Modeling equilibrium adsorption isotherms of human immunoglobulin G onto fibroin microparticles using machine learning and physics-informed neural networks

Abstract Accurate modeling of adsorption equilibrium is essential for designing and optimizing bioseparation processes. This study investigates the modeling of immunoglobulin G (IgG) adsorption equilibrium isotherms onto fibroin microparticles under different physicochemical conditions using five distinct modeling strategies. Fifteen experimental isotherms with different conditions, including buffer type, pH, temperature, and agitation, were modeled using classical approaches, machine learning (ML), physics-informed neural networks (PINNs), symbolic regression (PySR), and a hybrid PINN–PySR framework. Classical models showed moderate performance, with Langmuir providing the best fit (root mean square error, RMSE = 7.03–29.66 mg g −1 ). The ML model achieved the highest predictive accuracy (RMSE = 0.81–21.71 mg g −1 ) but often produced physically inconsistent curves. In contrast, PINNs incorporated physical constraints such as monotonicity, concavity, and saturation, yielding slightly higher errors (RMSE = 9.51–37.16 mg g −1 ) but preserving physically realistic isotherm shapes. Results highlight a trade-off between predictive accuracy and physical consistency. PINNs significantly improved curve smoothness and adherence to expected adsorption behavior, particularly under interpolated conditions not included in training. Additionally, the PINN framework provides a unified parameterization across varying conditions, avoiding separate fits for each experiment. Overall, PINNs represent a robust and reliable approach for adsorption modeling, combining predictive capability with fundamental physical consistency.