X. Xie

X. Xie, M. Mohebujjaman, L. G. Rebholz et al.

We propose a calibrated filtered reduced order model (CF-ROM) framework for the numerical simulation of general nonlinear PDEs that are amenable to reduced order modeling. The novel CF-ROM framework consists of two steps: (i) In the first step, we use explicit ROM spatial filtering of the nonlinear PDE to construct a filtered ROM. This filtered ROM is low-dimensional, but is not closed (because of the nonlinearity in the given PDE). (ii) In the second step, we use a calibration procedure to close the filtered ROM, i.e., to model the interaction between the resolved and unresolved modes. To this end, we use a linear or quadratic ansatz to model this interaction and close the filtered ROM. To find the new coefficients in the closed filtered ROM, we solve an optimization problem that minimizes the difference between the full order model data and our ansatz. Although we use a fluid dynamics setting to illustrate how to construct and use the CF-ROM framework, we emphasize that it is built on general ideas of spatial filtering and optimization and is independent of (restrictive) phenomenological arguments. Thus, the CF-ROM framework can be applied to a wide variety of PDEs.

H. Yi, H. Ren, C. Hu et al.

Federated Learning (FL) has become a cornerstone of privacy protection, shifting the paradigm towards localizing sensitive data while only sending model gradients to a central server. This strategy is designed to reinforce privacy protections and minimize the vulnerabilities inherent in centralized data storage systems. Despite its innovative approach, recent empirical studies have highlighted potential weaknesses in FL, notably regarding the exchange of gradients. In response, this study introduces a novel, efficacious method aimed at safeguarding against gradient leakage, namely, ``AdaDefense". Following the idea that model convergence can be achieved by using different types of optimization methods, we suggest using a local stand-in rather than the actual local gradient for global gradient aggregation on the central server. This proposed approach not only effectively prevents gradient leakage, but also ensures that the overall performance of the model remains largely unaffected. Delving into the theoretical dimensions, we explore how gradients may inadvertently leak private information and present a theoretical framework supporting the efficacy of our proposed method. Extensive empirical tests, supported by popular benchmark experiments, validate that our approach maintains model integrity and is robust against gradient leakage, marking an important step in our pursuit of safe and efficient FL.

C. Rodriguez, Thierry Garaix, X. Xie et al.

The problem addressed in this paper is how to calculate the amount of personnel required to ensure the activity of a home health care (HHC) center on a tactical horizon. Design of quantitative approaches for this question is challenging. The number of caregivers has to be determined for each profession in order to balance the coverage of patients in a region and the workforce cost over several months. Unknown demand in care and spatial dimensions, combination of skills to cover a care and individual trips visiting patients make the underlaying optimization problem very hard. Few studies are dedicated to staff dimensioning for HHC compared to patient to nurses assignment/sequencing and centers location problems. We propose an original two-stage approach based on integer linear stochastic programming, that exploits historical medical data. The first stage calculates (near-)optimal levels of resources for possible demand scenarios , while the second stage computes the optimal number of caregiver for each profession to meet a target coverage indicator. For decision-makers, our algorithm gives the number of employees for each category required to satisfy the demand without any recourse (overtime, external resources) with fixed probability and confidence interval. The approach has been tested on various instances built from data of the French agency of hospitalization data (ATIH).

L. C. Berselli, D. Wells, X. Xie et al.

Spatial filtering has been central in the development of large eddy simulation reduced order models (LES-ROMs) and regularized reduced order models (Reg-ROMs), In this paper, we perform a numerical investigation of spatial filtering. To this end, we consider one of the simplest Reg-ROMs, the Leray ROM (L-ROM), which uses ROM spatial filtering to smooth the flow variables and decreases the amount of energy aliased to the lower index ROM basis functions. We also propose a new form of ROM differential filter and use it as a spatial filter for the L-ROM. We investigate the performance of this new form of ROM differential filter in the numerical simulation of a flow past a circular cylinder at a Reynolds number $Re=760$.