Physics-informed Gaussian process regression of in operando capacitance for carbon supercapacitors

Abstract

Amorphous porous carbons are one of the most popular electrode materials for energy storage owing to their high electrical conductivity, large specific surface area and low-production cost. Both physics-based models and machine learning (ML) methods have been used to correlate the electrochemical behavior of carbon electrodes, including electric-double-layer (EDL) capacitance, energy density, charging dynamics, and the Ragone diagram. While ML methods are applicable to systems remote from equilibrium, the lack of physical inputs may lead to erroneous predictions of in operando capacitance at high charging–discharging rates for electrodes with high mesopore surface areas. In this work, we introduce a physics-informed Gaussian process regression (PhysGPR) method to predict the capacitance of pristine carbon electrodes in aqueous solutions of 6 M KOH over a broad range of conditions. We demonstrate that PhysGPR has major advantages in comparison with conventional GPR (ConvGPR) and other ML methods such as artificial neuron network (ANN) for predicting in operando capacitance as a function of the pore characteristics and the scan rate. By incorporating physical models into a supervised setting, PhysGPR provides better numerical performance in comparison with alternative ML methods, avoids unphysical predictions such as negative capacitance or increasing EDL capacitance with rising charging–discharging rate, and works well in a wider range of parameter space, especially for materials with a high mesopore surface area, thereby offering a faithful description of the capacitive behavior of carbon electrodes.