Entropic risk aware end to end learning for stochastic optimiza 2027 Applied

Integrated energy systems (IES) face coupled uncertainties from variable renewable generation, electricity and heat demands, and electricity prices. Forecasting models optimized only for statistical accuracy may therefore produce scenarios that are poorly aligned with downstream economic and risk-sensitive operation. This study develops an end-to-end framework that combines Mamba-based joint scenario generation with differentiable two-stage stochastic scheduling. The forecaster generates aligned multi-horizon trajectories for wind power, photovoltaic output, electric load, heat load, and electricity price. A scenario-wise entropic imbalance-exposure score is embedded in the scheduling layer. A threshold-based Entropic Value-at-Risk (EVaR)-inspired loss complements prediction and regret objectives during training. Simulation tests compare deterministic, stochastic, and entropic risk-aware cases. The complete Sto-EVaR case achieved the lowest operating cost, decision regret, empirical EVaR, and 95th-percentile cost while maintaining forecast accuracy comparable to the stochastic baseline. It also reduced realized electrical and thermal imbalance in the representative dispatch window. These results indicate that jointly learning uncertainty scenarios from prediction, economic, and entropic risk signals significantly enhances operational performance.