Enhanced multi-fidelity modelling for digital twin and uncertainty quantification

The increasing significance of digital twin technology across engineering and industrial domains, such as aerospace, infrastructure, and automotive, is undeniable. However, the lack of detailed application-specific information poses challenges to its seamless implementation in practical systems. Data-driven models play a crucial role in digital twins, enabling real-time updates and predictions by leveraging data and computational models. Nonetheless, the fidelity of available data and the scarcity of accurate sensor data often hinder the efficient learning of surrogate models, which serve as the connection between physical systems and digital twin models. To address this challenge, we propose a novel framework that begins by developing a robust multi-fidelity surrogate model, subsequently applied for tracking digital twin systems. Our framework integrates polynomial correlated function expansion (PCFE) with the Gaussian process (GP) to create an effective surrogate model called H-PCFE. Going a step further, we introduce deep-HPCFE, a cascading arrangement of models with different fidelities, utilizing nonlinear auto-regression schemes. These auto-regressive schemes effectively address the issue of erroneous predictions from low-fidelity models by incorporating space-dependent cross-correlations among the models. To validate the efficacy of the multi-fidelity framework, we first assess its performance in uncertainty quantification using benchmark numerical examples. Subsequently, we demonstrate its applicability in the context of digital twin systems.

Physics informed WNO

Deep neural operators are recognized as an effective tool for learning solution operators of complex partial differential equations (PDEs). As compared to laborious analytical and computational tools, a single neural operator can predict solutions of PDEs for varying initial or boundary conditions and different inputs. A recently proposed Wavelet Neural Operator (WNO) is one such operator that harnesses the advantage of time-frequency localization of wavelets to capture the manifolds in the spatial domain effectively. While WNO has proven to be a promising method for operator learning, the data-hungry nature of the framework is a major shortcoming. In this work, we propose a physics-informed WNO for learning the solution operators of families of parametric PDEs without labeled training data. The efficacy of the framework is validated and illustrated with four nonlinear spatiotemporal systems relevant to various fields of engineering and science.