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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

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.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

PDG: A Composite Method Based on the Resolution of the Identity

The Gaussian-3 (G3) composite approach for thermochemical properties is revisited in light of the enhanced computational efficiency and reduced memory costs by applying the resolution-of-the-identity (RI) approximation for two-electron repulsion integrals (ERIs) to the computationally demanding component methods in the G3 model: the energy and gradient computations via the second-order Møller–Plesset perturbation theory (MP2) and the energy computations using the coupled-cluster singles–doubles method augmented with noniterative triples corrections [CCSD(T)]. Efficient implementation of the RI-based methods is achieved by employing a hybrid distributed/shared memory model based on MPI and OpenMP. The new variant of the G3 composite approach based on the RI approximation is termed the RI-G3 scheme, or alternatively the PDG method. The accuracy of the new RI-G3/PDG scheme is compared to the “standard” G3 composite approach that employs the memory-expensive four-center ERIs in the MP2 and CCSD(T) calculations. Taking the computation of the heats of formation of the closed-shell molecules in the G3/99 test set as a test case, it is demonstrated that the RI approximation introduces negligible changes to the mean absolute errors relative to the standard G3 model (less than 0.1 kcal/mol), while the standard deviations remain unaltered. Furthermore, the efficiency and memory requirements for the RI-MP2 and RI-CCSD(T) methods are compared to the standard MP2 and CCSD(T) approaches, respectively. The hybrid MPI/OpenMP-based RI-MP2 energy plus gradient computation is found to attain a 7.5× speedup over the standard MP2 calculations. For the most demanding CCSD(T) calculations, the application of the RI approximation is found to nearly halve the memory demand, confer about a 4–5× speedup for the CCSD iterations, and reduce the computational time for the compute-intensive triples correction step by several hours.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Discrete element model for powder grain interactions under high compressive stress

A reduced order, nonlocal model is proposed for the contact force between initially spherical particles under compression. The model in effect provides the normal component of the interaction force between elements in the discrete element method (DEM). It is applicable to high relative density and large stress in powder compaction. It takes into account the mutual interaction between multiple points of contact, in contrast to the usual assumption in DEM of pair interactions. The mathematical form of the model is derived from a variational formulation that leads to the momentum balance for the forces on each grain. The model is calibrated mainly using detailed three dimensional peridynamic simulations of single grains under compressive loading by rigid plates that move radially with prescribed velocity. This calibration takes into account the large deformation and fracture of the grains. The interaction model also includes terms for the unloading behavior and adhesion. Finally, as validation, the model is applied to test data on the compaction of microcrystalline cellulose bulk powder.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Recent Advances toward Efficient Calculation of Higher Nuclear Derivatives in Quantum Chemistry

In this article, we provide an overview of state-of-the-art techniques that are being developed for efficient calculation of second and higher nuclear derivatives of quantum mechanical (QM) energy. Calculations of nuclear Hessians and anharmonic terms incur high costs and memory and scale poorly with system size. Three emerging classes of methods—machine learning (ML), automatic differentiation (AD), and matrix completion (MC)—have demonstrated promise in overcoming these challenges. We illustrate studies that employ unsupervised ML methods to reduce the need for multiple Hessian calculations in dynamics simulations and those that utilize supervised ML to construct approximate potential energy surfaces and estimate Hessians and anharmonic terms at reduced cost. By extension, if electronic structure operations could be written in a manner similar to functions underlying ML methods, rapid differentiation or AD routines can be employed to inexpensively calculate higher arbitrary-order derivatives. While ML approaches are typically black-box, we describe methods such as compressed sensing (CS) and MC, which explicitly leverage problem-specific mathematical properties of higher derivatives such as sparsity and low-rank, to complete higher derivative information using only a small, incomplete sample. The three classes of methods facilitate reliable predictions of observables ranging from infrared spectra to thermal conductivity and constitute a promising way forward in accurately capturing otherwise intractable higher-order responses of QM energy to nuclear perturbations.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2020

Evaluation of Engineered Barrier Systems (FY19 Report)

