Soft state-of-charge estimation for adsorption energy storage: Black-box and physics-informed approaches

Abstract

Adsorption-based thermochemical energy storage is an emerging technology with strong potential for waste-heat recovery and integration into sector-coupled energy systems. However, operating such complex systems remains challenging and requires in-depth data analysis. One of the key challenges is the real-time, precise tracking of State-of-Charge (SOC) instead of relying on temperature difference in the external adsorption and desorption loops. In this context, this work develops and validates machine learning models as soft sensors of the key states in adsorption-based thermal energy storage systems, overcoming the real-time limitations of conventional physics-based approaches. Using experimental data collected through an edge computing platform, we evaluate both black-box Neural Networks (NNs) and Physics-Informed Neural Networks (PINNs). The goal of using instantaneous sensor data is to reconstruct (estimate) the unmeasurable current states, mainly the refrigerant update and the adsorption-desorption temperatures in real-time. The proposed PINN introduces a specialized physical loss coupling thermochemical energy balances with adsorption kinetics, driven by instantaneous edge inputs for direct SOC tracking. The comparative evaluation demonstrates that PINN consistently achieves higher predictive accuracy than the conventional NN across all key outputs, relative to a high-fidelity white-box dynamic model. For the adsorption and desorption mass fractions, the PINN attains R 2 values of 0.939 and 0.938, respectively, improving upon the NN's 0.922 and 0.905. Similarly, for adsorption and desorption temperature estimations, the PINN achieves R 2 values of 0.994 and 0.992 compared to the NN's 0.989 and 0.985. These improvements correspond to 15 – 25% reductions in MSE, MAE, and RMSE, confirming a more precise reconstruction of key thermodynamic states. When applied to SOC estimation, the PINN further demonstrates enhanced fidelity with R 2 value of 0.939 versus 0.922 for the NN, highlighting its ability to generalize the coupled adsorption-desorption behavior by integrating the system's thermochemical energy balance and driving force relationships into the learning process. A robustness test with noisy measurements, reflecting real-world industrial conditions, confirmed that the PINN outperforms the standard NN due to its embedded physical constraints.