A Conditional Koopman World Model for Distribution-Aware Electricity Load Forecasting

Electric load and price time series exhibit typical damped oscillation patterns with periodic cycles and spike mean reversion, which are dominated by the dynamic evolution of power supply and demand contradictions. Existing time series forecasting models rarely incorporate such physical inductive biases, making it challenging to simultaneously achieve stable long-horizon rollouts, event-conditioned forecasting, and counterfactual simulation. To address this issue, this paper proposes the Power World Model (PWM), a conditional Koopman world model for distribution-aware electricity forecasting. Leveraging the dual core mechanisms of amplitude-conserving rotation and amplitude-dissipating contraction inherent to damped oscillation, PWM constructs a latent state space through delay embedding and designs a structurally decomposable condition-affine Koopman operator. The operator structurally limits the spectral radius to no more than 1, ensuring bounded and stable long-horizon forecasting results. Unlike conventional conditional forecasting methods that integrate conditional information at the input layer, our method embeds conditional signals into the state transition operator, enabling efficient event-conditioned forecasting and low-cost counterfactual rollouts. Under a unified experimental protocol across multiple public datasets and a private power dataset, PWM achieves state-of-the-art point prediction accuracy, outperforming existing mainstream time series forecasting models. Mechanism validations on synthetic load-shedding events demonstrate that PWM can effectively improve prediction performance in extreme scenarios.