The ocean's role in modulating the observed 1–7 Pg C yr<sup>−1</sup> inter-annual variability in atmospheric CO<sub>2</sub> growth rate is an important, but poorly constrained process due to current spatio-temporal limitations in ocean carbon measurements. Here, we investigate and develop a non-linear empirical approach to predict inorganic CO<sub>2</sub> concentrations (total carbon dioxide (<i>C</i><sub>T</sub>) and total alkalinity (<i>A</i><sub>T</sub>)) in the global ocean mixed layer from hydrographic properties (temperature, salinity, dissolved oxygen and nutrients). The benefit of this approach is that once the empirical relationship is established, it can be applied to hydrographic datasets that have better spatio-temporal coverage, and therefore provide an additional constraint to diagnose ocean carbon dynamics globally. Previous empirical approaches have employed multiple linear regressions (MLR) and relied on ad hoc geographic and temporal partitioning of carbon data to constrain complex global carbon dynamics in the mixed layer. Synthesizing a new global <i>C</i><sub>T</sub>/<i>A</i><sub>T</sub> carbon bottle dataset consisting of ~33 000 measurements in the open ocean mixed layer, we develop a neural network based approach to better constrain the non-linear carbon system. The approach classifies features in the global biogeochemical dataset based on their similarity and homogeneity in a self-organizing map (SOM; Kohonen, 1988). After the initial SOM analysis, which includes geographic constraints, we apply a local linear optimizer to the neural network, which considerably enhances the predictive skill of the new approach. We call this new approach SOMLO, or self-organizing multiple linear output. Using independent bottle carbon data, we compare a traditional MLR analysis to our SOMLO approach to capture the spatial <i>C</i><sub>T</sub> and <i>A</i><sub>T</sub> distributions. We find the SOMLO approach improves predictive skill globally by 19% for <i>C</i><sub>T</sub>, with a global capacity to predict <i>C</i><sub>T</sub> to within 10.9 μmol kg<sup>−1</sup> (9.2 μmol kg<sup>−1</sup> for <i>A</i><sub>T</sub>). The non-linear SOMLO approach is particularly powerful in complex but important regions like the Southern Ocean, North Atlantic and equatorial Pacific, where residual standard errors were reduced between 25 and 40% over traditional linear methods. We further test the SOMLO technique using the Bermuda Atlantic time series (BATS) and Hawaiian ocean time series (HOT) datasets, where hydrographic data was capable of explaining 90% of the seasonal cycle and inter-annual variability at those multi-decadal time-series stations.