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At least 487 records · Page 27

A compute-bound formulation of Galerkin model reduction for linear time-invariant dynamical systems

This work aims to advance computational methods for projection-based reduced-order models (ROMs) of linear time-invariant (LTI) dynamical systems. For such systems, current practice relies on ROM formulations expressing the state as a rank-1 tensor (i.e., a vector), leading to computational kernels that are memory bandwidth bound and, therefore, ill-suited for scalable performance on modern architectures. This weakness can be particularly limiting when tackling many-query studies, where one needs to run a large number of simulations. This work introduces a reformulation, called rank-2 Galerkin, of the Galerkin ROM for LTI dynamical systems which converts the nature of the ROM problem from memory bandwidth to compute bound. We present the details of the formulation and its implementation, and demonstrate its utility through numerical experiments using, as a test case, the simulation of elastic seismic shear waves in an axisymmetric domain. We quantify and analyze performance and scaling results for varying numbers of threads and problem sizes. In conclusion, we present an end-to-end demonstration of using the rank-2 Galerkin ROM for a Monte Carlo sampling study. We show that the rank-2 Galerkin ROM is one order of magnitude more efficient than the rank-1 Galerkin ROM (the current practice) and about 970 times more efficient than the full-order model, while maintaining accuracy in both the mean and statistics of the field.

97 MATHEMATICS AND COMPUTING↗

GP Cosmology Surrogate v1.0

GP Cosmology Surrogate is a Python library for building and training a generalized multi-output Gaussian process (GP) framework of @takhtaganov2021cosmic. In this approach, the surrogate is constructed sequentially, guided by a Bayesian optimization acquisition function that targets reduction of emulation error in the regions most consistent with the observational data. This adaptive design concentrates computational resources where they have the greatest impact on inference accuracy. The library supports efficient training for separable GP kernels, which allows the use of Kronecker algebra to handle high-dimensional input spaces and large numbers of correlated outputs. This makes it well suited for applications such as modeling cosmological power spectra, large-scale physical simulations, and multi-output hyperparameter tuning. By combining scalable multi-output GP modeling with data-driven adaptive sampling, GPsurrogate enables parameter inference and optimization with substantially fewer simulations than conventional space-filling designs.

Lukic, Zarija [Lawrence Berkeley National Laborato↗

Entropy-Bayesian Inversion of Time-Lapse Tomographic GPR data for Monitoring Dielectric Permittivity and Soil Moisture Variations

In this study, we evaluate the possibility of monitoring soil moisture variation using tomographic ground penetrating radar travel time data through Bayesian inversion, which is integrated with entropy memory function and pilot point concepts, as well as efficient sampling approaches. It is critical to accurately estimate soil moisture content and variations in vadose zone studies. Many studies have illustrated the promise and value of GPR tomographic data for estimating soil moisture and associated changes, however, challenges still exist in the inversion of GPR tomographic data in a manner that quantifies input and predictive uncertainty, incorporates multiple data types, handles non-uniqueness and nonlinearity, and honors time-lapse tomograms collected in a series. To address these challenges, we develop a minimum relative entropy (MRE)-Bayesian based inverse modeling framework that non-subjectively defines prior probabilities, incorporates information from multiple sources, and quantifies uncertainty. The framework enables us to estimate dielectric permittivity at pilot point locations distributed within the tomogram, as well as the spatial correlation range. In the inversion framework, MRE is first used to derive prior probability distribution functions (pdfs) of dielectric permittivity based on prior information obtained from a straight-ray GPR inversion. The probability distributions are then sampled using a Quasi-Monte Carlo (QMC) approach, and the sample sets provide inputs to a sequential Gaussian simulation (SGSim) algorithm that constructs a highly resolved permittivity/velocity field for evaluation with a curved-ray GPR forward model. The likelihood functions are computed as a function of misfits, and posterior pdfs are constructed using a Gaussian kernel. Inversion of subsequent time-lapse datasets combines the Bayesian estimates from the previous inversion (as a memory function) with new data. The memory function and pilot point design takes advantage of the spatial-temporal correlation of the state variables. We first apply the inversion framework to a static synthetic example and then to a time-lapse GPR tomographic dataset collected during a dynamic experiment conducted at the Hanford Site in Richland, WA. We demonstrate that the MRE-Bayesian inversion enables us to merge various data types, quantify uncertainty, evaluate nonlinear models, and produce more detailed and better resolved estimates than straight-ray based inversion; therefore, it has the potential to improve estimates of inter-wellbore dielectric permittivity and soil moisture content and to monitor their temporal dynamics more accurately.

