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A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling
Numerical solvers of partial differential equations (PDEs) have been widely employed for simulating physical systems. However, the computational cost remains a major bottleneck in various scientific and engineering applications, which has motivated the development of reduced-order models (ROMs). Recently, machine-learning-based ROMs have gained significant popularity and are promising for addressing some limitations of traditional ROM methods, especially for advection dominated systems. In this chapter, we focus on a particular framework known as Latent Space Dynamics Identification (LaSDI), which transforms the high-fidelity data, governed by a PDE, to simpler and low-dimensional latent-space data, governed by ordinary differential equations (ODEs). These ODEs can be learned and subsequently interpolated to make ROM predictions. Each building block of LaSDI can be easily modulated depending on the application, which makes the LaSDI framework highly flexible. In particular, we present strategies to enforce the laws of thermodynamics into LaSDI models (tLaSDI), enhance robustness in the presence of noise through the weak form (WLaSDI), select high-fidelity training data efficiently through active learning (gLaSDI, GPLaSDI), and quantify the ROM prediction uncertainty through Gaussian processes (GPLaSDI). We demonstrate the performance of different LaSDI approaches on Burgers equation, a non-linear heat conduction problem, and a plasma physics problem, showing that LaSDI algorithms can achieve relative errors of less than a few percent and up to thousands of times speed-ups.
Combustion of petroleum-based transportation fuels and their blends with biofuels: a new approach for developing surrogates and understanding the effects of blending
Accurate and versatile reaction mechanisms are necessary to simulate combustion of transportation fuels blended with biofuels for improving fuel efficiency, reducing fuel consumption and mitigating the formation and emissions of combustion products harmful to the atmosphere. This project involved a combined effort of simulation and experimentation of liquid fuel burning using a combustion configuration amenable to numerical modeling with a level of detail not previously achieved for blends of biofuels with gasoline certification and surrogate fuels. The configuration of an isolated droplet burning under conditions where gas transport arises solely from fuel evaporation was selected as the platform for experiments and numerical modeling. The spherical symmetry and one-dimensional gas transport that results enabled simulating the droplet burning process with an precedented level of detail. Processes associated with unsteady gas and liquid transport, formation of particulate and gaseous products, radiation, multicomponent phase equilibrium at the droplet surface and moving boundary effects from droplet evaporation, were incorporated in a single numerical framework. The numerical model was based on the open source code OPENSmoke++ (OS) adapted to incorporate the effects noted above. In addition to simulation, an experimental design was developed for the isolated droplet configuration to acquire the data needed for validating the numerical model. Several broad accomplishments of the project were the following: demonstrating generally excellent agreement between measured and simulated combustion parameters for the fuel blends examined that included mixtures of heptane and isobutanol as a model system, and surrogates comprised of up to seven miscible components mixed with ethanol or isobutanol as representative biofuel additives; using a new approach to validate reaction mechanisms of biofuel blends which incorporated fuel evaporation into the process along with developing an experimental design for acquiring data to compare with simulations; and showing that a wealth of information could be obtained on the combustion physics of biofuels from experiments requiring volumes on the order of only nanoliters at a time thus opening the way to evaluating biofuels synthesized by new processes early in development.
Computational framework for modeling of physical process
Techniques, systems, and devices are described for providing a computational frame for estimating high-dimensional stochastic behaviors. In one exemplary aspect, a method for performing numerical estimation includes receiving a set of measurements of a stochastic behavior. The set of correlated measurements follows a non-standard probability distribution and is non-linearly correlated. Also, a non-linear relationship exists between a set of system variables that describes the stochastic behavior and a corresponding set of measurements. The method includes determining, based on the set of measurements, a numerical model of the stochastic behavior. The numerical model comprises a feature space comprising non-correlated features corresponding to the stochastic behavior. The non-correlated features have a dimensionality of M and the set of measurements has a dimensionality of N, M being smaller than N. The method includes generating a set of approximated system variables corresponding to the set of measurements based on the numerical model.
