Abstract: A method for pattern completion based on the application of artificial neural networks and possessing many operational objectives of the ordinary kriging approach, neural kriging, is developed. A neural kriging (NK) network is described, implemented in a parallelizing algorithm, and applied to develop maps of discrete spatially distributed fields (e.g., log hydraulic conductivity). NK is, in the case of two discrete field values, similar to indicator kriging. It uses a feed-forward counterpropagation training approach because field observations are available and because fast yet reliable results are obtained. NK is data-driven and requires no estimate of a covariance function. The optimal design of the NK network is found to depend on the number of hidden units in a more complex way than expected. The quality of the estimate of each pixel of the NK maps can be presented as well, as in kriging, to help identify areas in which additional information will be most beneficial. A comparison with a reference field shows that the NK network produces unbiased errors relative to sample bias and reproduces the variogram of a quantized random field with reasonable accuracy. Ordinary kriging (OK) followed by quantization can also perform well; however, estimation errors in the variogram selected for use in OK (in this case the range cofficient in particular) must be carefully examined and treated. The NK method can provide multiple realizations of the estimated field, all of which respect observations; hence conditional simulation is demonstrably possible. The combination of simplicity, interpolation, reasonably accurate prediction statistics, ability to provide conditional simulations, and computational speed suggest that artificial neural networks can be useful tools in geohydrology when applied to specific well-defined problems for which they are well suited, such as aquifer characterization.
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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).