Forward Sensitivity Analysis and Mode Dependent Control for Closure Modeling of Galerkin Systems

Model reduction by projection-based approaches is often associated with losing some of the important features that contribute towards the dynamics of the retained scales. As a result, a mismatch occurs between the predicted trajectories of the original system and the truncated one. We put forth a framework to apply a continuous time control signal in the latent space of the reduced order model (ROM) to account for the effect of truncation. We set the control input using parameterized models by following energy transfer principles. Our methodology relies on observing the system behavior in the physical space and using the projection operator to restrict the feedback signal into the latent space. Then, we leverage the forward sensitivity method (FSM) to derive relationships between the feedback and the desired mode-dependent control. We test the performance of the proposed approach using two test cases, corresponding to viscous Burgers and vortex merger problems at high Reynolds number. Results show that the ROM trajectory with the applied FSM control closely matches its target values in both the data-dense and data-sparse regimes

PyOED: An Extensible Suite for Data Assimilation and Model-Constrained Optimal Design of Experiments

This paper describes the first version (v1.0) of PyOED, a highly extensible scientific package that enables developing and testing model-constrained optimal experimental design (OED) for inverse problems. Specifically, PyOED aims to be a comprehensive Python toolkit for model-constrained OED. The package targets scientists and researchers interested in understanding the details of OED formulations and approaches. It is also meant to enable researchers to experiment with standard and innovative OED technologies with a wide range of test problems (e.g., simulation models). Thus, PyOED is continuously being expanded with a plethora of Bayesian inversion, DA, and OED methods as well as new scientific simulation models, observation error models, and observation operators. These pieces are added such that they can be permuted to enable testing OED methods in various settings of varying complexities. The PyOED core is completely written in Python and utilizes the inherent object-oriented capabilities; however, the current version of PyOED is meant to be extensible rather than scalable. Specifically, PyOED is developed to ``enable rapid development and benchmarking of OED methods with minimal coding effort and to maximize code reutilization.'' PyOED will be continuously expanded with a plethora of Bayesian inversion, DA, and OED methods as well as new scientific simulation models, observation error models, and observation operators. This paper provides a brief description of the PyOED layout and philosophy and provides a set of exemplary test cases and tutorials to demonstrate how the package can be utilized.Comment: 26 pages, 7 figures, 21 code snippet

A Multifidelity deep operator network approach to closure for multiscale systems

Projection-based reduced order models (PROMs) have shown promise in representing the behavior of multiscale systems using a small set of generalized (or latent) variables. Despite their success, PROMs can be susceptible to inaccuracies, even instabilities, due to the improper accounting of the interaction between the resolved and unresolved scales of the multiscale system (known as the closure problem). In the current work, we interpret closure as a multifidelity problem and use a multifidelity deep operator network (DeepONet) framework to address it. In addition, to enhance the stability and accuracy of the multifidelity-based closure, we employ the recently developed "in-the-loop" training approach from the literature on coupling physics and machine learning models. The resulting approach is tested on shock advection for the one-dimensional viscous Burgers equation and vortex merging using the two-dimensional Navier-Stokes equations. The numerical experiments show significant improvement of the predictive ability of the closure-corrected PROM over the un-corrected one both in the interpolative and the extrapolative regimes.Comment: 24 pages, 21 figure

Fibulin-2 is required for basement membrane integrity of mammary epithelium

Fibulin-2 (FBLN2) is a secreted extracellular matrix glycoprotein which has been associated with tissue development and remodelling. In the mouse mammary gland, FBLN2 can be detected during ductal morphogenesis in cap cells and myoepithelial cells at puberty and early pregnancy, respectively. In an attempt to assign its function, we knocked down Fbln2 in the mouse mammary epithelial cell line EpH4. FBLN2 reduction led to an increase in the size of spheroidal structures when compared to scrambled control shRNA-transduced cells plated on Matrigel matrix. This phenotype was associated with a disruption of the collagen IV sheath around the epithelial spheroids and downregulation of integrin β1, suggesting a role for FBLN2 in stabilizing the basement membrane (BM). In contrast to mice, in normal adult human breast tissue, FBLN2 was detected in ductal stroma, and in the interlobular stroma, but was not detectable within the lobular regions. In tissue sections of 65 breast cancers FBLN2 staining was lost around malignant cells with retained staining in the neighbouring histologically normal tissue margins. These results are consistent with a role of FBLN2 in mammary epithelial BM stability, and that its down-regulation in breast cancer is associated with loss of the BM and early invasion

Nonlinear proper orthogonal decomposition for convection-dominated flows

Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when integrated with a time series predictive model. In this Letter, we put forth a nonlinear proper orthogonal decomposition (POD) framework, which is an end-to-end Galerkin-free model combining autoencoders with long short-term memory networks for dynamics. By eliminating the projection error due to the truncation of Galerkin models, a key enabler of the proposed nonintrusive approach is the kinematic construction of a nonlinear mapping between the full-rank expansion of the POD coefficients and the latent space where the dynamics evolve. We test our framework for model reduction of a convection-dominated system, which is generally challenging for reduced order models. Our approach not only improves the accuracy, but also significantly reduces the computational cost of training and testing. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research under Award Number DE-SC0019290. O.S. gratefully acknowledges the Early Career Research Program (ECRP) support of the U.S. Department of Energy. O.S. also gratefully acknowledges the financial support of the National Science Foundation under Award No. DMS-2012255. T.I. acknowledges support through National Science Foundation Grant No. DMS-2012253.acceptedVersio