58 GEOSCIENCES↗

Entropy-Bayesian Inversion of Time-Lapse Tomographic GPR data for Monitoring Dielectric Permittivity and Soil Moisture Variations

In this study, we evaluate the possibility of monitoring soil moisture variation using tomographic ground penetrating radar travel time data through Bayesian inversion, which is integrated with entropy memory function and pilot point concepts, as well as efficient sampling approaches. It is critical to accurately estimate soil moisture content and variations in vadose zone studies. Many studies have illustrated the promise and value of GPR tomographic data for estimating soil moisture and associated changes, however, challenges still exist in the inversion of GPR tomographic data in a manner that quantifies input and predictive uncertainty, incorporates multiple data types, handles non-uniqueness and nonlinearity, and honors time-lapse tomograms collected in a series. To address these challenges, we develop a minimum relative entropy (MRE)-Bayesian based inverse modeling framework that non-subjectively defines prior probabilities, incorporates information from multiple sources, and quantifies uncertainty. The framework enables us to estimate dielectric permittivity at pilot point locations distributed within the tomogram, as well as the spatial correlation range. In the inversion framework, MRE is first used to derive prior probability density functions (pdfs) of dielectric permittivity based on prior information obtained from a straight-ray GPR inversion. The probability distributions are then sampled using a Quasi-Monte Carlo (QMC) approach, and the sample sets provide inputs to a sequential Gaussian simulation (SGSIM) algorithm that constructs a highly resolved permittivity/velocity field for evaluation with a curved-ray GPR forward model. The likelihood functions are computed as a function of misfits, and posterior pdfs are constructed using a Gaussian kernel. Inversion of subsequent time-lapse datasets combines the Bayesian estimates from the previous inversion (as a memory function) with new data. The memory function and pilot point design takes advantage of the spatial-temporal correlation of the state variables. We first apply the inversion framework to a static synthetic example and then to a time-lapse GPR tomographic dataset collected during a dynamic experiment conducted at the Hanford Site in Richland, WA. We demonstrate that the MRE-Bayesian inversion enables us to merge various data types, quantify uncertainty, evaluate nonlinear models, and produce more detailed and better resolved estimates than straight-ray based inversion; therefore, it has the potential to improve estimates of inter-wellbore dielectric permittivity and soil moisture content and to monitor their temporal dynamics more accurately.

Bayesian Inversion↗

Pattern Recognition for a Flight Dynamics Monte Carlo Simulation

The design, analysis, and verification and validation of a spacecraft relies heavily on Monte Carlo simulations. Modern computational techniques are able to generate large amounts of Monte Carlo data but flight dynamics engineers lack the time and resources to analyze it all. The growing amounts of data combined with the diminished available time of engineers motivates the need to automate the analysis process. Pattern recognition algorithms are an innovative way of analyzing flight dynamics data efficiently. They can search large data sets for specific patterns and highlight critical variables so analysts can focus their analysis efforts. This work combines a few tractable pattern recognition algorithms with basic flight dynamics concepts to build a practical analysis tool for Monte Carlo simulations. Current results show that this tool can quickly and automatically identify individual design parameters, and most importantly, specific combinations of parameters that should be avoided in order to prevent specific system failures. The current version uses a kernel density estimation algorithm and a sequential feature selection algorithm combined with a k-nearest neighbor classifier to find and rank important design parameters. This provides an increased level of confidence in the analysis and saves a significant amount of time.

