Physics-informed data assimilation and data-driven reduced order model
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Mathematics and Computing↗
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Data-driven variational multiscale reduced order models
We propose a new data-driven reduced order model (ROM) framework that centers around the hierarchical structure of the variational multiscale (VMS) methodology and utilizes data to increase the ROM accuracy at a modest computational cost. The VMS methodology is a natural fit for the hierarchical structure of the ROM basis: In the first step, we use the ROM projection to separate the scales into three categories: (i) resolved large scales, (ii) resolved small scales, and (iii) unresolved scales. In the second step, we explicitly identify the VMS–ROM closure terms, i.e., the terms representing the interactions among the three types of scales. In the third step, we use available data to model the VMS–ROM closure terms. Thus, instead of phenomenological models used in VMS for standard numerical discretizations (e.g., eddy viscosity models), we utilize available data to construct new structural VMS–ROM closure models. Specifically, we build ROM operators (vectors, matrices, and tensors) that are closest to the true ROM closure terms evaluated with the available data. We test the new data-driven VMS–ROM in the numerical simulation of four test cases: (i) the 1D Burgers equation with viscosity coefficient v = 10 -3 ; (ii) a 2D flow past a circular cylinder at Reynolds numbers, Re = 100, Re = 500, and Re= 1000; (iii) the quasi-geostrophic equations at Reynolds number Re = 450 and Rossby number Ro = 0.0036; and (iv) a 2D flow over a backward facing step at Reynolds number Re = 1000. The numerical results show that the data-driven VMS–ROM is significantly more accurate than standard ROMs.
42 ENGINEERING↗
Anomaly Detection in Sequential Health Care Data using Higher-Order Network Representation
The ever-increasing use of information technology (IT) in health care presents new challenges to patient care. Information errors arising from the use of Health IT and their implications on care delivery and patient outcomes have been widely reported. Information errors can lead to changes in clinical decisions, care processes, and care outcomes, among others. An altered care process, for example, could interrupt the sequence of care, which could lead to changes in care decisions and/or changes in care outcomes. We define interruptions in the care process as anomalies in the care sequence. In this paper, we present a new approach based on the higher-order network (HON) representation to detect anomalies in sequential health care data using electronic health records. The results show that there are higher-order dependencies in health care data; and that the use of HON representation is more effective than the first-order network representation for detecting anomalies in sequential health care data.
Niu, Haoran↗
Efficient high-dimensional variational data assimilation with machine-learned reduced-order models
Abstract. Data assimilation (DA) in geophysical sciences remains the cornerstone of robust forecasts from numerical models. Indeed, DA plays a crucial role in the quality of numerical weather prediction and is a crucial building block that has allowed dramatic improvements in weather forecasting over the past few decades. DA is commonly framed in a variational setting, where one solves an optimization problem within a Bayesian formulation using raw model forecasts as a prior and observations as likelihood. This leads to a DA objective function that needs to be minimized, where the decision variables are the initial conditions specified to the model. In traditional DA, the forward model is numerically and computationally expensive. Here we replace the forward model with a low-dimensional, data-driven, and differentiable emulator. Consequently, gradients of our DA objective function with respect to the decision variables are obtained rapidly via automatic differentiation. We demonstrate our approach by performing an emulator-assisted DA forecast of geopotential height. Our results indicate that emulator-assisted DA is faster than traditional equation-based DA forecasts by 4 orders of magnitude, allowing computations to be performed on a workstation rather than a dedicated high-performance computer. In addition, we describe accuracy benefits of emulator-assisted DA when compared to simply using the emulator for forecasting (i.e., without DA). Our overall formulation is denoted AIEADA (Artificial Intelligence Emulator-Assisted Data Assimilation).