This report describes research and development (R&D) activities conducted during fiscal year 2019 (FY19) specifically related to the Engineered Barrier System (EBS) R&D Work Package in the Spent Fuel and Waste Science and Technology (SFWST) Campaign supported by the United States (U.S.) Department of Eneregy (DOE). The R&D activities focus on understanding EBS component evolution and interactions within the EBS, as well as interactions between the host media and the EBS. A primary goal is to advance the development of process models that can be implemented directly within the Genreric Disposal System Analysis (GDSA) platform or that can contribute to the safety case in some manner such as building confidence, providing further insight into the processes being modeled, establishing better constraints on barrier performance, etc.The FY19 EBS activities involved not only modeling and analysis work, but experimental work as well. The report documents the FY19 progress made in seven different research areas as follows: (1) thermal analysis for the disposal of dual purpose canisters (DPCs) in sedimentary host rock using the semianalytical method, (2) tetravalent uranium solubility and speciation, (3) modeling of high temperature, thermal-hydrologic-mechanical-chemical (THMC) coupled processes, (4) integration of coupled thermalhydrologic- chemical (THC) model with GDSA using a Reduced-Order Model, (5) studying chemical controls on montmorillonite structure and swelling pressure, (6) transmission x-ray microscope for in-situ nanotomography of bentonite and shale, and (7) in-situ electrochemical testing of uranium dioxide under anoxic conditions. The R&D team consisted of subject matter experts from Sandia National Laboratories, Lawrence Berkeley National Laboratory (LBNL), Los Alamos National Laboratory (LANL), Pacific Northwest National Laboratory (PNNL), the Bureau de Recherches Géologiques et Minières (BRGM), the University of California Berkeley, and Mississippi State University. In addition, the EBS R&D work leverages international collaborations to ensure that the DOE program is active and abreast of the latest advances in nuclear waste disposal. For example, the FY19 work on modeling coupled THMC processes at high temperatures relied on the bentonite properties from the Full-scale Engineered Barrier EXperiment (FEBEX) Field Test conducted at the Grimsel Test Site in Switzerland. Overall, significant progress has been made in FY19 towards developing the modeling tools and experimental capabilities needed to investigate the performance of EBS materials and the associated interactions in the drift and the surrounding near-field environment under a variety of conditions including high temperature regimes.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2026

Engineering-Scale Validation of Novel Algae CO 2 Capture and Bioproducts Technology

The purpose of this project was to advance and scale the algae-based technology Helios-NRG has been developing for capture of CO 2 from the flue gas of coal-burning power plants with conversion of the CO 2 to high-value products. In order to encourage the process becoming commercial and be adoptable, it is essential that the cost of CO 2 be close to net zero or slightly revenue positive. Two methods to achieve this are reducing the cost of operations through efficiencies and selling of products derived from conversion. Helios and the project team partners have accomplished the goals of furthering the technology to be more scalable and substantially lower cost with a defined pathway for commercialization.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2023

Sparsity for Gradient-Based Optimization of Wind Farm Layouts

Optimizing wind farm layouts is an important step in designing an efficient wind farm. Optimizing wind farm layouts is also a difficult task due to computation times increasing with the number of turbines present in the farm. The most computationally expensive part of gradient-based optimization is calculating the gradient. In order to reduce the expense of gradient calculation, we performed a study on the use of sparsity in wind farm layout optimization. This paper presents the findings of the sparsity study and provides a method to use sparsity in wind farm layout optimization. We tested this sparsity method by optimizing multiple farms with sparse methods and compared the results to optimizations of the same farms using traditional methods. By using the sparse method to optimize multiple farms, we found that the objective results were comparable between sparse and traditional methods and that sparse methods were 4 times faster than traditional methods on average. We expect more speedups with improved methodology and larger wind farms. By using sparse methods, it is possible to solve the wind farm layout optimization problem more efficiently, thus allowing for a more thorough study of the wind farm layout design space without excessive computational costs. Further work is required to refine the method and prepare for testing on real-world wind farm layout applications.

gradient↗
DOE OSTI2021

Probing atomic-scale symmetry breaking by rotationally invariant machine learning of multidimensional electron scattering

