Leveraging Differentiable Climate-Economy Models for Hybrid Modeling and Inverse Problems

Robust carbon cycle science and effective carbon market governance depend on accurate monitoring, transparent modelling and credible representation of climate–economic feedbacks. Integrated Assessment Models (IAMs) such as RICE provide a long-standing framework for linking carbon emissions, climate dynamics and economic development and are widely used to inform mitigation pathways, carbon pricing and international climate policy. However, traditional IAMs rely on hand-calibrated parameters, simplified damage functions and fixed ethical assumptions, limiting their ability to integrate observational data, quantify uncertainty and support evidence-based carbon management. We build on recent advances in machine learning for climate policy and introduce RICE-N-JAX, a fully differentiable implementation of the multi-region RICE-N model (Zhang et al., 2025). RICE-N extends classical IAMs with multi-agent reinforcement learning to model strategic interactions and international climate negotiations. Our JAX-based reimplementation makes the entire climate–economic simulation fast and differentiable, including carbon emissions, climate response, production, trade, mitigation decisions and negotiation dynamics. Differentiability enables a new class of hybrid, data-driven climate–economic models. Our current research focuses on two key directions. First, we develop non-parametric hybrid damage functions in which the traditional analytical damage formulation is replaced by neural or spline-based surrogates trained on empirical and scenario data. This allows the damage–temperature relationship to be learned directly from data. Second, we perform inverse modelling of ethical and behavioural parameters, such as regional risk aversion, time preferences and mitigation bias, by calibrating the model against emissions, GDP and temperature trajectories from the Shared Socioeconomic Pathways (SSPs). This enables the recovery of latent normative assumptions embedded in scenario narratives and provides a data-informed basis for policy analysis. Finally, differentiability supports gradient-based calibration, uncertainty quantification, and sensitivity analysis of carbon price trajectories, mitigation pathways, and long-term climate impacts. We demonstrate a proof-of-concept end-to-end calibration of climate damage functions and show how parameter uncertainty propagates into future economic and emissions outcomes. By bridging process-based climate–economic theory with hybrid, knowledge-guided machine learning, RICE-N-JAX provides a foundation for fast and data-driven carbon-cycle modelling. The framework supports policy-relevant applications ranging from carbon pricing and climate clubs to carbon market design, illustrating how hybrid ML can strengthen the scientific basis of carbon management and climate mitigation.References: Zhang, T., Williams, A. R., Wozny, P., Cohrs, K.-H., Ponse, K., Jiralerspong, M., Phade, S. R., Srinivasa, S., Li, L., Zhang, Y., Gupta, P., Acar, E., Rish, I., Bengio, Y., and Zheng, S.: AI for global climate cooperation: Modeling global climate negotiations, agreements, and long-term cooperation in RICE-N, Proceedings of the 42nd International Conference on Machine Learning (ICML 2025), 2025