Computational framework for modeling of physical process
Techniques, systems, and devices are described for providing a computational frame for estimating high-dimensional stochastic behaviors. In one exemplary aspect, a method for performing numerical estimation includes receiving a set of measurements of a stochastic behavior. The set of correlated measurements follows a non-standard probability distribution and is non-linearly correlated. Also, a non-linear relationship exists between a set of system variables that describes the stochastic behavior and a corresponding set of measurements. The method includes determining, based on the set of measurements, a numerical model of the stochastic behavior. The numerical model comprises a feature space comprising non-correlated features corresponding to the stochastic behavior. The non-correlated features have a dimensionality of M and the set of measurements has a dimensionality of N, M being smaller than N. The method includes generating a set of approximated system variables corresponding to the set of measurements based on the numerical model.
Independent Review of Groundwater Remediation Strategy for Hexavalent Chromium and RDX Groundwater Plumes at Los Alamos National Laboratory (Rev. 1)
Site operations at the Los Alamos National Laboratory (LANL) resulted in the release of oxidized chromium, Cr(VI), into Sandia Canyon from cooling tower effluent from 1956 until 1972. The chromium traveled with the surface water approximately 3 miles downstream before migrating below ground surface. Chromium concentrations exceed 50 μg/L in the upper portion of the aquifer. Another LANL groundwater plume of concern is associated with RDX (Royal Demolition Explosives, 1,3,5-trinitro-1,3,5-triazine). Between 1951 and 1996, RDX was released to the mesa-top facilities' process water outfall, adjacent and underlying soils, and alluvial sediments, along with surface water in Cañon de Valle. Between 2000 and 2010, two remedial actions were deployed, removing much of the near-surface RDX, however, recharge due to precipitation has transported RDX into the perched-intermediate zone and into the regional aquifer. The report documents an independent technical review by scientists from the Department of Energy (DOE) Network of National Laboratories for Environmental Management and Stewardship (NNLEMS) to provide recommendations for potential near term actions to address and optimize remediation for both the Cr(VI) and RDX plumes. The proposed near-term remedial actions include design of pump and treat systems for Cr(VI) and monitoring and study for natural attenuation for RDX. The review assesses existing data, conceptual and numerical modeling, and it recommends a technical integration process to support identifying and implementing strategic, effective and efficient remedies. The DOE Environmental Management Los Alamos Field Office (EM-LA) and their cleanup contractor Newport News Nuclear-BWTX, LLC Los Alamos (N3B) provided the information required for the review. Interviews were also conducted with regulators to obtain the full spectrum of technical, regulatory and scientific perspectives. The independent review team was impressed by the capabilities, experiences, innovativeness, and insightfulness of the technical representatives from both the regulator, the New Mexico Environment Department (NMED) and N3B. Incorporation of vadose zone flow pathways in the conceptual site model (CSM) and configuring the numerical modeling for the site was generally state-of-the-practice (or better). This could be considered state-of-the-art by addressing uncertainties related to spatial extent of hydraulic windows. The reviews from the regulators were thorough and often provided useful concepts for consideration and future/study resolutions. The overarching consensus recommendation of independent review team is that the LANL groundwater plumes should be addressed in context of the emerging "management of complex sites" paradigm.
Internal Passage Heat Transfer Prediction Using Multiblock Grids and a Kappa-Omega Turbulence Model
Numerical simulations of the three-dimensional flow and heat transfer in a rectangular duct with a 180 C bend were performed. Results are presented for Reynolds numbers of 17,000 and 37,000 and for aspect ratios of 0.5 and I.O. A kappa-omega turbulence model with no reference to distance to a wall is used. Direct comparison between single block and multiblock grid calculations are made. Heat transfer and velocity distributions are compared to available literature with good agreement. The multi-block grid system is seen to produce more accurate results compared to a single-block grid with the same number of cells.
Time-dependent models of radiatively driven stellar winds. I - Nonlinear evolution of instabilities for a pure absorption model
Numerical radiation-hydrodynamics simulations of the nonlinear evolution of instabilities in radiatively driven stellar winds have been performed. The results show a strong tendency for the unstable flow to form rather sharp rarefactions in which the highest speed material has very low density. The qualitative features of the model agree well with the reqirements of displaced narrow absorption components in UV lines.
