Extrapolation -- the ability to make inferences that go beyond the scope of one's experiences -- is a hallmark of human intelligence. By contrast, the generalization exhibited by contemporary neural network algorithms is largely limited to interpolation between data points in their training corpora. In this paper, we consider the challenge of learning representations that support extrapolation. We introduce a novel visual analogy benchmark that allows the graded evaluation of extrapolation as a function of distance from the convex domain defined by the training data. We also introduce a simple technique, context normalization, that encourages representations that emphasize the relations between objects. We find that this technique enables a significant improvement in the ability to extrapolate, considerably outperforming a number of competitive techniques.
Yang, Yuan; Pan, Ming; Beck, Hylke; Fisher, Colby; Beighley, R. Edward; Kao, Shih-Chieh; Hong, Yang; Wood, Eric
Abstract:
Conventional basin-by-basin approaches to calibrate hydrologic models are limited to gauged basins and typically result in spatially discontinuous parameter fields. Moreover, the consequent low calibration density in space falls seriously behind the need from present-day applications like high resolution river hydrodynamic modeling. In this study we calibrated three key parameters of the Variable Infiltration Capacity (VIC) model at every 1/8° grid-cell using machine learning-based maps of four streamflow characteristics for the conterminous United States (CONUS), with a total of 52,663 grid-cells. This new calibration approach, as an alternative to parameter regionalization, applied to ungauged regions too. A key difference made here is that we tried to regionalize physical variables (streamflow characteristics) instead of model parameters whose behavior may often be less well understood. The resulting parameter fields no longer presented any spatial discontinuities and the patterns corresponded well with climate characteristics, such as aridity and runoff ratio. The calibrated parameters were evaluated against observed streamflow from 704/648 (calibration/validation period) small-to-medium-sized catchments used to derive the streamflow characteristics, 3941/3809 (calibration/validation period) small-to-medium-sized catchments not used to derive the streamflow characteristics) as well as five large basins. Comparisons indicated marked improvements in bias and Nash-Sutcliffe efficiency. Model performance was still poor in arid and semiarid regions, which is mostly due to both model structural and forcing deficiencies. Although the performance gain was limited by the relative small number of parameters to calibrate, the study and results here served as a proof-of-concept for a new promising approach for fine-scale hydrologic model calibrations.
