Retrieving the inherent optical properties of water from remote sensing multispectral reflectance measurements is difficult due to both the complex nature of the forward modeling and the inherent nonlinearity of the inverse problem. In such cases, neural network (NN) techniques have a long history in inverting complex nonlinear systems. The process we adopt utilizes two NNs in parallel. The first NN is used to relate the remote sensing reflectance at available MODIS-visible wavelengths (except the $678\mathrm{nm}$ fluorescence channel) to the absorption and backscatter coefficients at $442\mathrm{nm}$ (peak of chlorophyll absorption). The second NN separates algal and nonalgal absorption components, outputting the ratio of algal-to-nonalgal absorption. The resulting synthetically trained algorithm is tested using both the NASA Bio-Optical Marine Algorithm Data Set (NOMAD), as well as our own field datasets from the Chesapeake Bay and Long Island Sound, New York. Very good agreement is obtained, with $R^2$ values of 93.75%, 90.67%, and 86.43% for the total, algal, and nonalgal absorption, respectively, for the NOMAD. For our field data, which cover absorbing waters up to about $6{\mathrm{m}}^{-1}$ , $R^2$ is 91.87% for the total measured absorption.