Transition mixing study empirical model report
The empirical model developed in the NASA Dilution Jet Mixing Program has been extended to include the curvature effects of transition liners. This extension is based on the results of a 3-D numerical model generated under this contract. The empirical model results agree well with the numerical model results for all tests cases evaluated. The empirical model shows faster mixing rates compared to the numerical model. Both models show drift of jets toward the inner wall of a turning duct. The structure of the jets from the inner wall does not exhibit the familiar kidney-shaped structures observed for the outer wall jets or for jets injected in rectangular ducts.
Application of Raytracing Through the High Resolution Numerical Weather Model HIRLAM for the Analysis of European VLBI
An important limitation for the precision in the results obtained by space geodetic techniques like VLBI and GPS are tropospheric delays caused by the neutral atmosphere, see e.g. [1]. In recent years numerical weather models (NWM) have been applied to improve mapping functions which are used for tropospheric delay modeling in VLBI and GPS data analyses. In this manuscript we use raytracing to calculate slant delays and apply these to the analysis of Europe VLBI data. The raytracing is performed through the limited area numerical weather prediction (NWP) model HIRLAM. The advantages of this model are high spatial (0.2 deg. x 0.2 deg.) and high temporal resolution (in prediction mode three hours).
Line emission from H II blister models
Numerical techniques to calculate the thermal and geometric properties of line emission from H II 'blister' regions are presented. It is assumed that the density distributions of the H II regions are a function of two dimensions, with rotational symmetry specifying the shape in three-dimensions. The thermal and ionization equilibrium equations of the problem are solved by spherical modeling, and a spherical sector approximation is used to simplify the three-dimensional treatment of diffuse ionizing radiation. The global properties of H II 'blister' regions near the edges of a molecular cloud are simulated by means of the geometry/density distribution, and the results are compared with observational data. It is shown that there is a monotonic increase of peak surface brightness from the i = 0 deg (pole-on) observational position to the i = 90 deg (edge-on) position. The enhancement of the line peak intensity from the edge-on to the pole-on positions is found to depend on the density, stratification, ionization, and electron temperature weighting. It is found that as i increases, the position of peak line brightness of the lower excitation species is displaced to the high-density side of the high excitation species.
Interaction of Delaminations and Matrix Cracks in a CFRP Plate, Part II: Simulation Using an Enriched Shell Finite Element Model
Numerical simulations are presented of a recently developed test which creates multiple delaminations in a CFRP laminate specimen that grow and interact via transverse matrix cracks. A novel shell element enriched with the Floating Node Method, and a damage algorithm based on the Virtual Crack Closure Technique, were used to successfully simulate the tests. Additionally, a 3D high mesh fidelity model based on cohesive zones and continuum damage mechanics was used to simulate the tests and act as a representative of other similar state-of-the-art high mesh fidelity modeling techniques to compare to the enriched shell element. The enriched shell and high mesh fidelity models had similar levels of accuracy and generally matched the experimental data. With runtimes of 36 minutes for the shell model and 55 hours for the high mesh fidelity model, the shell model is 92 times faster than the high- fidelity simulation.
Calibrating uncertain parameters in melt pool simulations of additive manufacturing
Melt pool scale numerical modeling of additive manufacturing (AM) processes can provide predictive capabilities and theoretical insight into the process-property-structure-performance relationships for AM parts. Despite capabilities of numerical models to solve complex multi-physics problems, it is often important to consider a tradeoff between detailed physics and computational cost. Therefore, sources of uncertainty in both experimental conditions and the parameters needed for modeling require models to be validated against empirical evidence. Here, a method is proposed to calibrate uncertain parameters used in continuum-scale melt pool models for powder bed fusion (PBF) AM. Both a simplified heat transfer model and a heat transfer and fluid flow model were investigated. A surrogate model and Markov chain-based optimization algorithm calibrated melt pool geometry for models within experimental variation of the target melt pool width and depth from the NIST AM-Bench 2018-02 dataset. The melt pool temperature distributions, solidification parameters, and simulated multi-layer solidification microstructures were compared between the two models. Similar results from both models indicate that calibrated, lower fidelity numerical models may be used in place of higher fidelity models to generate melt pool solidification data. Finally, these calibrated models therefore enable lower computational cost melt pool simulations without a noticeable decrease in simulation accuracy for grain-scale microstructure simulations.