Restrepo, Carolina↗

From PeleC to PeleACC, to PeleC++

PeleC is an Exascale Computing Project application for simulating compressible combustion in complex geometries. It has been built on top of the popular AMReX library. In the beginning of the Exascale Computing Project, PeleC was focused on KNL. It uses a mixture of C++, C, and kernels written in Fortran to obtain performance by focusing on vectorization. Recently we have taken two approaches in deciding PeleC's future for obtaining performance on exascale GPU machines. In the first programming model, we decorated the Fortran kernels with OpenACC directives. This expedited our ability to run at large scales on Summit's GPUs, where we achieved a significant speedup over the CPUs on Summit. The second programming model involved rewriting the Fortran kernels in C++ and using AMReX's Kokkos-like lambda abstractions for running on the GPU. This resulted in similar speedups on Summit's GPUs over merely utilizing the CPUs. Both approaches involved AMReX's management of memory transfers between the device and host. In this work, we compare and contrast the benefits and pitfalls to both programming approaches regarding performance, performance portability, and productivity. We also discuss advantages we have found in taking the time to modernize our code and why have chosen a specific pathway to prepare our code for the future DOE exascale machines.

exascale computing↗

Image-Based Failure Assessment of Li-Ion Batteries

In energy storage materials, strong electrochemical-mechanical coupling and highly anisotropic material properties contribute to the formation and propagation of micro-cracking during charge/discharge cycling, resulting in reduced performance and service life. In this work, a digital twin is created to investigate the performance of a heterogeneous Li-ion battery cathode and simulate degradation accumulation. Pixel-based model construction is used to represent the complex material geometries from microstructural images supplied by the National Renewable Energy Laboratory (NREL). Because of the expected large deformation and crack opening, the reproducing kernel particle method (RKPM), a meshfree method with discretization at the image pixels, is used to approximate the field variables: electrostatic potential, concentration, and displacement. An interface modified reproducing kernel (IM-RK) is constructed by scaling a smooth kernel function with an interface-distance function to achieve strategic discontinuity types (i.e. weak discontinuities for strain discontinuities and strong discontinuities for cracks) and alleviate Gibbs oscillations near these transition zones. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. IM-RK is additionally used to inform how crack evolution in turn affects the coupled electro-chemo-mechanical behavior of the Li-ion battery cathode.

image-based modeling↗

Model predictive control of mixing controlled compression ignition operation for low reactivity fuels

Using gasoline or other low reactivity fuels with a pilot injection or port fuel injection in a compression ignition engine has shown great potential in reducing NOx emissions while keeping high thermal efficiency compared to diesel. However, excessive combustion noise is caused by a high maximum pressure rise rate in the cylinder due to the higher fractions of premixed charge of the low-reactivity fuel. This noise can result in structural damage to engine components and as such, combustion noise limits the range of the operating parameters and makes the control of such engines challenging. In this study, a simulation environment was built up in MATLAB/Simulink leveraging a physics-based zero-dimension combustion model to capture the in-cylinder pressure time traces as well as metrics relevant to thermal efficiency and combustion noise. Here, in order to also facilitate the control of emissions, machine learning models were investigated to capture NOx emissions. A kernel-based extreme learning machine (K-ELM) performed best and had a coefficient of correlation (R-squared) of 0.998. The combustion and NOx emission models are valid for not only conventional gasoline fuel but also oxygenated alternative fuel blends at three different pilot injection strategies. In order to track key combustion metrics while keeping noise and emissions within constraints, a model predictive control (MPC) was applied for a compression ignition engine operating with a range of potential fuels and fuel injection strategies. The MPC is validated under different scenarios, including a load step change, fuel type change, and injection strategy change, with proportional–integral (PI) control as the baseline. The simulation results show that MPC reduces about 26% of ringing intensity in the transient process and 17% at the steady state for E30. Generally, MPC can optimize the overall performance through modifying the main injection timing, pilot fuel mass, and exhaust gas recirculation (EGR) fraction.

