Abstract: The extended Kalman filter (EKF) has long been recognized as a powerful, yet computationally intensive, methodology for stochastic parameter estimation. Three improvements to traditional algorithms are presented and applied to heterogeneous transmissivity estimation. First, the costly EKF covariance updates are replaced by more efﬁcient approximations. Second, the zonation structure of the distributed parameter ﬁeld being estimated is dynamically determined and reﬁned using a partitional clustering algorithm. Third, a new method of merging ﬁrst and second moments of random ﬁelds that have heterogeneous statistics is introduced. We apply this method, called random ﬁeld union, as an alternative to conventional random ﬁeld averaging for the systematic shrinking of covariance matrices as the dimensionality of the parameter space is reduced. The effects of these three improvements are examined. In applications to steady state groundwater ﬂow test problems, we show that the ﬁrst and second improvements reduce the computational time requirements dramatically, while the second and third can improve the accuracy and stability of the results. The resulting integrated method is successfully applied to a larger, more realistic calibration test case under steady and cyclostationary ﬂow conditions (similar to regular seasonal ﬂuctuations). When ﬂow is steady, the method can be viewed as iterative; when ﬂow is transient, the method is fully recursive.
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Bongard's work focuses on understanding the general nature of cognition, regardless of whether it is found in humans, animals or robots. This unique approach focuses on the role that morphology and evolution plays in cognition. Addressing these questions has taken him into the fields of biology, psychology, engineering and computer science.
Danforth is an applied mathematician interested in modeling a variety of physical, biological, and social phenomenon. He has applied principles of chaos theory to improve weather forecasts as a member of the Mathematics and Climate Research Network, and developed a real-time remote sensor of global happiness using messages from Twitter: the Hedonometer. Danforth co-runs the Computational Story Lab with Peter Dodds, and helps run UVM's reading group on complexity.
Laurent studies the interaction of structure and dynamics. His research involves network theory, statistical physics and nonlinear dynamics along with their applications in epidemiology, ecology, biology, and sociology. Recent projects include comparing complex networks of different nature, the coevolution of human behavior and infectious diseases, understanding the role of forest shape in determining stability of tropical forests, as well as the impact of echo chambers in political discussions.
Hines' work broadly focuses on finding ways to make electric energy more reliable, more affordable, with less environmental impact. Particular topics of interest include understanding the mechanisms by which small problems in the power grid become large blackouts, identifying and mitigating the stresses caused by large amounts of electric vehicle charging, and quantifying the impact of high penetrations of wind/solar on electricity systems.
Bagrow's interests include: Complex Networks (community detection, social modeling and human dynamics, statistical phenomena, graph similarity and isomorphism), Statistical Physics (non-equilibrium methods, phase transitions, percolation, interacting particle systems, spin glasses), and Optimization(glassy techniques such as simulated/quantum annealing, (non-gradient) minimization of noisy objective functions).