Neural networks outshine regression in forecasting Germany’s energy demand to 2050

Germany has staked its energy future on one of the most ambitious decarbonization programs in the world, yet the country’s own long-term demand projections remain stubbornly difficult to pin down. A new comparative study has now put four forecasting models head to head on the same national dataset, and the results carry an uncomfortable message: the most accurate model on historical data is not the most trustworthy one when asked to look thirty years ahead. A support vector regression machine delivered the sharpest predictions over Germany’s recent past, but when pushed toward 2050 it spiraled into an implausible surge in energy demand, while a modest artificial neural network produced both competitive accuracy and a physically credible trajectory.

The research team assembled thirty years of annual observations for Germany, spanning 1992 to 2021, drawn from a harmonized international statistical source. Nine explanatory variables were selected to capture macroeconomic conditions, demographics, energy consumption by carrier, and efficiency: gross domestic product, population, residential consumption level, oil products, natural gas, electricity, an energy-efficiency index, biofuels and waste, and coal and peat products. Final energy consumption, the target variable, was standardized alongside every predictor before training. The dataset was split so that seventy percent of observations trained the models and the remaining thirty percent served as an untouched out-of-sample test, with a further validation fraction carved from the training set to guide hyperparameter selection.

Four modeling families entered the contest. Multiple linear regression served as the transparent econometric benchmark, fitted by ordinary least squares across all 511 possible combinations of the nine predictors. A vector error correction model, estimated on seven variables sharing the same integration order, was included to characterize long-run equilibrium relationships among the non-stationary time series. On the machine learning side, support vector regression with both linear and radial basis function kernels and a parsimonious artificial neural network built in TensorFlow represented the flexible, nonlinear camp. Crucially, the two machine learning models were not left to default settings: their hyperparameters were tuned by particle swarm optimization, a swarm-inspired search that moves candidate solutions through the parameter space, and by Bayesian optimization, which builds a probabilistic surrogate model and selects the next configuration by maximizing expected improvement.

Before any forecasting began, the statistical structure of the data was mapped in detail. Correlation analysis showed final energy consumption moving strongly with oil products, residential consumption, gross domestic product, and biofuels, while revealing substantial interdependence among the predictors themselves. An augmented Dickey-Fuller test established that most series were non-stationary in levels, and the Johansen procedure then identified five cointegrating relationships among the seven integrated series, evidence that the variables share stable long-run equilibria despite drifting individually. Granger causality tests added texture on timing: natural gas carried predictive information for final energy consumption at lags of two and three years, biofuels at lag two, while residential consumption and electricity only showed predictive power at lags of seven and eight years, hinting at slow, infrastructure-bound adjustment. Notably, gross domestic product, population, and oil products showed no statistically significant Granger causality within the tested lag structure.

When the models were scored on held-out data, the nonlinear approaches pulled ahead. The best multiple linear regression achieved a test mean absolute error of roughly 12.8 TWh with an R-squared of 0.951, and a reduced five-predictor specification came close with far fewer variables. The support vector regression with a radial basis function kernel topped the table, reaching a test mean absolute error of 9.19 TWh and an R-squared of 0.9735, while the optimized neural network followed closely at 10.05 TWh and 0.965. The baseline neural network, before tuning, lagged at 14.34 TWh, underscoring how much careful hyperparameter optimization mattered. Deeper networks and fancier activation functions added nothing, suggesting that the dominant relationships in the data are simple enough for a small architecture to capture.

The econometric reference model told a more cautionary tale. Fitted with five cointegrating equations, the vector error correction model projected rising final energy consumption through 2050. Reducing the assumed cointegration rank to just two, a change affecting nothing but the specification of the long-run equilibrium structure, flipped the projection into a continuous decline reaching roughly 750 TWh by 2050 and increased in-sample error by about a quarter. A hybrid version, augmented with externally projected explanatory variables, proved unstable outright, because the policy-driven future trajectories no longer preserved the historically estimated cointegrating relationships. With only thirty annual observations, Johansen-based rank determination carries limited statistical power, and the study’s authors conclude that such models, while valuable for dissecting historical equilibria, should be treated with caution when the forecast horizon extends beyond the regime used for estimation.

