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

Reduced order modeling of fluid flows: Machine learning, Kolmogorov barrier, closure modeling, and partitioning

In this paper, we put forth a long short-term memory (LSTM) nudging framework for the enhancement of reduced order models (ROMs) of fluid flows utilizing noisy measurements. We build on the fact that in a realistic application, there are uncertainties in initial conditions, boundary conditions, model parameters, and/or field measurements. Moreover, conventional nonlinear ROMs based on Galerkin projection (GROMs) suffer from imperfection and solution instabilities due to the modal truncation, especially for advection-dominated flows with slow decay in the Kolmogorov width. In the presented LSTM-Nudge approach, we fuse forecasts from a combination of imperfect GROM and uncertain state estimates, with sparse Eulerian sensor measurements to provide more reliable predictions in a dynamical data assimilation framework. We illustrate the idea with the viscous Burgers problem, as a benchmark test bed with quadratic nonlinearity and Laplacian dissipation. We investigate the effects of measurements noise and state estimate uncertainty on the performance of the LSTM-Nudge behavior. We also demonstrate that it can sufficiently handle different levels of temporal and spatial measurement sparsity. This first step in our assessment of the proposed model shows that the LSTM nudging could represent a viable realtime predictive tool in emerging digital twin systems

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

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

Anterior abdominal wall ectopic testes: A report of two cases

Undescended testis (UDT) is a common anomaly of the male reproductive system  affecting about 2% to 4% of male infants more commonly preterms. If the testis remains in the line of normal descent, it is classified as an UDT. If it is not in the line of  normal descent, it is termed an ectopic testis. Common sites of ectopic testes are  perineal, transverse ectopia, pubopenile and femoral. To the best of our knowledge only two cases of anterior abdominal wall ectopic testis have been reported in the literature.  We present here two cases of anterior abdominal wall testis,  one of which was  associated with indirect inguinal hernia.Keywords: anomalies of the testis, ectopic testis, empty scrotu

Model-data fusion in digital twins of large scale dynamical systems

Digital twins (DTs) are virtual entities that serve as the real-time digital counterparts of actual physical systems across their life-cycle. In a typical application of DTs, the physical system provides sensor measurements and the DT should incorporate the incoming data and run different simulations to assess various scenarios and situations. As a result, an informed decision can be made to alter the physical system or at least take necessary precautions, and the process is repeated along the system's life-cycle. Thus, the effective deployment of DTs requires fulfilling multi-queries while communicating with the physical system in real-time. Nonetheless, DTs of large-scale dynamical systems, as in fluid flows, come with three grand challenges that we address in this dissertation.First, the high dimensionality makes full order modeling (FOM) methodologies unfeasible due to the associated computational time and memory costs. In this regard, reduced order models (ROMs) can potentially accelerate the forward simulations by orders of magnitude, especially for systems with recurrent spatial structures. However, traditional ROMs yield inaccurate and unstable results for turbulent and convective flows. Therefore, we propose a hybrid variational multi-scale framework that benefits from the locality of modal interactions to deliver accurate ROMs. Furthermore, we adopt a novel physics guided machine learning technique to provide on-the-fly corrections and elevate the trustworthiness of the resulting ROM in the sparse data and incomplete governing equations regimes.Second, complex natural or engineered systems are characterized by multi-scale, multi-physics, and multi-component nature. The efficient simulation of such systems requires quick communication and information sharing between several heterogeneous computing units. In order to address this challenge, we pioneer an interface learning (IL) paradigm to ensure the seamless integration of hierarchical solvers with different scales, physics, abstractions, and geometries without compromising the integrity of the computational setup. We demonstrate the IL paradigm for non-iterative domain decomposition and the FOM-ROM coupling in multi-fidelity computations.Third, fluid flow systems are continuously evolving and thus the validity of the DT should be warranted across varying operating conditions and flow regimes. To do so, we embed data assimilation (DA) techniques to enable the DT to self-adapt based on in-situ observational data and efficiently replicate the physical system. In addition, we combine DA algorithms with machine learning models to build a robust framework that collectively addresses the model closure problem, the error in prior information, and the measurement noise

Identifying the common interaction networks of amoeboid motility and cancer cell metastasis

The recently analyzed genome of Naegleria gruberi, a free-living amoeboflagellate of the Heterolobosea clade, revealed a remarkably complex ancestral eukaryote with a rich repertoire of cytoskeletal-, motility- and signaling-genes. This protist, which diverged from other eukaryotic lineages over a billion years ago, possesses the ability for both amoeboid and flagellar motility. In a phylogenomic comparison of two free living eukaryotes with large proteomic datasets of three metastatic tumour entities (malignant melanoma, breast- and prostate-carcinoma), we find common proteins with potential importance for cell motility and cancer cell metastasis. To identify the underlying signaling modules, we constructed for each tumour type a protein-protein interaction network including these common proteins. The connectivity within this interactome revealed specific interactions and pathways which constitute prospective points of intervention for novel anti-metastatic tumour therapies