A neural network that fits historical emissions well can perform poorly on data it has not seen. A Scientific Reports study published on 23 October makes that distinction visible: a conventional model led during training, a sine-cosine-optimised model led on the test set, and a more elaborate hybrid led across the combined sample.[1][2]
The researchers used monthly US data from January 1986 to December 2025, with natural-gas use, renewable-energy consumption, oil prices and economic- and monetary-policy uncertainty as predictors. A conventional multilayer perceptron, or MLP, was compared with versions trained using different optimisation methods. The proposed hybrid adds kernel regularisation to an existing optimisation approach.[1][2]
The test result changes the ranking
Selected R² results from the same evaluation
| Model | Training | Testing | Full sample |
|---|---|---|---|
| Conventional MLP | 0.7437 | −4.06221 | 0.1612 |
| MLP–SCA | 0.4877 | 0.44541 | 0.5591 |
| MLP–KR–GRLEO–AEFA | 0.6124 | 0.02240 | 0.5943 |
The conventional model’s strong training result accompanied a sharply negative test R². The authors interpret this as evidence of overfitting. MLP–SCA, which uses a sine-cosine optimisation algorithm, performed best on the held-out test period. The proposed kernel-regularised hybrid improved the aggregate result, but its test score was much weaker than MLP–SCA’s.[2]
Predicting an unseen period is not always forecasting ahead
The paper specifies a chronological 80/20 split. Its more consequential limitation is that the model uses contemporaneous inputs: variables from the same period as the emissions it predicts. The authors explicitly distinguish this from forecasting at defined future horizons.[2]
A planner making a forecast months ahead may not yet have the natural-gas consumption or uncertainty readings used to predict those months. Publication delays matter too. A prospective forecasting test would use only information available at the prediction date and evaluate later observations, ideally across repeated forecast origins.[2]
Permutation importance identified natural-gas and renewable-energy consumption as influential predictors within the fitted system. It does not establish the effect of changing either through policy. The study offers a comparison of predictive methods for observed economic conditions; its own test results show why a full-sample winner should not automatically become the model chosen for future planning.[2]
Sources & further reading
- A hybrid artificial neural network approach to forecasting CO₂ emissions in the United States under policy uncertainty and energy consumption Scientific Reports · 23 Oct 2026 · Accessed 26 Oct 2026
- US CO₂ prediction study — full accepted manuscript Scientific Reports · 23 Oct 2026 · Accessed 26 Oct 2026