58 GEOSCIENCES↗
Data-Driven Reduced-Order Modeling of Convective Heat Transfer in Porous Media
This work presents a data-driven Reduced-Order Model (ROM) for parametric convective heat transfer problems in porous media. The intrusive Proper Orthogonal Decomposition aided Reduced-Basis (POD-RB) technique is employed to reduce the porous medium formulation of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations coupled with heat transfer. Instead of resolving the exact flow configuration with high fidelity, the porous medium formulation solves a homogenized flow in which the fluid-structure interactions are captured via volumetric flow resistances with nonlinear, semi-empirical friction correlations. A supremizer approach is implemented for the stabilization of the reduced fluid dynamics equations. The reduced nonlinear flow resistances are treated using the Discrete Empirical Interpolation Method (DEIM), while the turbulent eddy viscosity and diffusivity are approximated by adopting a Radial Basis Function (RBF) interpolation-based approach. The proposed method is tested using a 2D numerical model of the Molten Salt Fast Reactor (MSFR), which involves the simulation of both clean and porous medium regions in the same domain. For the steady-state example, five model parameters are considered to be uncertain: the magnitude of the pumping force, the external coolant temperature, the heat transfer coefficient, the thermal expansion coefficient, and the Prandtl number. For transient scenarios, on the other hand, the coastdown-time of the pump is the only uncertain parameter. The results indicate that the POD-RB-ROMs are suitable for the reduction of similar problems. The relative L2 errors are below 3.34% for every field of interest for all cases analyzed, while the speedup factors vary between 54 (transient) and 40,000 (steady-state).
German, Péter (ORCID:0000000307285283)↗
Making sense of vacancy correlations with single-crystal diffuse scattering data
Local ordering of atoms within a crystalline structure is increasingly recognized as essential to understanding the properties of a variety of interesting materials. This is shown by the success of pair distribution function (PDF) analysis of scattering data from powder samples to investigate departures from perfectly crystalline order (Billinge & Kanatzidis, 2004; Egami & Billinge, 2012). Diffuse scattering from single crystals can also be a powerful probe of local order, potentially providing key information that would be difficult to obtain from PDF methods; however, difficulties in both measurement and interpretation of data have too often restricted their use by a larger community. In this issue of IUCrJ, Rothet al.(2020) demonstrate how simple concepts can be applied to better understand single-crystal diffuse scattering from half-Heusler systems.
36 MATERIALS SCIENCE↗
Evolution of the ATLAS event data model for the HL-LHC
The upcoming high-luminosity run of the CERN Large Hadron Collider (HL-LHC) will yield an unprecedented volume of data. In order to process this data, the ATLAS collaboration is evolving its offline software to be able to use heterogeneous resources such as graphical processing units (GPUs) and field-programmable gate arrays (FPGAs). To reduce conversion overheads, the event data model (EDM) should be compatible with the requirements of these resources. While the ATLAS EDM has long allowed representing data as a structure of arrays, further evolution of the EDM can enable more efficient sharing of data between CPU and GPU resources. Some of this work will be summarized here, including extensions to allow controlling how memory for event data is allocated and the implementation of jagged vectors.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
FunMC^2: A Filter for Uncertainty Visualization of Marching Cubes on Multi-Core Devices
Visualization is an important tool for scientists to extract understanding from complex scientific data. Scientists need to understand the uncertainty inherent in all scientific data in order to interpret the data correctly. Uncertainty visualization has been an active and growing area of research to address this challenge. Algorithms for uncertainty visualization can be expensive, and research efforts have been focused mainly on structured grid types. Further, support for uncertainty visualization in production tools is limited. In this paper, we adapt an algorithm for computing key metrics for visualizing uncertainty in Marching Cubes (MC) to multi-core devices and present the design, implementation, and evaluation for a Filter for uncertainty visualization of Marching Cubes on Multi-Core devices (FunMC2). FunMC2 accelerates the uncertainty visualization of MC significantly, and it is portable across multi-core CPUs and GPUs. Evaluation results show that FunMC2 based on OpenMP runs around 11× to 41× faster on multi-core CPUs than the corresponding serial version using one CPU core. FunMC2 based on a single GPU is around 5× to 9× faster than FunMC2 running by OpenMP. Moreover, FunMC2 is flexible enough to process ensemble data with both structured and unstructured mesh types. Furthermore, we demonstrate that FunMC2 can be seamlessly integrated as a plugin into ParaView, a production visualization tool for post-processing.