42 ENGINEERING↗

Quantum Dynamics at Scale: Ultrafast Control of Emergent Functional Materials

Confluence of extreme-scale quantum dynamics simulations (i.e. quantum@scale) and cutting-edge x-ray free-electron laser experiments are revolutionizing materials science. An archetypal example is the exciting concept of using picosecond light pulses to control emergent material properties on demand in atomically-thin layered materials. This paper describes efforts to scale our quantum molecular dynamics engine toward the United States' first exaflop/s computer, under an Aurora Early Science Program project named "Metascalable layered material genome". Key algorithmic and computing techniques incorporated are: (1) globally-scalable and locally-fast solvers within a linear-scaling divide-conquer-recombine algorithmic framework; (2) algebraic `BLASification' of computational kernels; and (3) data alignment and loop restructuring, along with register and cache blocking, for enhanced vectorization and efficient memory access. The resulting weak-scaling parallel efficiency was 0.93 on 131,072 Intel Xeon Phi cores for a 56.6 million atom (or 169 million valence-electron) system, whereas the various code transformations achieved 5-fold speedup. The optimized simulation engine allowed us for the first time to establish a significant effect of substrate on the dynamics of layered material upon electronic excitation.

Algebraic BLASification↗

MLMOD: Machine Learning Methods for Data-Driven Modeling in LAMMPS

MLMOD is a software package for incorporating machine learning approaches and models into simulations of microscale mechanics and molecular dynamics in LAMMPS. Recent machine learning approaches provide promising data-driven approaches for learning representations for system behaviors from experimental data and high fidelity simulations. The package facilitates learning and using data-driven models for (i) dynamics of the system at larger spatial-temporal scales (ii) interactions between system components, (iii) features yielding coarser degrees of freedom, and (iv) features for new quantities of interest characterizing system behaviors. MLMOD provides hooks in LAMMPS for (i) modeling dynamics and time-step integration, (ii) modeling interactions, and (iii) computing quantities of interest characterizing system states. The package allows for use of machine learning methods with general model classes including Neural Networks, Gaussian Process Regression, Kernel Models, and other approaches. Here we discuss our prototype C++/Python package, aims, and example usage. For related papers, examples, updates, and additional information see https://github.com/atzberg/mlmod and http://atzberger.org/.

97 MATHEMATICS AND COMPUTING↗

Acceleration of the Parameterization of Unified Microphysics Across Scales (PUMAS) on the Graphics Processing Unit (GPU) With Directive-Based Methods

Cloud microphysics is one of the most time-consuming components in a climate model. In this study, we port the cloud microphysics parameterization in the Community Atmosphere Model (CAM), known as Parameterization of Unified Microphysics Across Scales (PUMAS), from CPU to GPU to seek a computational speedup. The directive-based methods (OpenACC and OpenMP target offload) are determined as the best fit specifically for our development practices, which enable a single version of source code to run either on the CPU or GPU, and yield a better portability and maintainability. Their performance is first examined in a PUMAS stand-alone kernel and the directive-based methods can outperform a CPU node as long as there is enough computational burden on the GPU. A consistent behavior is observed when we run PUMAS on the GPU in a practical CAM simulation. A 3.6× speedup of the PUMAS execution time, including data movement between CPU and GPU, is achieved at a coarse horizontal resolution (8 NVIDIA V100 GPUs against 36 Intel Skylake CPU cores). This speedup further increases up to 5.4× at a high resolution (24 NVIDIA V100 GPUs against 108 Intel Skylake CPU cores), which highlights the fact that GPU favors larger problem size. This study demonstrates that using GPU in a CAM simulation can save noticeable computational costs even with a small portion of code being GPU-enabled. Therefore, we are encouraged to port more parameterizations to GPU to take advantage of its computational benefit.