Abstract The 4D scanning transmission electron microscopy (STEM) method maps the structure and functionality of solids on the atomic scale, yielding information-rich data sets describing the interatomic electric and magnetic fields, structural and electronic order parameters, and other symmetry breaking distortions. A critical bottleneck is the dearth of analytical tools that can reduce complex 4D-STEM data to physically relevant descriptors. We propose an approach for the systematic exploration of 4D-STEM data using rotationally invariant variational autoencoders (rrVAE), which disentangle the general rotation of the object from other latent representations. The implementation of purely rotational rrVAE is discussed as are applications to simulated data for graphene and zincblende structures. The rrVAE analysis of experimental 4D-STEM data of defects in graphene is illustrated and compared to the classical center-of-mass analysis. This approach is universal for probing symmetry-breaking phenomena in complex systems and can be implemented for a broad range of diffraction methods.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Equation-of-motion internally contracted multireference unitary coupled-cluster theory

The accurate computation of excited states remains a challenge in electronic structure theory, especially for systems with a ground state that requires a multireference treatment. In this work, we introduce a novel equation-of-motion (EOM) extension of the internally contracted multireference unitary coupled-cluster framework (ic-MRUCC), termed EOM-ic-MRUCC. EOM-ic-MRUCC follows the transform-then-diagonalize approach, in analogy to its non-unitary counterpart. By employing a projective approach to optimize the ground state, the method retains additive separability and proper scaling with system size. We show that excitation energies are size-intensive if the EOM operator satisfies the “killer” and the projective conditions. Furthermore, we propose to represent changes in the reference state upon electron excitation via projected many-body operators that span the active orbitals and show that the EOM equations formulated in this way are invariant with respect to active orbital rotations. We test the EOM-ic-MRUCC method truncated to single and double excitations by computing the potential energy curves for several excited states of a BeH2 model system, the HF molecule, and water undergoing symmetric dissociation. Across these systems, our method delivers accurate excitation energies and potential energy curves within 5 mE h (∼0.14 eV) from full configuration interaction. Here, we find that truncating the Baker–Campbell–Hausdorff series to fourfold commutators contributes negligible errors (on the order of 10 −5 E h or less), offering a practical route to highly accurate excited-state calculations with reduced computational overhead.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Implementation of an Experimental Setup Based on the Three-Omega Method for Thermal Conductivity Measurements of Molten Salts

Molten salt reactors (MSRs) are one of the most promising next-generation nuclear reactor designs which use molten salts as the fuel and coolant. To design, model, predict, license, and operate MSRs, the behavior of the fuel and coolant must be understood as a function of temperature and irradiation, i.e., burnup. Of particular importance and complexity is the reliable and reproducible measurement of thermal conductivity of molten salts at high temperatures (> 500 °C). Thermal conductivity provides information on the rate at which heat passes through a specified material and is dependent on chemical composition. Currently, in the national laboratory complex, several methods for measuring thermal conductivity on molten salt systems are under development, however, to date, consistent data have not been produced. Typically, thermal conductivity measurements of high-temperature melts have been conducted by using the Transient Hot Wire (THW) method where thermal conductivity is determined by the change in temperature over time at a certain distance from a heating wire. Another time-dependent technique is the laser flash method, commonly used for solid samples. Laser flash requires prior measurements of density and heat capacity to calculate the thermal conductivity of the sample, introducing additional measurement errors. Steady state and time-dependent measurements such as THW and laser flash have errors from convection and ambient temperature fluctuations (heat radiation). In order to produce high fidelity thermal conductivity data, a measurement technique needs to be developed that will reduce the effect of convection at high temperatures by measuring in a very fast time window. In addition, to measure on actinide and irradiated salts the sample size should be small. Therefore, this project aims to develop a frequency-domain technique based on the three-omega (3?) method, previously proven to work on solids, nanofluids and low temperature solar salts (25 to 250 °C). If the 3?-device can be designed with materials that can withstand high temperatures (>500 °C) and can be configured to reduce errors due to convection, then it would prove to be a valuable technique for ensuring thermal conductivity on molten salt systems needed for MSR development. For this proposal, the 3? instrument will be designed, assembled, and tested on non-radioactive salts before being used on actinide bearing salts. In addition, a thermal model will be developed to determine the thermal conductivity of the sample from the measured thermal oscillation of the sensor. Because 3? is a direct method that requires a small volume of sample and works in a very fast time window, it will aid in suppressing the interference due to convection which is ideal when working with high temperature liquid samples.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Hydrodynamic and Radiographic Toolbox (HART)

