also the first to empirically analyze the relative robustness of eddy tracking algorithms.

As spatio-temporal data have become ubiquitous, an increasing challenge facing computer scientists is that of identifying discrete patterns in continuous spatio-temporal fields. In this paper, we introduce a parameter-free pattern mining application that is able to identify dynamic anomalies in ocean data, known as ocean eddies. Despite ocean eddy monitoring being an active field of research, we provide one of the first quantitative analyses of the performance of the most used monitoring algorithms. We present an incomplete information validation technique, that uses the performance of two methods to construct an imperfect ground truth to test the significance of patterns discovered as well as the relative performance of pattern mining algorithms. These methods, in addition to the validation schemes discussed provide researchers new directions in analyzing large unlabeled climate datasets.

Swirls of ocean currents known as ocean eddies are a crucial component of the ocean's dynamics. In addition to dominating the ocean's kinetic energy, eddies play a significant role in the transport of water, salt, heat, and nutrients. Therefore, understanding current and future eddy patterns is a central climate challenge to address future sustainability of marine ecosystems. The emergence of sea surface height observations from satellite radar altimeter has recently enabled researchers to track eddies at a global scale. The majority of studies that identify eddies from observational data employ highly parametrized connected component algorithms using expert filtered data, effectively making reproducibility and scalability challenging. In this paper, we frame the challenge of monitoring ocean eddies as an unsupervised learning problem. We present a novel change detection algorithm that automatically identifies and monitors eddies in sea surface height data based on heuristics derived from basic eddy properties. Our method is accurate, efficient, and scalable. To demonstrate its performance we analyze eddy activity in the Nordic Sea (60-80N and 20W-20E), an area that has received limited attention and has proven to be difficult to analyze using other methods.