54 ENVIRONMENTAL SCIENCES↗

Data-driven learning of nonlocal models: from high-fidelity simulations to constitutive laws

We show that machine learning can improve the accuracy of simulations of stress waves in one-dimensional composite materials. We propose a data-driven technique to learn nonlocal constitutive laws for stress wave propagation models. The method is an optimization-based technique in which the nonlocal kernel function is approximated via Bernstein polynomials. The kernel, including both its functional form and parameters, is derived so that when used in a nonlocal solver, it generates solutions that closely match high-fidelity data. The optimal kernel therefore acts as a homogenized nonlocal continuum model that accurately reproduces wave motion in a smaller-scale, more detailed model that can include multiple materials. We apply this technique to wave propagation within a heterogeneous bar with a periodic microstructure. Several one-dimensional numerical tests illustrate the accuracy of our algorithm. The optimal kernel is demonstrated to reproduce high-fidelity data for a composite material in applications that are substantially different from the problems used as training data.

97 MATHEMATICS AND COMPUTING↗

Meter-Scale 3-D Models of the Martian Surface from Combining MOC and MOLA Data

We have extended our previous efforts to derive through controlled photoclinometry, accurate, calibrated, high-resolution topographic models of the martian surface. The process involves combining MGS MOLA topographic profiles and MGS MOC Narrow Angle images. The earlier work utilized, along with a particular MOC NA image, the MOLA topographic profile that was acquired simultaneously, in order to derive photometric and scattering properties of the surface and atmosphere so as to force the low spatial frequencies of a one-dimensional MOC photoclinometric model to match the MOLA profile. Both that work and the new results reported here depend heavily on successful efforts to: 1) refine the radiometric calibration of MOC NA; 2) register the MOC to MOLA coordinate systems and refine the pointing; and 3) provide the ability to project into a common coordinate system, simultaneously acquired MOC and MOLA with a single set of SPICE kernels utilizing the USGS ISIS cartographic image processing tools. The approach described in this paper extends the MOC-MOLA integration and cross-calibration procedures from one-dimensional profiles to full two-dimensional photoclinometry and image simulations. Included are methods to account for low-frequency albedo variations within the scene.

Soderblom, Laurence A.↗

Modeling error PDF optimization based wavelet neural network modeling of dynamic system and its application in blast furnace ironmaking

In general, the modeling errors of dynamic system model are a set of random variables. The traditional performance index of modeling such as means square error (MSE) and root means square error (RMSE) can not fully express the connotation of modeling errors with stochastic characteristics both in the dimension of time domain and space domain. Therefore, the probability density function (PDF) is introduced to completely describe the modeling errors in both time scales and space scales. Based on it, a novel wavelet neural network (WNN) modeling method is proposed by minimizing the two-dimensional (2D) PDF shaping of modeling errors. First, the modeling error PDF by the tradional WNN is estimated using data-driven kernel density estimation (KDE) technique. Then, the quadratic sum of 2D deviation between the modeling error PDF and the target PDF is utilized as performance index to optimize the WNN model parameters by gradient descent method. Since the WNN has strong nonlinear approximation and adaptive capability, and all the parameters are well optimized by the proposed method, the developed WNN model can make the modeling error PDF track the target PDF, eventually. Simulation example and application in a blast furnace ironmaking process show that the proposed method has a higher modeling precision and better generalization ability compared with the conventional WNN modeling based on MSE criteria. Furthermore, the proposed method has more desirable estimation for modeling error PDF that approximates to a Gaussian distribution whose shape is high and narrow.

Modelling↗

A high-order computational framework for particle-resolved simulations of disperse multiphase flows

This work presents a high-order numerical approach for particle-resolved simulations of disperse multiphase flows, where the Navier-Stokes equations for fluid flow are solved using a high-order spectral element method in the Eulerian framework, and the particle phase is directly simulated with a discrete element method. The coupling between particles and fluids is explicitly handled using an adapted direct-forcing immersed boundary method. Unlike the conventional schemes, a high-order barycentric Lagrange interpolation method and a Gaussian projection kernel are used to ensure accurate momentum exchange between local boundary points and surrounding fluid nodes in the framework of high-order fluid solver. Benchmark tests of increasing complexity are conducted to demonstrate the accuracy and efficiency of our method. Here, it is found that our approach exhibits an excellent convergence performance, as the fluid element/grid is refined and the number of boundary points increases. Compared to conventional low-order methods, the proposed high-order framework enables the use of substantially larger fluid elements while maintaining high accuracy in modeling fluid-particle interactions, owing to the enhanced resolution of high-order basis functions. Moreover, since the primary unknowns are stored at element or grid nodes, the high-order approach offers improved efficiency in both CPU memory usage and total computational cost.

