The Nearest Neighbor model is the textit{de facto} hermodynamic model of RNA secondary structure formation and is a cornerstone of RNA structure prediction and sequence design. The current functional form (Turner 2004) contains approx13,000 nderlying thermodynamic parameters, and fitting these to both experimental and structural data is computationally challenging. Here, we leverage recent advances in textit{differentiable folding} a method for directly computing gradients of the RNA folding algorithms, to devise an efficient, scalable, and flexible means of parameter optimization that uses known RNA structures and thermodynamic experiments. Our method yields a significantly improved parameter set that outperforms existing baselines on all metrics, including an increase in the average predicted probability of ground-truth sequence-structure pairs for a single RNA family by over 23 orders of magnitude. Our framework provides a path towards drastically improved RNA models, enabling the flexible incorporation of new experimental data, definition of novel loss terms, large training sets, and even treatment as a module in larger deep learning pipelines. We make available a new database, RNAometer, with experimentally-determined stabilities for small RNA model systems.