B-LSTM-MIONet: Bayesian LSTM-based Neural Operators for Learning the Response of Complex Dynamical Systems to Length-Variant Multiple Input Functions

Rapid surrogate models derived from observational data now substantially reduce the computational cost to solve practical problems like solid mechanics [1], structural health monitoring [2, 3, 4], field problem solutions [5], fault diagnosis [6, 7], medical imaging [8, 9], autonomous driving [10], and power grid simulation [11] A significant challenge in current neural network surrogate models lies in their generalization capability. Addressing this, the foundational work [12] introduced Operator Learning, a novel method aimed at learning the mapping between different function spaces. Building on this, [13] developed the Deep Operator Neural Network (DeepONet), capable of being trained with limited datasets while minimizing generalization errors. This influential research has been applied in various domains, including the prediction of linear instability waves in high-speed boundary layers [14], forecasting power grid's post-fault trajectories [15], learning nonlinear operators in oscillatory function spaces for seismic wave responses [4], and analyzing nanoscale heat transport [16]. Additionally, several advancements of DeepONet have been proposed, such as Bayesian DeepONet [17, 18], DeepONet with proper orthogonal decomposition [19], multiscale DeepONet [4], a neural operator with coupled attention [20], physics-informed DeepONet [21, 22], and the multiple-input deep neural operators (MIONet) [23].