Hybrid NN–ODE Modeling of Fossil Fuel Competition

Europe’s fossil-based electricity mix has shifted rapidly in recent years, raising a practical question: can we model competitive substitution among fuels with a framework that is both predictive and interpretable? We address this by combining a compact neural network (NN) with a three-dimensional Lotka–Volterra (LV) system to study monthly EU coal, natural gas, and oil-fired generation shares from the second semester of 2017 to 2023. After converting the series to row-wise shares that sum to one, we use the first 70% of the sample to learn smooth trajectories and data-driven derivatives with the NN and then estimate the LV interaction coefficients through a constrained nonlinear fit. We advance the calibrated LV system over the final 30% holdout with a fourth-order Runge–Kutta (RK4) scheme and evaluate forecasts using the RMSE and MAE for each fuel share series. For comparison, we report the results against both a neural network-only forecasting baseline and a classical ARIMA benchmark, both trained on the same 70% window and evaluated on the same 30% holdout. The hybrid NN–LV model achieves competitive forecast errors while yielding interpretable interaction patterns consistent with substitution pressures (for example, negative cross-effects between coal and gas). Finally, we run counterfactual shock experiments to illustrate how a change in one fuel’s share propagates through the mix under the learned LV dynamics, highlighting the usefulness of embedding a simple mechanistic structure within a data-driven estimator.