An evolve-then-correct reduced order model for hidden fluid dynamics

In this paper, we put forth an evolve-then-correct reduced order modeling approach that combines intrusive and nonintrusive models to take hidden physical processes into account. Specifically, we split the underlying dynamics into known and unknown components. In the known part, we first utilize an intrusive Galerkin method projected on a set of basis functions obtained by proper orthogonal decomposition. We then formulate a recurrent neural network emulator based on the assumption that observed data is a manifestation of all relevant processes. We further enhance our approach by using an orthonormality conforming basis interpolation approach on a Grassmannian manifold to address off-design conditions. The proposed framework is illustrated here with the application of two-dimensional co-rotating vortex simulations under modeling uncertainty. The results demonstrate highly accurate predictions underlining the effectiveness of the evolve-then-correct approach toward realtime simulations, where the full process model is not known a priori

Accelerating Science: A Computing Research Agenda

The emergence of "big data" offers unprecedented opportunities for not only accelerating scientific advances but also enabling new modes of discovery. Scientific progress in many disciplines is increasingly enabled by our ability to examine natural phenomena through the computational lens, i.e., using algorithmic or information processing abstractions of the underlying processes; and our ability to acquire, share, integrate and analyze disparate types of data. However, there is a huge gap between our ability to acquire, store, and process data and our ability to make effective use of the data to advance discovery. Despite successful automation of routine aspects of data management and analytics, most elements of the scientific process currently require considerable human expertise and effort. Accelerating science to keep pace with the rate of data acquisition and data processing calls for the development of algorithmic or information processing abstractions, coupled with formal methods and tools for modeling and simulation of natural processes as well as major innovations in cognitive tools for scientists, i.e., computational tools that leverage and extend the reach of human intellect, and partner with humans on a broad range of tasks in scientific discovery (e.g., identifying, prioritizing formulating questions, designing, prioritizing and executing experiments designed to answer a chosen question, drawing inferences and evaluating the results, and formulating new questions, in a closed-loop fashion). This calls for concerted research agenda aimed at: Development, analysis, integration, sharing, and simulation of algorithmic or information processing abstractions of natural processes, coupled with formal methods and tools for their analyses and simulation; Innovations in cognitive tools that augment and extend human intellect and partner with humans in all aspects of science.Comment: Computing Community Consortium (CCC) white paper, 17 page

Philosophical Perspectives

This entry follows in the footsteps of Anselin’s famous 1989 NCGIA working paper entitled “What is special about spatial?” (a report that is very timely again in an age when non-spatial data scientists are ignorant of the special characteristics of spatial data), where he outlines three unrelated but fundamental characteristics of spatial data. In a similar vein, I am going to discuss some philosophical perspectives that are internally unrelated to each other and could warrant individual entries in this Body of Knowledge. The first one is the notions of space and time and how they have evolved in philosophical discourse over the past three millennia. Related to these are aspects of absolute versus relative conceptions of these two fundamental constructs. The second is a brief introduction to key philosophical approaches and how they impact geospatial science and technology use today. The third is a discussion of which of the promises of the Quantitative Revolution in Geography and neighboring disciplines have been fulfilled by GIScience (and what is still missing). The fourth and final one is an introduction to the role that GIScience may play in what has recently been formalized as theory-guided data science

Predictive Learning with Heterogeneity in Populations

University of Minnesota Ph.D. dissertation. October 2017. Major: Computer Science. Advisor: Vipin Kumar. 1 computer file (PDF); x, 119 pages.Predictive learning forms the backbone of several data-driven systems powering scientific as well as commercial applications, e.g., filtering spam messages, detecting faces in images, forecasting health risks, and mapping ecological resources. However, one of the major challenges in applying standard predictive learning methods in real-world applications is the heterogeneity in populations of data instances, i.e., different groups (or populations) of data instances show different nature of predictive relationships. For example, different populations of human subjects may show different risks for a disease even if they have similar diagnosis reports, depending on their ethnic profiles, medical history, and lifestyle choices. In the presence of population heterogeneity, a central challenge is that the training data comprises of instances belonging from multiple populations, and the instances in the test set may be from a different population than that of the training instances. This limits the effectiveness of standard predictive learning frameworks that are based on the assumption that the instances are independent and identically distributed (i.i.d), which are ideally true only in simplistic settings. This thesis introduces several ways of learning predictive models with heterogeneity in populations, by incorporating information about the context of every data instance, which is available in varying types and formats in different application settings. It introduces a novel multi-task learning framework for problems where we have access to some ancillary variables that can be grouped to produce homogeneous partitions of data instances, thus addressing the heterogeneity in populations. This thesis also introduces a novel strategy for constructing mode-specific ensembles in binary classification settings, where each class shows multi-modal distribution due to the heterogeneity in their populations. When the context of data instances is implicitly defined such that the test data is known to comprise of contextually similar groups, this thesis presents a novel framework for adapting classification decisions using the group-level properties of test instances. This thesis also builds the foundations of a novel paradigm of scientific discovery, termed as theory-guided data science, that seeks to explore the full potential of data science methods but without ignoring the treasure of knowledge contained in scientific theories and principles