With a multi-lab and university team, we propose to develop new methods for a Hydrodynamic and Radiographic Toolbox (HART) that will enable a fuller and more extensive use of experimental radiographic data towards better characterizing and reducing uncertainties in predictive modeling of weapons performance. We will achieve this by leveraging recent developments in areas of computational imaging, statistical and machine learning, and reduced order modeling of hydrodynamics. In terms of software practices, by partnering with XCP (RISTRA Project) we will conform to recent XCP standards that are inline with modern software practices and standards and ensure compatibility and ease of inter-operability with existing codes. Three new activities under this proposal include (a) the development and use of deep learning-based surrogates to accelerate reconstruction and variational inference of density fields from radiographs of hydrotests, (b) a model-data fusion strategy that couples deep learning-based density reconstructions with fast hydrodynamics simulators to better constrain the reconstruction, and (c) a method for treating asymmetries using techniques adopted from limited view tomography. All three new activities will be based on improved treatment of scatter, noise, beam spot movement, detector blur, and flat fielding in the forward model, and a use of sophisticated priors to aid in the re construction. The improvements to the forward model and improved algorithmic design of the reconstruction when complete will be contained in the iterative reconstruction code SHIVA—a code project that we have recently initiated. The many ways in which machine learning can be used in the reconstruction work will be contained in a code HERMES that has been initiated with DTRA support. For example, the significant levels of acceleration that will likely be achieved by the use of machine learning techniques will permit us (and are required) to quantify uncertainties in density retrievals. Next, the two-way coupling between density reconstruction and model-based simulation of the hydrodynamics will be contained in code EREBUS, and will permit a fuller realization of the potential of the data to constrain the hydrodynamic model and better address issues related to asymmetries in the problem. Finally, we anticipate that the better consistency with physics achieved in our reconstructions will allow them to be used by X-Division more so than today.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2026

Control Parameter Sensitivity Study for Inverter-Based-Resource Dominated Grids: A Small Signal Stability Approach and Framework

The growing adoption of renewable energy is driving the prevalence of inverter-based resources (IBRs) within power grids. Future power grids will integrate both grid-following IBRs (GFM-IBRs) and grid-forming IBRs (GFL-IBRs) alongside synchronous generators. Therefore, it is crucial to perform stability studies that account for all components and especially control interactions related to IBRs. Extensive research has performed to study the IBR-related stability, however, the sensitivity study of IBRs' control parameters on system stability has not been adequately studied yet, especially from a systematic way. Therefore, this paper conducts a small signal stability analysis for a generic grid with multiple types of resources and develops an analytical framework for assessing the sensitivity of control parameters affecting stability margins. To achieve that, the non-autonomous reduced-order non-linear dynamic model is developed for a generic power system with multiple synchronous generator-based resources (SGBRs), GFM-IBRs, and GFL-IBRs. Based on the analytic model, a systematic framework for parametric sensitivity on systems' asymptotic stability is developed. A parameter sensitivity analysis based on eigenvalue methods is proposed. The impact of the droop controllers of GFM-IBRs, PQ-dispatch and the PLL controller of GFL-IBR on the system asymptotic stability is discussed. This sensitivity study is aiming to provide deep insights on control parameters' impact on system stability, and gives direction for parameter tuning in case of instability.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Computational Tools and Workflows for Quantitative Risk Assessment and Decision Support for Geologic Carbon Storage Sites: Progress and Insights from the U.S. DOE’s National Risk Assessment Partnership