The starkest divergence appeared among the conditional-mean models. By 2050, multiple linear regression settled near 2130 TWh and the neural network near 2140 TWh, the latter corresponding to a decline of about twelve percent relative to 2008 levels, with a ninety-five percent prediction interval of roughly 1909 to 2505 TWh. The support vector regression, by contrast, forecast a sharp climb to approximately 3760 TWh, far above any historical maximum, wrapped in an exceptionally wide and asymmetric interval spanning 2716 to 3829 TWh. That interval, constructed with a leave-one-out conformal procedure, primarily reflected extrapolation instability rather than genuine uncertainty about future demand. The radial basis kernel, it appears, amplifies the projected growth in electricity and bioenergy consumption into an implausible trajectory, even though the same model was the most accurate predictor within the observed data range.

Permutation importance analysis on the neural network identified oil products, biofuels, electricity, natural gas, and coal as the most influential predictors, with oil products contributing a mean absolute error increase of roughly 114 TWh when shuffled. The macroeconomic and demographic variables registered effects of about nine TWh or less. The authors are careful to note, however, that these five leading predictors jointly account for approximately ninety-four percent of historical final energy consumption as accounting components, so their dominance partly reflects the energy balance itself rather than independent causal influence. They function instead as transition-pathway indicators, translating assumptions about fossil phase-out, electrification, and bioenergy deployment into projected demand.

Applying the tuned neural network to five contrasting decarbonization pathways revealed how much the assumptions matter. Under the base case, final energy consumption falls from 2323 TWh in 2021 to about 2140 TWh by 2050. A delayed-transition scenario that preserves natural gas as a bridge fuel yields the highest residual demand at 2195 TWh, while deep electrification and green-gas pathways land near 1999 and 2085 TWh respectively. The accelerated-neutrality scenario produces an intriguing non-monotonic result: demand drops to 1871 TWh around 2040 before edging back up to 1941 TWh by 2050, as growing electricity and bioenergy consumption partially offsets the fossil contraction. Only the efficiency-and-sufficiency pathway, which prioritizes demand reduction, pushes consumption down to roughly 1476 TWh, a 39.3 percent reduction relative to 2008.

The headline implication is sobering. Across all five scenarios, projected 2050 demand spans 719 TWh, a spread that exceeds the differences between the competing forecasting models themselves, meaning that assumptions about the energy transition shape the outlook more than the choice of algorithm. And even the most ambitious pathway falls short of Germany’s legally anchored target of reducing final energy consumption by forty-five percent relative to 2008 by 2045, a goal that historical progress had advanced by only about four percent as of 2021. The study’s authors conclude that fuel substitution alone cannot close the gap and that stronger efficiency improvements and demand-side measures would be required. They also stress that every projection remains conditional on the assumed trajectories of the explanatory variables, and that the scenario framework represents sector coupling only at the aggregate energy-balance level, without resolving end-use technologies or infrastructure constraints. Within those limits, the comparison delivers a clear methodological verdict: for long-horizon forecasting under structural change, a parsimonious, well-regularized neural network offers the best balance of accuracy, generalization, and plausible extrapolation, while raw predictive skill on historical data is no guarantee of a trustworthy view of the future.

Subject of Research: Comparative evaluation of regression and machine learning models for long-term energy demand forecasting in Germany

Article Title: Evaluating regression models and machine learning for long-term energy demand forecasting – Germany

Article References: Osman, M., & Movsessian, M. M. (2026). Evaluating regression models and machine learning for long-term energy demand forecasting – Germany. Energy Reports, 16, Article 109799. https://doi.org/10.1016/j.egyr.2026.109799

Image Credits: AI Generated

DOI: 10.1016/j.egyr.2026.109799

Keywords: energy demand forecasting, Germany, machine learning, support vector regression, artificial neural network, vector error correction model, Bayesian optimization, particle swarm optimization, cointegration, energy transition, final energy consumption, scenario analysis