Meta-modelling paths of simple climate models using neural networks and dirichlet polynomials: an application to DICE

Efficiently assessing temperature trajectories driven by carbon emissions is crucial for actuarial sciences in the context of climate change and the transition toward net-zero emissions by 2050, as temperature directly affects the frequency and severity of climate-related risks—such as heatwaves, floods, and agricultural losses—that underpin insurance liabilities. We propose a statistical-machine-learning framework to generate temperature projections (from which downscaling to actuarially relevant spatial or temporal granularity can be performed) from carbon-emission scenarios aligned with Shared Socioeconomic Pathways. We design a neural network (NN) meta-model as an efficient surrogate for mapping emission trajectories into temperature trajectories in an infinite-horizon setting. Our approach combines a projection on generalized Dirichlet polynomials—whose coefficients are used as inputs to the NN—with a suitable time change to handle the infinite horizon. We establish theoretical accuracy guarantees for both the encoding and the neural network approximation. Numerical experiments demonstrate that the framework achieves high accuracy and a computational efficiency improvement by a factor of 100 compared to traditional ODE solvers of the climate model. As an application to actuarial sciences, we illustrate the use of the meta-model to quantify the distribution of future scorching days.