An integral component of many NASA missions involves remote sensing of the environment, both terrestrial and celestial. This is a challenging problem, since quantities of interest typically can not be directly measured but instead must be inferred. These inferences are made by solving inverse problems, where complex forward models are inverted to estimate parameters of the model. These parameters correspond to physical properties of the environment. Because of the complexity of many forward models, inversion is usually accomplished by minimizing the difference between observations and model predictions through adjustment of model parameters. This minimization process is computationally demanding, since it requires evaluating the forward model many times and minimizing a function of many variables. In this project, we propose to develop, using low-cost high performance hardware accelerators, a fast general-purpose parameter fitting software tool suite for fitting model parameters to observed data. The tool suite will allow NASA scientists to use state of the art high performance computing resources to speed their work. In the Phase I of this project we have shown that the three key components of model fitting, namely model evaluation, gradient calculation and cost functional minimization, can be accelerated using graphical processing unit (GPU) technology. The Phase I work has laid the foundation for Phase II of the project, where the components investigated and developed will be integrated into a parameter fitting tool suite. During Phase II, we will work closely with NASA scientists from the Stratospheric Aerosol and Gas Experiment (SAGE) III mission, the Solar Dynamics Observatory (SDO) and other missions to develop further capabilities of the tool suite.