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The effects of economic growth on the environment have received increased attention as global warming and other environmental problems become more serious. Many empirical studies explain the nexus between carbon dioxide emissions and economic growth with such models as the environmental Kuznets curve (EKC) theory. However, the assumptions of these models have never received strict verification with a large available data set and therefore may not be appropriate to describe the relationship. In this study, the nexus is modeled for 67 countries from 1971 to 2010 using a novel symbolic regression method. From the experimental results, several conclusions as follows could be reached. Firstly, there is no universal model fitting every country, and symbolic regression could discover a set of reasonable models for a specific country or region. Secondly, four models, including the inverted N-shaped, M-shaped, inverted U-shaped and monotonically increasing, are frequently found without domain experts’ intervention in these countries, whereas the M-shaped model has received little attention in previous studies but exhibits promising performance. Thirdly, the relationship is diversified due to the difference of regions and economic development, where developed countries generally follow the inverted N-shaped and M-shaped models to explain the relationship, whereas developing countries are more likely to refer to the inverted N-shaped, inverted U-shaped and monotonically increasing models. Finally, several policy suggestions are presented.

Numerous models have been proposed to forecast the future trends of oil production and almost all of them are based on some predefined assumptions with various uncertainties. In this study, we propose a novel data-driven approach that uses symbolic regression to model oil production. We validate our approach on both synthetic and real data, and the results prove that symbolic regression could effectively identify the true models beneath the oil production data and also make reliable predictions. Symbolic regression indicates that world oil production will peak in 2021, which broadly agrees with other techniques used by researchers. Our results also show that the rate of decline after the peak is almost half the rate of increase before the peak, and it takes nearly 12 years to drop 4% from the peak. These predictions are more optimistic than those in several other reports, and the smoother decline will provide the world, especially the developing countries, with more time to orchestrate mitigation plans.