Robust PINN modeling via sensitivity-based adaptive sampling: Integration of optimal sensor placement and structural uncertainty handling

Physics-informed neural networks (PINNs) have emerged as promising surrogate models for systems governed by partial differential equations (PDEs), yet their practical implementation faces challenges in training efficiency and robustness to uncertainties. This study refines and improves a recently proposed sensitivity-based adaptive sampling (SBS) methodology to address these challenges specifically for twice-differentiable PDE systems. We first conduct a systematic investigation of SBS hyper-parameters, including prediction horizon and adaptation rate, revealing their crucial role in training performance. To enhance PINN model robustness facing uncertainties, we propose two approaches: (1) incorporating sensor measurements at sensitivity-identified locations into the loss function, and (2) augmenting the PINN architecture with direct sensor data inputs. Results show that our proposed approaches achieve superior generalization capabilities and robustness. Furthermore, we demonstrate that the SBS methodology can serve for optimal sensor placement by identifying locations that maximize information gain for model training. • A method is proposed for enhancing PINN training via optimal location of sampling points. • Small prediction horizons and conservative adaptation rates optimize performance. • Direct sensor data input improves PINN robustness over loss function modifications. • The proposed framework enables optimal sensor placement by identifying high-information zones. • Inlet velocity input enables PINN generalization to unseen flow conditions.