Interpretable and Accurate Multi-Energy Loads Forecasting via Continuous-Time Modeling

High-precision interpretable forecasting of multi-energy loads is crucial for planning and optimizing Integrated Energy Systems (IES). Current methods have three key limitations: (1) reliance on black-box models obscures feature interactions; (2) traditional modal decomposition methods ignore cross-modal correlations and fail to efficiently extract global cycle-trend characteristics; (3) limitations in sampling frequency prevent capturing fast dynamic characteristics of energy loads. To address these, we propose a dual resolution channel multi-period cross reconstruction parallel closed-form continuous-time network (DMP-PCFC) for multi-energy load forecasting. This method includes a multi-period cross-reconstruction network which equivalent to the signal sifter for decoupling original sequences and nonlinear mapping across periods, and models hidden states of energy loads using neuron state iterative differential equations. A parallel Closed-form continuous-time neural network (PCFC) based on chunked parallelization reduces inference time from <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O(T)</i> (change with input sequence length) to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O(P)</i> (fixed cycle length). To overcome inherent sampling resolution limitations, a dual-resolution channel model with weight-sharing PCFC is used for simultaneous inference. Extensive experiments and continuous wavelet transform (CWT) on the IES dataset at Arizona State University’s Tempe campus show that DMP-PCFC offers higher prediction accuracy and greater interpretability than existing methods, providing a new paradigm for downstream tasks based on other research methods, making it valuable for IES engineering applications. The code is publicly available at https://github.com/nuist-xf/DMP-PCFC.