A Hybrid Deep Learning and Quantum-Optimization Framework for Predictive Modelling of Biogas-Based Energy Harvesting: A Farm-Scale Anaerobic Co-Digestion CHP Case Study

Abstract

Accurate forecasting of the electrical energy harvested from biogas-fuelled combined heat and power (CHP) plants is central to the economic and operational viability of anaerobic digestion (AD) as a dispatchable renewable energy pathway, yet the process is governed by strongly non-linear, multi-parameter microbial kinetics that are difficult for purely classical predictive models to capture and expensive to tune. This paper develops and evaluates a hybrid quantum-classical machine-learning framework, coupling a custom convolutional-recurrent deep neural network (“DeepEnergyNet”: 1-D convolution, long short-term memory and additive temporal attention, implemented and back-propagated from first principles) with two quantum optimisation components: a Quantum Approximate Optimization Algorithm (QAOA), simulated exactly on a 12-qubit state-vector, that solves a maximum-relevance-minimum-redundancy Quadratic Unconstrained Binary Optimization (QUBO) for process-variable feature selection; and Quantum-behaved Particle Swarm Optimization (QPSO) that tunes the network's hyperparameters. The framework is demonstrated on a literature-calibrated, physically consistent operational case study of a 3000 m³ farm-scale anaerobic co-digestion CHP plant (N = 6000 hourly records), built from published modified-Gompertz kinetics and IWA Anaerobic Digestion Model No. 1 (ADM1)-informed inhibition relationships, with injected sensor noise, missing data and outliers to emulate a real SCADA export. QAOA selected a physically interpretable 7-of-12 feature subset (best-observed-shot approximation ratio 0.9996 relative to the exact brute-force optimum), and QPSO converged the network's five hyperparameters within ten swarm iterations. On a chronologically held-out test partition, the resulting hybrid model (DL+QAOA+QPSO) achieved RMSE = 59.81 kWh, MAE = 41.55 kWh, MAPE = 12.82% and R² = 0.754, improving on an untuned deep-learning baseline (RMSE = 61.56 kWh) and on each quantum component applied in isolation, while converging in fewer training epochs (33 vs. 47). The hybrid framework narrowed the gap to a Random Forest benchmark (RMSE = 57.64 kWh) while offering, in addition, an interpretable and computationally economical route to feature and hyperparameter selection. All back-propagation gradients were verified against finite-difference estimates (maximum relative error 3.4×10⁻⁸) prior to use. These findings indicate that quantum-classical coupling is a practically viable and physically interpretable strategy for renewable-energy time-series forecasting, and outline a pathway toward NISQ-hardware validation of the QAOA component.