The 2005 Intergovernmental Panel on Climate Change (IPCC) Special Report on CCS raised the profile of CO2 capture and storage (CCS) as an important technology for reducing greenhouse gas (GHG) emissions. CCS is now recognized as a key component of most climate change mitigation scenarios. Since publication of that report the international research, development, and deployment (RD&D) community has advanced key technical aspects, clarified regulatory requirements, explored value chain and infrastructure solutions, and developed incentive paradigms to enable and promote large-scale deployment of CCS. These efforts have included research to better characterize geologic storage resources, to improve injection performance and storage efficiency, to assess and manage subsurface environmental risks, and to advance monitoring technologies to assure system conformance. These efforts have helped to build confidence in the viability of geologic carbon storage (GCS), but stakeholder concerns about long-term risks and liability associated with GCS remain a hurdle to broad acceptance and large-scale deployment of CCS. Since 2010, the U.S. DOE’s National Risk Assessment Partnership (NRAP) – a research collaboration between five contributing national laboratories – has worked to establish and demonstrate methods and tools to quantify and manage the subsurface environmental risks associated with GCS, amidst uncertainty. This work supports the Office of Fossil Energy and Carbon Management Carbon Transport and Storage Program’s goal of advancing safe and secure commercial-scale GCS deployment. To address the technical challenge of simulating the physical response of the GCS site to large-scale CO2 injection, NRAP has adopted an approach that relies on coupling computationally efficient reduced-order and/or data-driven proxy models of important system components (i.e., storage reservoir, sealing caprock, leakage pathways, intermediate formations, overlying groundwater aquifers, and the atmosphere) in integrated assessment framework. That integrated model of the physical system is complemented with fit-for purpose functionality to support site characterization and risk-related decisions. The recently released NRAP Phase II toolset includes the Open-Source Integrated Assessment Model (NRAP-Open-IAM) for evaluation of trends in leakage risk and potential impact, tools to support monitoring design optimization (Designs for Risk Evaluation and Management – DREAM v3.0 and Passive Seismic Monitoring Tool - PSMT), and tools for state of stress evaluation (State-of-Stress Analysis Tool - SOSAT) and forecasting induced seismicity risk. The NRAP team has also released a pair of reports describing conceptual workflows to incorporate physics-based, quantitative risk assessment into many of the design, planning, operation, and closure decisions for GCS projects. An online catalogue highlights published studies where these tools and methods are demonstrated. In this presentation, the utility of these products to assess risks and address key stakeholder questions will be highlighted through examples, and related insights about the safety and security of geologic carbon storage in qualified storage sites will be discussed. The prospect of rapid, large-scale deployment of GCS technology to aggressively reduce anthropogenic CO2 emissions requires careful consideration of interference between multiple commercial-scale storage projects within a basin. Going forward, NRAP is expanding and adapting site-scale risk quantification tools and methods to enable assessment of risks and inform management decisions for basin-scale deployment. Increasingly, this work will leverage next-generation approaches for surrogate modelling, fast prediction, and advanced visualization enabled by machine learning and artificial intelligence to promote virtual learning, scenario evaluation, and augment risk-based decision making.

quantitative risk assessment, geologic carbon stor↗
DOE OSTI2022

Adaptive experimental design for multi-fidelity surrogate modeling of multi-disciplinary systems

We present an adaptive algorithm for constructing surrogate models of multi-disciplinary systems composed of a set of coupled components. With this goal we introduce “coupling” variables with a priori unknown distributions that allow surrogates of each component to be built independently. Once built, the surrogates of the components are combined to form an integrated-surrogate that can be used to predict system-level quantities of interest at a fraction of the cost of the original model. The error in the integrated-surrogate is greedily minimized using an experimental design procedure that allocates the amount of training data, used to construct each component-surrogate, based on the contribution of those surrogates to the error of the integrated-surrogate. Here, the multi-fidelity procedure presented is a generalization of multi-index stochastic collocation that can leverage ensembles of models of varying cost and accuracy, for one or more components, to reduce the computational cost of constructing the integrated-surrogate. Extensive numerical results demonstrate that, for a fixed computational budget, our algorithm is able to produce surrogates that are orders of magnitude more accurate than methods that treat the integrated system as a black-box.

42 ENGINEERING↗
DOE OSTI2025

Hardware acceleration for HPS algorithms in two and three dimensions

We provide a flexible, open-source framework for hardware acceleration, namely massively-parallel execution on general-purpose graphics processing units (GPUs), applied to the hierarchical Poincaré–Steklov (HPS) family of algorithms for building fast direct solvers for linear elliptic partial differential equations. To take full advantage of the power of hardware acceleration, we propose two variants of HPS algorithms to improve performance on two- and three-dimensional problems. In the two-dimensional setting, we introduce a novel recomputation strategy that minimizes costly data transfers to and from the GPU; in three dimensions, we modify and extend the adaptive discretization technique of Geldermans and Gillman [1] to greatly reduce peak memory usage. We provide an open-source implementation of these methods written in JAX, a high-level accelerated linear algebra package, which allows for the first integration of a high-order fast direct solver with automatic differentiation tools. We conclude with extensive numerical examples showing our methods are fast and accurate on two- and three-dimensional problems.