Wang, Jay↗
The growth of density perturbations in the last ~10 billion years from tomographic large-scale structure data
In order to investigate the origin of the ongoing tension between the amplitude of matter fluctuations measured by weak lensing experiments at low redshifts and the value inferred from the cosmic microwave background anisotropies, we reconstruct the evolution of this amplitude from z ~ 2 using existing large-scale structure data. To do so, we decouple the linear growth of density inhomogeneities from the background expansion, and constrain its redshift dependence making use of a combination of 6 different data sets, including cosmic shear, galaxy clustering and CMB lensing. We analyze these data under a consistent harmonic-space angular power spectrum-based pipeline. We show that current data constrain the amplitude of fluctuations mostly in the range 0.2 < z < 0.7, where it is lower than predicted by . This difference is mostly driven by current cosmic shear data, although the growth histories reconstructed from different data combinations are consistent with each other, and we find no evidence of systematic deviations in any particular experiment. In spite of the tension with , the data are well-described by the model, albeit with a lower value of S 8 ≡ σ 8 (Ω m /0.3) 0.5 . As part of our analysis, we find constraints on this parameter of S 8 = 0.7781 ± 0.0094 (68% confidence level), reaching almost percent-level errors comparable with CMB measurements, and 3.4σ away from the value found by .
79 ASTRONOMY AND ASTROPHYSICS↗
Data-driven reduced-order models for port-Hamiltonian systems with operator inference
Hamiltonian operator inference has been developed in Sharma et al. (2022) to learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. The method constructs a low-dimensional model using only data and knowledge of the functional form of the Hamiltonian. The resulting ROMs preserve the intrinsic structure of the system, ensuring that the mechanical and physical properties of the system are maintained. In this work, we extend this approach to port-Hamiltonian systems, which generalize Hamiltonian systems by including energy dissipation, external input, and output. Based on snapshots of the system’s state and output, together with the information about the functional form of the Hamiltonian, reduced operators are inferred through optimization and are then used to construct data-driven ROMs. To further alleviate the complexity of evaluating nonlinear terms in the ROMs, a hyper-reduction method via discrete empirical interpolation is applied. Accordingly, we derive error estimates for the ROM approximations of the state and output. Lastly, we demonstrate the structure preservation, as well as the accuracy of the proposed port-Hamiltonian operator inference framework, through numerical experiments on a linear mass–spring-damper problem and a nonlinear Toda lattice problem.
97 MATHEMATICS AND COMPUTING↗
A Parametric, Data-Driven, Non-Intrusive Reduced-Order Model Framework for Crystal Plasticity Simulations of Voids
The influence of the internal structure at micrometer length scales on the deformation of polycrystalline materials can be effectively captured using crystal plasticity finite element methods (CPFEM). However, the complexity and nonlinearity of the deformation equations CPFEM solves demand significant computational power and resources to achieve accurate predictions, limiting its broader application. To address this challenge, we have identified a reduced-order representation of the complex data in order to establish a computationally efficient reduced-order models (ROM) and drastically reduce the computational expense of CPFEM. Specifically, in this work, we developed a parametric, data-driven, and non-intrusive ROM framework for CPFEM using proper orthogonal decomposition (POD) and sparse variational Gaussian process (SVGP) regression for single-crystal microstructures under tensile loading conditions. The developed protocol enables one to compress field into a latent/low-dimensional space described by principal component analysis (PCA) via the singular value decomposition (SVD) algorithm. As a result, the high-dimensional data are reduced to a significantly smaller amount of dimensions with POD bases and POD coefficients. Furthermore, we deployed an ensemble of SVGPs—extended from the classical Gaussian process (GP) regression for scalability and handling big data—in a massively parallel manner to train and predict latent POD coefficients using known POD bases from a set of previously obtained simulations results. Lastly, using the predicted POD coefficients, we reconstructed the full-field results and showed reasonable agreement compared with the true values obtained from running CPFEM. The developed framework is validated with a set of CPFEM simulations of a single embedded void in single-crystal aluminum alloy. While the framework is broadly applicable, this work specifically focuses on single-crystal microstructures, a single load case (e.g., tensile), and a specific void geometry (spherical).
Anisotropy↗
Reduced number of counters for reliable messaging
A shared memory maintained by sender processes stores a sequence number counter per destination process. A sender process increments the sequence number counter in the shared memory in sending a message to a destination process. The sender process sends a data packet comprising the message and at least a sequence number specified by the sequence number counter. All of the sender processes share a sequence number counter per destination process, each of the sender processes incrementing the sequence number counter in sending a respective message. Receiver processes run on the hardware processor, each of the receiver processes maintaining a local memory counter on the memory, the local memory counter associated with a sending node. The local memory counter stores a sequence number of a message received from the sending node. The receiver process delivers incoming data packets ordered by sequence numbers of the data packets.
