For adaptive-optics systems to compensate for atmospheric turbulence effects, the wave-front perturbation must be measured with a wave front sensor (WPS), and key parameters of the atmosphere and the adaptive-optics system must be known. Two parameters of particular interest include the Fried coherence length r(0) and the WPS slope measurement error. Statistics-based optimal techniques, such as the minimum variance phase reconstructor, have been developed to improve the imaging performance of adaptive-optics systems. However, these statistics-based models rely on knowledge of the current state of the key parameters. Neural networks provide nonlinear solutions to adaptive-optics problems while offering the possibility of adapting to changing seeing conditions. We address the use of neural networks for three tasks: (l) to reduce the WPS slope measurement error, (2) to estimate the Fried coherence length r(0), and (3) to estimate the variance of the WPS slope measurement error. All of these tasks are accomplished by using only the noisy WPS measurements as input. Where appropriate, we compare our method with classical statistics-based methods to determine if neural networks offer true benefits in performance. Although a statistics-based method is found to perform better than a neural network in reducing WPS slope measurement error, neural networks perform better in estimating the variance of the WPS slope measurement error, and both methods perform well in estimating r(0).