Numerical models constitute the most advanced physical-based methods for modeling complex ground water systems. Spatial and/or temporal variability of aquifer parameters, boundary conditions, and initial conditions (for transient simulations) can be assigned across the numerical model domain. While this constitutes a powerful modeling advantage, it also presents the formidable challenge of overcoming parameter uncertainty, which, to date, has not been satisfactorily resolved, inevitably producing model prediction errors. In previous research, artificial neural networks (ANNs), developed with more accessible field data, have achieved excellent predictive accuracy over discrete stress periods at site-specific field locations in complex ground water systems. In an effort to combine the relative advantages of numerical models and ANNs, a new modeling paradigm is presented. The ANN models generate accurate predictions for a limited number of field locations. Appending them to a numerical model produces an overdetermined system of equations, which can be solved using a variety of mathematical techniques, potentially yielding more accurate numerical predictions. Mathematical theory and a simple two-dimensional example are presented to overview relevant mathematical and modeling issues. Two of the three methods for solving the overdetermined system achieved an overall improvement in numerical model accuracy for various levels of synthetic ANN errors using relatively few constrained head values (i.e., cells), which, while demonstrating promise, requires further research. This hybrid approach is not limited to ANN technology; it can be used with other approaches for improving numerical model predictions, such as regression or support vector machines (SVMs).
[1]
Ferenc Szidarovszky,et al.
A neural network model for predicting aquifer water level elevations
,
2005,
Ground water.
[2]
Vladan Babovic,et al.
Neural networks as routine for error updating of numerical models
,
2001
.
[3]
Ferenc Szidarovszky,et al.
Artificial Neural Network Approach for Predicting Transient Water Levels in a Multilayered Groundwater System under Variable State, Pumping, and Climate Conditions
,
2003
.
[4]
L. L. Rogers,et al.
Optimization of groundwater remediation using artificial neural networks with parallel solute transport modeling
,
1994
.
[5]
David Anderson,et al.
Multimodel Ranking and Inference in Ground Water Modeling
,
2004,
Ground water.
[6]
G. de Marsily,et al.
Four decades of inverse problems in hydrogeology
,
2000
.
[7]
Ferenc Szidarovszky,et al.
Multiobjective Analysis of a Public Wellfield Using Artificial Neural Networks
,
2007,
Ground water.
[8]
Ferenc Szidarovszky,et al.
Predicting Conductance Due to Upconing Using Neural Networks
,
2005,
Ground water.
[9]
Ferenc Szidarovszky,et al.
Application of Artificial Neural Networks to Complex Groundwater Management Problems
,
2003
.
[10]
N Oreskes,et al.
Verification, Validation, and Confirmation of Numerical Models in the Earth Sciences
,
1994,
Science.