DPA-WNO: A gray box model for a class of stochastic mechanics problem

TL;DR

The paper introduces DPA-WNO, a hybrid physics-data model that combines a differentiable physics solver with Wavelet Neural Operator to improve interpretability and generalization in stochastic mechanics problems.

Contribution

It proposes a novel data-physics fusion framework, DPA-WNO, that enhances operator learning by integrating physics-based models with neural operators for uncertainty quantification.

Findings

Successfully applied to four benchmark problems in science and engineering.

Demonstrated improved interpretability and generalization over purely data-driven models.

Achieved accurate uncertainty quantification in time-dependent stochastic problems.

Abstract

The well-known governing physics in science and engineering is often based on certain assumptions and approximations. Therefore, analyses and designs carried out based on these equations are also approximate. 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 recently been proposed as a potential alternative to address the aforementioned challenges; however, the challenges are still persistent. We here argue that one of the possible solutions resides in data-physics fusion, where the data-driven model is used to correct/identify the missing physics. To that end, we propose a novel Differentiable Physics Augmented Wavelet Neural Operator (DPA-WNO). The proposed DPA-WNO blends a differentiable physics solver with the Wavelet Neural Operator (WNO), where the role of WNO is to model the missing physics. This empowers the proposed framework to exploit the capability of WNO to learn from data while retaining the interpretability and generalizability associated with physics-based solvers. We illustrate the applicability of the proposed approach in solving time-dependent uncertainty quantification problems due to randomness in the initial condition. Four benchmark uncertainty quantification and reliability analysis examples from various fields of science and engineering are solved using the proposed approach. The results presented illustrate interesting features of the proposed approach.