A Simulation-Based Physics-Informed Approach to Modeling Cognitive Dynamics in Engineering Education

Modeling cognitive dynamics in engineering education remains challenging because learning evolves through complex, nonlinear, and time-dependent processes influenced by prior knowledge, engagement, instructional interactions, and uncertainty. Existing data-driven approaches often provide accurate predictions but typically function as black-box models with limited interpretability, reduced robustness under limited-data conditions, and insufficient incorporation of continuous cognitive evolution. This study proposes a simulation-based computational framework, termed Cognitive Field Dynamics with Physics-Informed Neural Operators (CFD-PINO), to investigate continuous cognitive-state evolution within a controlled synthetic environment. Rather than claiming that physical laws directly govern human cognition, the framework uses reaction-diffusion dynamics and control theory as computational inspirations for representing latent cognitive-state evolution. Synthetic multimodal datasets comprising behavioral, performance, and instructional features were generated under predefined stochastic conditions to evaluate the proposed methodology. The computational framework integrates physics-informed neural operators, stochastic state estimation, optimal instructional control, and multimodal feature fusion to model spatiotemporal cognitive dynamics while maintaining consistency with governing computational constraints. Performance was evaluated against a clearly defined conventional baseline using repeated simulation experiments and quantitative prediction metrics. The simulation results demonstrate lower prediction errors, improved temporal stability, enhanced robustness to uncertainty, and more consistent cognitive-state estimation than the baseline model within the synthetic evaluation environment. These findings indicate that CFD-PINO provides a reproducible computational platform for investigating continuous cognitive modeling and adaptive instructional strategies. Because the present study is based entirely on synthetic data, the results should be interpreted as computational validation rather than empirical evidence of real educational processes. Future work will evaluate the framework using authentic educational datasets and compare it with additional state-of-the-art continuous-time learning models.