Deep neural network enabled corrective source term approach to hybrid analysis and modeling.

In this work, we introduce, justify and demonstrate the Corrective Source Term Approach (CoSTA)-a novel approach to Hybrid Analysis and Modeling (HAM). The objective of HAM is to combine physics-based modeling (PBM) and data-driven modeling (DDM) to create generalizable, trustworthy, accurate, computationally efficient and self-evolving models. CoSTA achieves this objective by augmenting the governing equation of a PBM model with a corrective source term generated using a deep neural network. In a series of numerical experiments on one-dimensional heat diffusion, CoSTA is found to outperform comparable DDM and PBM models in terms of accuracy - often reducing predictive errors by several orders of magnitude - while also generalizing better than pure DDM. Due to its flexible but solid theoretical foundation, CoSTA provides a modular framework for leveraging novel developments within both PBM and DDM. Its theoretical foundation also ensures that CoSTA can be used to model any system governed by (deterministic) partial differential equations. Moreover, CoSTA facilitates interpretation of the DNN-generated source term within the context of PBM, which results in improved explainability of the DNN. These factors make CoSTA a potential door-opener for data-driven techniques to enter high-stakes applications previously reserved for pure PBM.

Multi-fidelity information fusion with concatenated neural networks.

Recently, computational modeling has shifted towards the use of statistical inference, deep learning, and other data-driven modeling frameworks. Although this shift in modeling holds promise in many applications like design optimization and real-time control by lowering the computational burden, training deep learning models needs a huge amount of data. This big data is not always available for scientific problems and leads to poorly generalizable data-driven models. This gap can be furnished by leveraging information from physics-based models. Exploiting prior knowledge about the problem at hand, this study puts forth a physics-guided machine learning (PGML) approach to build more tailored, effective, and efficient surrogate models. For our analysis, without losing its generalizability and modularity, we focus on the development of predictive models for laminar and turbulent boundary layer flows. In particular, we combine the self-similarity solution and power-law velocity profile (low-fidelity models) with the noisy data obtained either from experiments or computational fluid dynamics simulations (high-fidelity models) through a concatenated neural network. We illustrate how the knowledge from these simplified models results in reducing uncertainties associated with deep learning models applied to boundary layer flow prediction problems. The proposed multi-fidelity information fusion framework produces physically consistent models that attempt to achieve better generalization than data-driven models obtained purely based on data. While we demonstrate our framework for a problem relevant to fluid mechanics, its workflow and principles can be adopted for many scientific problems where empirical, analytical, or simplified models are prevalent. In line with grand demands in novel PGML principles, this work builds a bridge between extensive physics-based theories and data-driven modeling paradigms and paves the way for using hybrid physics and machine learning modeling approaches for next-generation digital twin technologies.

Determination of wall tension in cerebral artery aneurysms by numerical simulation.

BACKGROUND AND PURPOSE: Cerebral artery aneurysms rupture when wall tension exceeds the strength of the wall tissue. At present, risk-assessment of unruptured aneurysms does not include evaluation of the lesions shape, yet clinical experience suggests that this is of importance. We aimed to develop a computational model for simulation of fluid-structure interaction in cerebral aneurysms based on patient specific lesion geometry, with special emphasis on wall tension. METHODS: An advanced isogeometric fluid-structure analysis model incorporating flexible aneurysm wall based on patient specific computed tomography angiogram images was developed. Variables used in the simulation model were retrieved from a literature review. RESULTS: The simulation results exposed areas of high wall tension and wall displacement located where aneurysms usually rupture. CONCLUSIONS: We suggest that analyzing wall tension and wall displacement in cerebral aneurysms by numeric simulation could be developed into a novel method for individualized prediction of rupture risk.