Structure of the dayside reconnection layer in resistive MHD and hybrid models
Numerical simulations were performed to investigate the structure of the reconnection layer at the dayside magnetopause. Two typical cases are examined in detail; both are asymmetric in magnetic field and plasma density. In case 1, the guide fields in the magnetosheath and in the magnetosphere are set at zero and thus the tangential magnetic fields on the two sides of the initial current sheet are exactly antiparallel. In case 2, the angle between the tangential magnetic fields on the two sides of the initial current sheet is 145 deg. The results obtained from a resistive MHD model and from a hybrid model are found to be different. In the MHD simulation of case 1, a 2-4 intermediate shock is found to bound the reconnection layer on the magnetosheath side, while an Alfven wave pulse bounds the reconnection layer on the magnetospheric side. In case 2, it is found that a time-dependent intermediate shock (TDIS) bounds the reconnection layer on the magnetosheath side, with a slow expansion wave propagating behind. With the MHD simulations, in the general case in which the tangential magnetic fields on the two sides of the initial current sheet are not exactly antiparallel, a rotational discontinuity across which the tangential magnetic field rotates, a large angle is found to bound the reconnection layer on the magnetosheath side.
Enhancement of EM Pump Performance through Modeling and Testing
Liquid sodium has seen development as a nuclear reactor coolant in the United States for over 50 years. While sodium has many desirable characteristics as a heat transfer fluid, its reactivity poses numerous engineering challenges for even the most basic plant components like pumps. Despite the challenges, mechanical pumps have seen success in sodium service albeit at the expense of simplicity and flexibility. In fact, significant failures of these pumps have been recorded which can be attributed to their complexity. Notwithstanding the complexity, mechanical pumps are still widely proposed for the main circuit pump of sodium cooled reactors. However, an alternative to mechanical pumps are Electromagnetic Induction Pumps (EMIPs) which use the principle of the Lorentz Force. EMIPs avoid mechanically moving parts in contact with sodium which simplifies the design by avoiding mechanical wear and seals. Therefore, these pumps are generally safer and more reliable than their mechanical counterparts. That being said, EMIPs suffer from relatively low efficiencies that range from 5% to 45%. Some of the inefficiencies are inherent to the EMIPs pumps; namely, inefficiencies arise in the form of resistive heating losses in the fluid itself. However, other inefficiencies arise from Edge Effects which include Finite Length and Finite Width effects. Due to the significant safety advantages EMIPs have compared to mechanical pumps, there is a strong motivation to integrate these technologies into the design of Generation IV liquid-metal-cooled nuclear power plants. However, EMIPs have low efficiencies partly attributed to Edge Effects. Much of the literature focusing on Edge Effects is dated or simply does not exist in the public domain. More recently, numerical models of EMIPs have shown promising results. However, these models are often custom solvers or use complex software suits which limit their application. This report describes the work completed to understand Edge Effects in two EMIPs designs. These designs are the Annular Linear Induction Pump (ALIP) and Permanent Magnet Induction Pump (PMIP) also known as a Moving Magnet Pump (MMP). The methodology developed during this project aim at measuring key performance parameters (pressure-flowrate and efficiency-slip performance) using high temperature liquid-sodium. Baseline experimental measurements were then used to verify the accuracy of numerical models developed in the software suit ANSYS/FLUENT. On the experimental side, instrumentation was developed to characterize the pressure-flowrate and efficiency-slip performance of both the ALIP and PMIP in high-temperature liquid-sodium. Additionally, instrumentation was developed to measure potential output pressure pulsations and the magnetic field distributions. Moreover, a specialized ALIP was constructed to study the impacts magnetic field tapering, also known as coil grading, on the Finite Length Effect. Lastly, experimental performance curves of the PMIP were collected at 300 oC and 600 oC and compared to analytical theory which accounted for Finite Width Effects. These results showed that the Finite Width Effect and non-uniform magnetic field in a PMIP impact the performance. On the numerical side, models were developed using the software suit FLUENT/ANSYS. These methods were initially compared against a simple MHD flow in a Permanent Magnet Electromagnet Flowmeter (PMEMFM). The results were significant in that they showed agreeance between the numerical model and demonstrated that PMEMFM’s could be calibrated numerically. These modeling methods were then applied to a prototypic PMIP. Results showed that this simple model provided reasonably accurate results of the PMIP p-Q performance.
