11 research outputs found
Lagrangian Data-Driven Reduced Order Modeling of Finite Time Lyapunov Exponents
There are two main strategies for improving the projection-based reduced
order model (ROM) accuracy: (i) improving the ROM, i.e., adding new terms to
the standard ROM; and (ii) improving the ROM basis, i.e., constructing ROM
bases that yield more accurate ROMs. In this paper, we use the latter. We
propose new Lagrangian inner products that we use together with Eulerian and
Lagrangian data to construct new Lagrangian ROMs. We show that the new
Lagrangian ROMs are orders of magnitude more accurate than the standard
Eulerian ROMs, i.e., ROMs that use standard Eulerian inner product and data to
construct the ROM basis. Specifically, for the quasi-geostrophic equations, we
show that the new Lagrangian ROMs are more accurate than the standard Eulerian
ROMs in approximating not only Lagrangian fields (e.g., the finite time
Lyapunov exponent (FTLE)), but also Eulerian fields (e.g., the streamfunction).
We emphasize that the new Lagrangian ROMs do not employ any closure modeling to
model the effect of discarded modes (which is standard procedure for
low-dimensional ROMs of complex nonlinear systems). Thus, the dramatic increase
in the new Lagrangian ROMs' accuracy is entirely due to the novel Lagrangian
inner products used to build the Lagrangian ROM basis
Combining Stochastic Parameterized Reduced-Order Models with Machine Learning for Data Assimilation and Uncertainty Quantification with Partial Observations
A hybrid data assimilation algorithm is developed for complex dynamical
systems with partial observations. The method starts with applying a spectral
decomposition to the entire spatiotemporal fields, followed by creating a
machine learning model that builds a nonlinear map between the coefficients of
observed and unobserved state variables for each spectral mode. A cheap
low-order nonlinear stochastic parameterized extended Kalman filter (SPEKF)
model is employed as the forecast model in the ensemble Kalman filter to deal
with each mode associated with the observed variables. The resulting ensemble
members are then fed into the machine learning model to create an ensemble of
the corresponding unobserved variables. In addition to the ensemble spread, the
training residual in the machine learning-induced nonlinear map is further
incorporated into the state estimation that advances the quantification of the
posterior uncertainty. The hybrid data assimilation algorithm is applied to a
precipitating quasi-geostrophic (PQG) model, which includes the effects of
water vapor, clouds, and rainfall beyond the classical two-level QG model. The
complicated nonlinearities in the PQG equations prevent traditional methods
from building simple and accurate reduced-order forecast models. In contrast,
the SPEKF model is skillful in recovering the intermittent observed states, and
the machine learning model effectively estimates the chaotic unobserved
signals. Utilizing the calibrated SPEKF and machine learning models under a
moderate cloud fraction, the resulting hybrid data assimilation remains
reasonably accurate when applied to other geophysical scenarios with nearly
clear skies or relatively heavy rainfall, implying the robustness of the
algorithm for extrapolation
An Energy-Based Lengthscale for Reduced Order Models of Turbulent Flows
In this paper, we propose a novel reduced order model (ROM) lengthscale that
is constructed by using energy distribution arguments. The new energy-based ROM
lengthscale is fundamentally different from the current ROM lengthscales, which
are built by using dimensional arguments. To assess the novel, energy-based ROM
lengthscale, we compare it with a standard, dimensionality-based ROM
lengthscale in two fundamentally different types of models: (i) the
mixing-length ROM (ML-ROM), which is a ROM closure model; and (ii) the
evolve-filter-relax ROM (EFR-ROM), which is a regularized ROM. We test the four
combinations (i.e., ML-ROM and EFR-ROM equipped with the energy-based and
dimensionality-based lengthscales) in the numerical simulation of the turbulent
channel flow at . The numerical investigation yields the
following conclusions: (i) The new energy-based ROM lengthscale is
significantly (almost two orders of magnitude) larger than the standard
dimensionality-based ROM lengthscale. As a result, the energy-based lengthscale
yields more stable ML-ROMs and EFR-ROMs than the dimensionality-based
lengthscale. (ii) The energy-based lengthscale displays the correct asymptotic
behavior with respect to the ROM dimension, whereas the dimensionality-based
lengthscale does not. (iii) The energy-based lengthscale yields ML-ROMs and