Kumar, Sameer↗
Improving the Quality of Geothermal Data Through Data Standards and Pipelines Within the Geothermal Data Repository: Preprint
For machine learning outputs to be applicable to real world problems, high quality data are needed to ensure high quality results. With the more recent emphasis on machine learning in geothermal, there is an increasing need for greater focus on the quality of the data available for use in these projects. For example, Geothermal Operational Optimization Using Machine Learning (GOOML) utilized large quantities of geothermal power plant operational data to inform power plant operational configurations to maximize power generation. High quality datasets result from dependable sensors or devices collecting data, high frequency of measurements, sufficient data points, adequate metadata, reliable storage of data, and sufficient data curation. Another component that contributes to high quality data is reusability, which can be enhanced through data standardization. Data Standardization creates consistency in formatting and contents of like datasets, lessening preprocessing requirements and ensuring adequate information provided by a given dataset. The Geothermal Data Repository (GDR) aims to help improve data quality through automated data standardization for high-value datasets through the implementation of data pipelines alongside reliable and accessible long-term storage for datasets. As such, the GDR has decided to shift away from recommending the use of Excel-based content models and towards the implementation of automated data pipelines. This takes the burden of data standardization off the user and project team and will increase the availability of standardized geothermal data available through the GDR. A set of recommendations, or a data standard for each data type will exist with each data pipeline in order to advise data collection for maximum usability for future research. This paper serves to describe the GDR's proposed transition towards data standardization through automated data pipelines, to discuss the need for and value of such a shift, and to call for suggestions from the community regarding the most useful data standards and pipelines.
data↗
Initial data for first-order causal viscous conformal fluids in general relativity
We solve the Einstein constraint equations for a first-order causal viscous relativistic hydrodynamic theory in the case of a conformal fluid. For such a theory, a direct application of the conformal method does not lead to a decoupling of the equations, even for constant-mean curvature initial data. We combine the conformal method applied to a background perfect fluid theory with a perturbative argument in order to obtain the result.
Disconzi, Marcelo (ORCID:0000000234497778)↗
Data-driven reduced-order models via regularised Operator Inference for a single-injector combustion process
Not Available
97 MATHEMATICS AND COMPUTING↗
A road map to cosmological parameter analysis with third-order shear statistics: III. Efficient estimation of third-order shear correlation functions and an application to the KiDS-1000 data
Context. Third-order lensing statistics contain a wealth of cosmological information that is not captured by second-order statistics. However, the computational effort it takes to estimate such statistics in forthcoming stage IV surveys is prohibitively expensive. Aims. We derive and validate an efficient estimation procedure for the three-point correlation function (3PCF) of polar fields such as weak lensing shear. We then use our approach to measure the shear 3PCF and the third-order aperture mass statistics on the KiDS-1000 survey. Methods We constructed an efficient estimator for third-order shear statistics that builds on the multipole decomposition of the 3PCF. We then validated our estimator on mock ellipticity catalogs obtained from N -body simulations. Finally, we applied our estimator to the KiDS-1000 data and presented a measurement of the third-order aperture statistics in a tomographic setup. Results. Our estimator provides a speedup of a factor of ∼100–1000 compared to the state-of-the-art estimation procedures. It is also able to provide accurate measurements for squeezed and folded triangle configurations without additional computational effort. We report a significant detection of tomographic third-order aperture mass statistics in the KiDS-1000 data (S/N = 6.69). Conclusions. Our estimator will make it computationally feasible to measure third-order shear statistics in forthcoming stage IV surveys. Furthermore, it can be used to construct empirical covariance matrices for such statistics.
Astronomy & Astrophysics↗
A comparison of neural network architectures for data-driven reduced-order modeling
The popularity of deep convolutional autoencoders (CAEs) has engendered new and effective reduced-order models (ROMs) for the simulation of large-scale dynamical systems. Despite this, it is still unknown whether deep CAEs provide superior performance over established linear techniques or other network-based methods in all modeling scenarios. To elucidate this, the effect of autoencoder architecture on its associated ROM is studied through the comparison of deep CAEs against two alternatives: a simple fully connected autoencoder, and a novel graph convolutional autoencoder. Through benchmark experiments, it is shown that the superior autoencoder architecture for a given ROM application is highly dependent on the size of the latent space and the structure of the snapshot data, with the proposed architecture demonstrating benefits on data with irregular connectivity when the latent space is sufficiently large.
42 ENGINEERING↗
Data-based reduced-order modeling of nonlinear two-time-scale processes
Not Available
Abdullah, Fahim (ORCID:000000025094788X)↗