A Computational Methodology for Simulating Thermal Loss Testing of the Advanced Stirling Convertor
The U.S. Department of Energy (DOE) and Lockheed Martin Space Systems Company (LMSSC) have been developing the Advanced Stirling Radioisotope Generator (ASRG) for use as a power system for space science missions. This generator would use two highefficiency Advanced Stirling Convertors (ASCs), developed by Sunpower Inc. and NASA Glenn Research Center (GRC). The ASCs convert thermal energy from a radioisotope heat source into electricity. As part of ground testing of these ASCs, different operating conditions are used to simulate expected mission conditions. These conditions require achieving a particular operating frequency, hot end and cold end temperatures, and specified electrical power output for a given net heat input. In an effort to improve net heat input predictions, numerous tasks have been performed which provided a more accurate value for net heat input into the ASCs, including the use of multidimensional numerical models. Validation test hardware has also been used to provide a direct comparison of numerical results and validate the multi-dimensional numerical models used to predict convertor net heat input and efficiency. These validation tests were designed to simulate the temperature profile of an operating Stirling convertor and resulted in a measured net heat input of 244.4 W. The methodology was applied to the multi-dimensional numerical model which resulted in a net heat input of 240.3 W. The computational methodology resulted in a value of net heat input that was 1.7 percent less than that measured during laboratory testing. The resulting computational methodology and results are discussed.
Closed coronal structures. II - Generalized hydrostatic model
Numerical computations of stationary solar coronal loop atmospheres are used to extend earlier analytical work. Two classes of loops are examined, namely symmetric loops with a temperature maximum at the top but now having a length greater than the pressure scale height and loops which have a local temperature minimum at the top. For the first class, new scaling laws are found which relate the base pressure and loop length to the base heating, the heating deposition scale height, and the pressure scale height. It is found that loops for which the length is greater than about two to three times the pressure scale height do not have stable solutions unless they have a temperature minimum at the top. Computed models with a temperature inversion at the top are permitted in a wider range of heating deposition scale height values than are loops with a temperature maximum at the top. These results are discussed in relation to observations showing a dependence of prominence formation and stability on the state of evolution of magnetic structures, and a general scenario is suggested for the understanding of loop evolution from emergence in active regions through the large-scale structure phase to opening in coronal holes.
Unveiling the Essential Parameters Driving Mineral Reactions during CO2 Storage in Carbonate Aquifers through Proxy Models
Numerical simulation is a commonly employed technique for studying carbon dioxide (CO2) storage processes in porous media, particularly saline aquifers. It enables the representation of diverse trapping mechanisms and the assessment of CO2 retention capacity within the subsurface. The intricate physicochemical phenomena involved necessitate the incorporation of multiphase flow, accurate depiction of fluid and rock properties, and their interactions. Among these factors, geochemical reaction rates and mechanisms are pivotal for successful CO2 trapping in carbonate reactive rocks. However, research on kinetic parameters and the influence of lithology on CO2 storage remains limited. This limitation is partly due to the challenges faced in laboratory experiments, where the time scale of the reactions and the lack of in situ conditions hinder accurate measurement of mineral reaction rates. This study employs proxy models constructed using response surfaces calibrated with simulation results to address uncertainties associated with geochemical reactions. Monte Carlo simulation is utilized to explore a broader range of parameters and identify influential factors affecting CO2 mineralization. The findings indicate that an open database containing kinetic parameters can support uncertainty assessment. Additionally, the proxy models effectively represent objective functions related to CO2 injectivity and mineralization, with calcite dissolution playing a predominant role. pH, calcite concentration, and CO2 injection rate significantly impact dolomite precipitation, while quartz content remains unaffected.