Corrosion morphology is a key factor that influences the reliability and service life of a structure. As most structures service under stress corrosion, there is a great need to understand the effect of stress on the formation conditions of different morphologies. This paper introduces a numerical method to simulate the evolution of surface morphologies. The results indicate that a corroded surface will become rougher and sharper with an increase in stress, and as a consequence, the corrosion morphology will transfer from a flatter surface to a pit and then a crevice. The critical stress values for different morphologies (crevice, pit, and a flatter surface) were captured. Among the three morphologies, the flatter surface and pit maintain a fixed shape, also known as stable morphology. As stress exceeds a critical value, crevices are generated, and the morphology evolution becomes unstable. On the basis of the simulation results, the influence of morphology on the service life of the structure was evaluated. The corrosion velocity of a rough surface exceeds that of a flat surface, and this reduces the service life of the structure more significantly. With a rise in applied stress, the acceleration of corrosion presents a quadratically increasing relationship with applied stress.

Artificial intelligence (AI) shows great potential to reduce the huge cost of solving partial differential equations (PDEs). However, it is not fully realized in practice as neural networks are defined and trained on fixed domains and boundaries. Herein, we propose local neural operator (LNO) for solving transient PDEs on varied domains. It comes together with a handy strategy including boundary treatments, enabling one pre-trained LNO to predict solutions on different domains. For demonstration, LNO learns Navier-Stokes equations from randomly generated data samples, and then the pre-trained LNO is used as an explicit numerical time-marching scheme to solve the flow of fluid on unseen domains, e.g., the flow in a lid-driven cavity and the flow across the cascade of airfoils. It is about 1000$\times$ faster than the conventional finite element method to calculate the flow across the cascade of airfoils. The solving process with pre-trained LNO achieves great efficiency, with significant potential to accelerate numerical calculations in practice.

Local neural operator (LNO) conception has provided a feasible way for scientific computations. The LNO learns transient partial differential equations from random field samples, and then the pre-trained LNO solves practical problems on specific computational domains. For applications, we may ask: Are the training samples rich enough? To what extent can we trust the solutions obtained from pre-trained LNO models for unknown cases? The generalizability of LNO could answer these questions. Here, we propose to use two plain scalar features, the amplitude and wavenumber of the input functions, to indicate the richness of training samples and to evaluate the generalization error of pre-trained LNO. In elastodynamic practices, we find that isolated evolving wavenumber modes for Lamé-Navier equation caused the training dataset to lack mode diversity. By data supplementation and model fine-tuning targeting to the discovered lack modes, the pre-trained and fine-tuned LNO model solves Lamb problem correctly and efficiently. These results and the proposed generalization criteria provide a paradigm for LNO applications.