In a model simulating dynamics of a system, parameters can represent system sensitivities and unresolved processes, therefore affecting model accuracy and uncertainty. Taking a light use efficiency (LUE) model as an example, which is a typical approach to estimate gross primary productivity (GPP), we propose a Simultaneous Parameter Inversion and Extrapolation approach (SPIE) to overcome issues stemming from plant-functional-type(PFT)-dependent parameterizations. SPIE refers to predicting model parameters using an artificial neural network based on collected variables, including PFT, climate types, bioclimatic variables, vegetation features, atmospheric nitrogen and phosphorus deposition and soil properties. The neural network was optimized to minimize GPP errors and constrain LUE model sensitivity functions. We compared SPIE with 11 typical parameter extrapolating methods, including PFT- and climate-specific parameterizations, global and PFT-based parameter optimization, site-similarity, and regression approaches. All methods were assessed using Nash-Sutcliffe model efficiency(NSE), determination coefficient and normalized root mean squared error, and contrasted with site-specific calibrations. Ten-fold cross-validated results showed that SPIE had the best performance across sites, various temporal scales and assessing metrics. None of the approaches performed similar to site-level calibrations(NSE=0.95), but SPIE was the only approach showing positive NSE(0.68). The Shapley value, layer-wise relevance and partial dependence showed that vegetation features, bioclimatic variables, soil properties and some PFTs are determining parameters. The proposed parameter extrapolation approach overcomes strong limitations observed in many standard parameterization methods. We argue that expanding SPIE to other models overcomes current limits and serves as an entry point to investigate the robustness and generalization of different models.