(when significant filtering is effected) EFR-ROMs whose parameters are less
sensitive (i.e., more robust) than the parameters of the ML-ROMs and EFR-ROMs
based on the dimensionality-based lengthscale. The novel energy-based
lengthscale could enable the development of better scale-aware ROM strategies
for flow-specific applications and is expected to have long term applications
in nuclear reactor thermal-hydraulics.Comment: arXiv admin note: substantial text overlap with arXiv:2108.0225
Commutation error in reduced order modeling of fluid flows
For reduced order models (ROMs) of fluid flows, we investigate theoretically and computationally whether differentiation and ROM spatial filtering commute, i.e., whether the commutation error (CE) is nonzero. We study the CE for the Laplacian and two ROM filters: the ROM projection and the ROM differential filter. Furthermore, when the CE is nonzero, we investigate whether it has any significant effect on ROMs that are constructed by using spatial filtering. As numerical tests, we use the Burgers equation with viscosities ν = 10− 1 and ν = 10− 3 and a 2D flow past a circular cylinder at Reynolds numbers Re = 100 and Re = 500. Our investigation (i) measures the size of the CE in these test problems and (ii) shows that the CE has a significant effect on ROM development for high viscosities, but not so much for low viscosities
Verifiability of the Data-Driven Variational Multiscale Reduced Order Model
International audienceIn this paper, we focus on the mathematical foundations of reduced order model (ROM) closures. First, we extend the verifiability concept from large eddy simulation to the ROM setting. Specifically, we call a ROM closure model verifiable if a small ROM closure model error (i.e., a small difference between the true ROM closure and the modeled ROM closure) implies a small ROM error. Second, we prove that the data-driven ROM closure studied here (i.e., the data-driven variational multiscale ROM) is verifiable. Finally, we investigate the verifiability of the data-driven variational multiscale ROM in the numerical simulation of the one-dimensional Burgers equation and a two-dimensional flow past a circular cylinder at Reynolds numbers Re=100 and Re=1000
A randomized controlled trial protocol comparing the feeds of fresh versus frozen mother’s own milk for preterm infants in the NICU
Abstract
Background
Necrotizing enterocolitis (NEC) is the leading cause of death among preterm infants born at < 30 weeks’ gestation. The incidence of NEC is reduced when infants are fed human milk. However, in many neonatal intensive care units (NICUs), it is standard practice to freeze and/or pasteurize human milk, which deactivates bioactive components that may offer additional protective benefits. Indeed, our pilot study showed that one feed of fresh mother’s own milk per day was safe, feasible, and can reduce morbidity in preterm infants. To further evaluate the benefits of fresh human milk in the NICU, a randomized controlled trial is needed.
Methods
Our prospective multicenter, double-blinded, randomized, controlled trial will include infants born at < 30 weeks’ gestation and admitted to one of 29 tertiary NICUs in China. Infants in the intervention (fresh human milk) group (n = 1549) will receive at least two feeds of fresh human milk (i.e., within 4 h of expression) per day from the time of enrollment until 32 weeks’ corrected age or discharge to home. Infants in the control group (n = 1549) will receive previously frozen human milk following the current standard protocols. Following informed consent, enrolled infants will be randomly allocated to the control or fresh human milk groups. The primary outcome is the composite outcome mortality or NEC ≥ stage 2 at 32 weeks’ corrected age, and the secondary outcomes are mortality, NEC ≥ stage 2, NEC needing surgery, late-onset sepsis, retinopathy of prematurity (ROP), bronchopulmonary dysplasia (BPD), weight gain, change in weight, increase in length, increase in head circumference, time to full enteral feeds, and finally, the number and type of critical incident reports, including feeding errors.
Discussion
Our double-blinded, randomized, controlled trial aims to examine whether fresh human milk can improve infant outcomes. The results of this study will impact both Chinese and international medical practice and feeding policy for preterm infants. In addition, data from our study will inform changes in health policy in NICUs across China, such that mothers are encouraged to enter the NICU and express fresh milk for their infants.
Trial registration
Chinese Clinical Trial Registry; #ChiCTR1900020577; registered January 1, 2019; http://www.chictr.org.cn/showprojen.aspx?proj=3427