42 ENGINEERING↗

QuadConv: Quadrature-based convolutions with applications to non-uniform PDE data compression

We present a new convolution layer for deep learning architectures which we call QuadConv — an approximation to continuous convolution via quadrature. Our operator is developed explicitly for use on non-uniform, mesh-based data, and accomplishes this by learning a continuous kernel that can be sampled at arbitrary locations. Moreover, the construction of our operator admits an efficient implementation which we detail and construct. As an experimental validation of our operator, we consider the task of compressing partial differential equation (PDE) simulation data from fixed meshes. Here, we show that QuadConv can match the performance of standard discrete convolutions on uniform grid data by comparing a QuadConv autoencoder (QCAE) to a standard convolutional autoencoder (CAE). Further, we show that the QCAE can maintain this accuracy even on non-uniform data. In both cases, QuadConv also outperforms alternative unstructured convolution methods such as graph convolution.

Compression↗

Enhancing the Survivability of Power Systems With Grid-Edge DERs Against DoS Attacks

Power system survivability, defined as the ability of a system to maintain steady-state functionality under varying operational conditions, reflects its resilience against disturbances. While existing research primarily focuses on physical-layer disturbances, the increasing prevalence of grid-edge DERs, which are primarily used for integrating renewable energy, has significantly expanded the cyber attack surface. As a result, operational disruptions caused by cyber threats are posing significant challenges to system survivability and cannot be overlooked. To fill this gap, we redefine system survivability to incorporate the cyber layer’s status and propose a Distributionally Robust Optimization (DRO) approach to enhance power system survivability against potential cyber-physical threats. In this paper, we first analyze the operational guidelines of systems with a high penetration of DERs under various cyber network conditions and redefine survivability in this context. Next, we focus on the most common cyber threat, Denial-of-Service (DoS) attacks, and develop a corresponding attack model. This model allows for the creation of a kernel-based ambiguity set that captures attack uncertainties using historical data. Finally, we transform the proposed DRO model as a tractable optimization problem, with its solution providing an optimal cyber redundancy plan to enhance system survivability in DoS attack scenarios. Simulation results on the IEEE 13-node and 123-node test feeders demonstrate the effectiveness of our proposed model in improving system survivability. This model can also be expanded to include other types of common attacks and serve as a comprehensive planning tool to improve overall cyber physical survival of the system.

cybersecurity↗

Mini-apps for high performance data analysis

Scaling-up scientific data analysis and machine learning algorithms for data-driven discovery is a grand challenge that we face today. Despite the growing need for analysis from science domains that are generating `Big Data' from instruments and simulations, building high-performance analytical workflows of data-intensive algorithms have been daunting because: (i) the `Big Data' hardware and software architecture landscape is constantly evolving, (ii) newer architectures impose new programming models, and (iii) data-parallel kernels of analysis algorithms and their performance facets on different architectures are poorly understood. To address these problems, we have: (i) identified scalable data-parallel kernels of popular data analysis algorithms, (ii) implemented `Mini-Apps' of those kernels using different programming models (e.g. Map Reduce, MPI, etc.), (iii) benchmarked and validated the performance of the kernels in diverse architectures. In this paper, we discuss two of those Mini-Apps and show the execution of principal component analysis built as a workflow of the Mini-Apps. We show that Mini-Apps enable scientists to (i) write domain-specific data analysis code that scales on most HPC hardware and (ii) and offers the ability (most times with over a 10x speed-up) to analyze data sizes 100 times the size of what off-the-shelf desktop/workstations of today can handle.

Sukumar, Sreenivas R.↗