Learning solution operators (i.e., mappings from input to output functions) have emerged as a powerful strategy in Scientific Machine Learning (SciML) for modeling complex systems. This approach enables fast predictions across a range of inputs (e.g., varying forcing or initial conditions) without repeated simulations. In this context, Fourier Neural Operators (FNOs) are at the forefront of data-driven operator learning. However, their generalization can be limited, especially for complex or out-of-distribution inputs. This work explores the integration of physical knowledge into a Physics-Informed FNO (PI-FNO) framework to model the dynamics of a Duffing oscillator under harmonic excitation. Focusing on Duffing systems with potentially chaotic responses, it is assessed how embedding physical constraints influences the learned solution space compared to a standard FNO. Additionally, two-stage training protocols are investigated to determine effective strategies for enhancing the robustness, accuracy, and generalization of neural operators in modeling highly nonlinear and possibly chaotic dynamical systems.
A Tue, study studied this question.