Differentiable physics augmented wavelet neural operator: A gray box model for a class of stochastic mechanics problem

The well-known governing physics in science and engineering often relies on certain assumptions and approximations, resulting in approximate analyses and designs. The emergence of data-driven models has, to a certain degree, addressed this challenge; however, the purely data-driven models often (a) lack interpretability, (b) are data-hungry, and (c) do not generalize beyond the training window. Operator learning has emerged as a potential solution, but the challenges are still persistent. A promising alternative resides in data-physics fusion, where data-driven models are employed to correct or identify the missing physics. Accordingly, we here introduce a novel Differentiable Physics Augmented Wavelet Neural Operator (DPA-WNO) for solving stochastic mechanics problems. The proposed DPA-WNO blends the concepts of differentiable physics with the Wavelet Neural Operator (WNO). This framework harnesses WNO’s ability to learn from data while retaining the interpretability and generalization of physics-based solvers. We illustrate the applicability of the proposed approach in solving uncertainty quantification and reliability analysis problems due to randomness in the initial condition. Three benchmark examples and one practical application from various fields of science and engineering are solved using the proposed approach. The results presented illustrate the efficacy of the proposed approach.