In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical engineering applications. Classical projection-based model reduction methods generate reduced systems by projecting full-order differential operators into low-dimensional subspaces. However, these techniques usually lead to severe instabilities in the presence of highly nonlinear dynamics, which dramatically deteriorates the accuracy of the reduced-order models. In contrast, our new framework exploits linear multistep networks, based on implicit Adams-Moulton schemes, to construct the reduced system. The advantage is that the method optimally approximates the full order model in the low-dimensional space with a given supervised learning task. Moreover, our approach is non-intrusive, such that it can be applied to other complex nonlinear dynamical systems with sophisticated legacy codes. We demonstrate the performance of our method through the numerical simulation of a two-dimensional flow past a circular cylinder with Reynolds number Re = 100. The results reveal that the new data-driven model is significantly more accurate than standard projection-based approaches

In this paper, we introduce the evolve-then-filter (EF) regularization method for reduced order modeling of convection-dominated stochastic systems. The standard Galerkin projection reduced order model (G-ROM) yield numerical oscillations in a convection-dominated regime. The evolve-then-filter reduced order model (EF-ROM) aims at the numerical stabilization of the standard G-ROM, which uses explicit ROM spatial filter to regularize various terms in the reduced order model (ROM). Our numerical results based on a stochastic Burgers equation with linear multiplicative noise. It shows that the EF-ROM is significantly better results than G-ROM.

Vaccination remains an important mitigation tool against COVID-19. We report 1-month safety and preliminary immunogenicity data from a substudy of an ongoing, open-label, phase 2/3 study of monovalent Omicron XBB.1.5-adapted BNT162b2 (single 30-μg dose). Healthy, participants ≥12 years old (N=412 [12‒17 years, N=30; 18‒55 years, N=174; >55 years, N=208]) who previously received ≥3 doses of a US-authorized mRNA vaccine, the most recent being an Omicron BA.4/BA.5-adapted bivalent vaccine ≥150 days before study vaccination, were vaccinated. Serum 50% neutralizing titers against Omicron XBB.1.5, EG.5.1, and BA.2.86 were measured 7 days and 1 month after vaccination in a subset of ≥18-year-olds (N=40) who were positive for SARS-CoV-2 at baseline. Seven-day immunogenicity was also evaluated in a matched group who received bivalent BA.4/BA.5-adapted BNT162b2 in a previous study (NCT05472038). There were no new safety signals; local reactions and systemic events were mostly mild to moderate in severity, adverse events were infrequent, and none led to study withdrawal. The XBB.1.5-adapted BNT162b2 induced numerically higher titers against Omicron XBB.1.5, EG.5.1, and BA.2.86 than BA.4/BA.5-adapted BNT162b2 at 7 days and robust neutralizing responses to all 3 sublineages at 1 month. These data support a favorable benefit-risk profile of XBB.1.5-adapted BNT162b2 30 μg. NCT05997290