Nonlinear Operator Mapping Wave Speed

Nonlinear operator mapping, specifically focusing on wave speed to solution mapping in partial differential equations (PDEs), aims to develop accurate and efficient computational methods for solving complex physical problems. Current research emphasizes the use of neural operator networks (ONets), including DeepONets and variations incorporating techniques like stochastic depth, to approximate these operators, often within the context of inverse problems and digital twin development. Improved generalization capabilities, particularly for out-of-distribution scenarios, and efficient handling of high-arity operators are key objectives, with potential applications ranging from surrogate modeling in engineering to enhanced physical field estimation.