Physically constrained eigenspace perturbation for turbulence model uncertainty estimation

Aerospace design is increasingly incorporating Design Under Uncertainty based approaches to lead to more robust and reliable optimal designs. These approaches require dependable estimates of uncertainty in simulations for their success. The key contributor of predictive uncertainty in Computational Fluid Dynamics (CFD) simulations of turbulent flows are the structural limitations of Reynolds-averaged Navier-Stokes models, termed model-form uncertainty. Currently, the common procedure to estimate turbulence model-form uncertainty is the Eigenspace Perturbation Framework (EPF), involving perturbations to the modeled Reynolds Stress tensor within physical limits. The EPF has been applied with success in design and analysis tasks in numerous prior works from the industry and academia. Owing to its rapid success and adoption in several commercial and open-source CFD solvers, in depth Verification and Validation of the EPF is critical. In this work, we show that under certain conditions, the perturbations in the EPF can lead to Reynolds stress dynamics that are not physically realizable. This analysis enables us to propose a set of necessary physics-based constraints, leading to a realizable EPF. We apply this constrained procedure to the illustrative test case of a converging-diverging channel, and we demonstrate that these constraints limit physically implausible dynamics of the Reynolds stress tensor, while enhancing the accuracy and stability of the uncertainty estimation procedure.Comment: The following article has been submitted to Physics of Fluid

Improved self-consistency of the Reynolds stress tensor eigenspace perturbation for Uncertainty Quantification

The limitations of turbulence closure models in the context of Reynolds-averaged NavierStokes (RANS) simulations play a significant part in contributing to the uncertainty of Computational Fluid Dynamics (CFD). Perturbing the spectral representation of the Reynolds stress tensor within physical limits is common practice in several commercial and open-source CFD solvers, in order to obtain estimates for the epistemic uncertainties of RANS turbulence models. Recent research revealed, that there is a need for moderating the amount of perturbed Reynolds stress tensor tensor to be considered due to upcoming stability issues of the solver. In this paper we point out that the consequent common implementation can lead to unintended states of the resulting perturbed Reynolds stress tensor. The combination of eigenvector perturbation and moderation factor may actually result in moderated eigenvalues, which are not linearly dependent on the originally unperturbed and fully perturbed eigenvalues anymore. Hence, the computational implementation is no longer in accordance with the conceptual idea of the Eigenspace Perturbation Framework. We verify the implementation of the conceptual description with respect to its self-consistency. Adequately representing the basic concept results in formulating a computational implementation to improve self-consistency of the Reynolds stress tensor perturbationComment: The following article has been submitted to AIP/Physics of Fluid

Physics-constrained Random Forests for Turbulence Model Uncertainty Estimation

To achieve virtual certification for industrial design, quantifying the uncertainties in simulation-driven processes is crucial. We discuss a physics-constrained approach to account for epistemic uncertainty of turbulence models. In order to eliminate user input, we incorporate a data-driven machine learning strategy. In addition to it, our study focuses on developing an a priori estimation of prediction confidence when accurate data is scarce.Comment: Workshop on Synergy of Scientific and Machine Learning Modeling, SynS & ML ICM

Architecture Matters: Investigating the Influence of Differential Privacy on Neural Network Design

One barrier to more widespread adoption of differentially private neural networks is the entailed accuracy loss. To address this issue, the relationship between neural network architectures and model accuracy under differential privacy constraints needs to be better understood. As a first step, we test whether extant knowledge on architecture design also holds in the differentially private setting. Our findings show that it does not; architectures that perform well without differential privacy, do not necessarily do so with differential privacy. Consequently, extant knowledge on neural network architecture design cannot be seamlessly translated into the differential privacy context. Future research is required to better understand the relationship between neural network architectures and model accuracy to enable better architecture design choices under differential privacy constraints

Evaluation of physics constrained data-driven methods for turbulence model uncertainty quantification

In order to achieve a virtual certification process and robust designs for turbomachinery, the uncertainty bounds for Computational Fluid Dynamics have to be known. The formulation of turbulence closure models implies a major source of the overall uncertainty of Reynolds-averaged Navier-Stokes simulations. We discuss the common practice of applying a physics constrained eigenspace perturbation of the Reynolds stress tensor in order to account for the model form uncertainty of turbulence models. Since the basic methodology often leads to overly generous uncertainty estimates, we extend a recent approach of adding a machine learning strategy. The application of a data-driven method is motivated by striving for the detection of flow regions, which are prone to suffer from a lack of turbulence model prediction accuracy. In this way any user input related to choosing the degree of uncertainty is supposed to become obsolete. This work especially investigates an approach, which tries to determine an a priori estimation of prediction confidence, when there is no accurate data available to judge the prediction. The flow around the NACA 4412 airfoil at near-stall conditions demonstrates the successful application of the data-driven eigenspace perturbation framework. Furthermore, we especially highlight the objectives and limitations of the underlying methodology

Sleep in Pediatric Primary Care: A Review of the Literature

Primary care is a critical setting for screening and management of pediatric sleep difficulties. This review summarizes studies examining the prevalence of sleep problems in primary care settings as well as current practices in screening, diagnosis, and management, including behavioral recommendations and medications. Potential barriers to effectively addressing sleep are also reviewed. Despite the high prevalence of pediatric sleep problems in primary care, rates of screening and management are low. Primary care providers receive minimal sleep training and have resulting gaps in knowledge and confidence. Parents similarly have gaps in knowledge and many factors contribute to their identification of sleep as problematic. Recommendations to improve the provision of sleep services in pediatric primary care are made in the areas of research, practice, and education

Human-Centered Design for Data-Sparse Tailored Privacy Information Provision

One way to reduce privacy risks for consumers when using the internet is to inform them better about the privacy practices they will encounter. Tailored privacy information provision could outperform the current practice where information system providers do not much more than posting unwieldy privacy notices. Paradoxically, this would require additional collection of data about consumers\u27 privacy preferences—which constitute themselves sensitive information so that sharing them may expose consumers to additional privacy risks. This chapter presents insights on how this paradoxical interplay can be outmaneuvered. We discuss different approaches for privacy preference elicitation, the data required, and how to best protect the sensitive data inevitably to be shared with technical privacy-preserving mechanisms. The key takeaway of this chapter is that we should put more thought into what we are building and using our systems for to allow for privacy through human-centered design instead of static, predefined solutions which do not meet consumer needs