Fast direct solvers↗
DOE OSTI2022

Impact of FERC Order 2222 on DER Participation Rules in US Electricity Markets

Electricity markets in the bulk grid are beginning to implement market mechanisms that support the procurement of flexible capabilities from wide range of technologies, including distributed energy resources (DERs). The flexibility of these resources will help counterbalance supply uncertainties from large-scale integration of variable renewable generation. To encourage development of distributed and aggregated market participants, FERC Order 2222 was issued in September 2020 to require each Independent System Operator (ISO) in the US to implement rules that enable broader participation from aggregations of DERs in the bulk market. The following paper first describes the generic design of ISO markets before introducing the new market participation rules that ISOs have proposed for compliance with Order 2222. The paper then describes how software performance issues may continue to affect the eligibility requirements and offer structures for DER aggregations participating in ISOs, noting that continued research on computational methods may help reduce burdens for DER integration. The prospects for transmission and distribution system coordination is second major issue discussed, which will require minor changes to existing processes in the short term. In the longer term, there is more opportunity for more wide-ranging reforms, such as the development of a Distribution System Operator (DSO) framework. Newly proposed market rules may affect how Transactive Energy Systems (TES) will help facilitate efficient formation of DER aggregations and operation of the individual DERs within an aggregation. Within the TES context, the challenge is to fully understand how resource eligibility and operational and planning coordination methods will affect the design and implementation of TES.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Machine-Learned Manifold-Based Models for Large Eddy Simulation of Turbulent Combustion

Reduced-order manifold combustion models are commonly used to lower the cost of reacting Large Eddy Simulations (LES) and may be derived either from physical principles as in flamelet models or from data-driven methods like Principal Component Analysis (PCA). In either case, neural networks are increasingly used as part of these models to provide a nonlinear mapping between a small set of pre-defined variables that parameterize the manifold and outputs of interest, such as reaction rates. In this work, we propose a new manifold-based modeling approach that combines the definition of the manifold-parameterizing variables (linear combinations of species), the nonlinear mapping to the outputs, and closure of filtered quantities for LES into the structure of a single neural network. This allows the process used to train the neural network to simultaneously optimize both the functional form of the model and the identities of the inputs to the model. The new approach can flexibly incorporate thermochemical data from any combustion system; if trained on data from 1D flames it can be interpreted as an optimized flamelet model, but it can also be used to learn models from data from more complex configurations. This work presents a priori evaluations of the new approach in both contexts. Evaluation using data from 1D premixed flames demonstrates the physical interpretability of the manifold variables generated by the new approach. Evaluation using data from direct numerical simulations of turbulent flames shows improved predictions relative to either flamelet or PCA-based models in a more complex configuration.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

Landau discriminants

Scattering amplitudes in quantum field theories have intricate analytic properties as functions of the energies and momenta of the scattered particles. In perturbation theory, their singularities are governed by a set of nonlinear polynomial equations, known as Landau equations, for each individual Feynman diagram. The singularity locus of the associated Feynman integral is made precise with the notion of the Landau discriminant, which characterizes when the Landau equations admit a solution. In order to compute this discriminant, we present approaches from classical elimination theory, as well as a numerical algorithm based on homotopy continuation. These methods allow us to compute Landau discriminants of various Feynman diagrams up to 3 loops, which were previously out of reach. For instance, the Landau discriminant of the envelope diagram is a reducible surface of degree 45 in the three-dimensional space of kinematic invariants. We investigate geometric properties of the Landau discriminant, such as irreducibility, dimension and degree. In particular, we find simple examples in which the Landau discriminant has codimension greater than one. Furthermore, we describe a numerical procedure for determining which parts of the Landau discriminant lie in the physical regions. In order to study degenerate limits of Landau equations and bounds on the degree of the Landau discriminant, we introduce Landau polytopes and study their facet structure. Finally, we provide an efficient numerical algorithm for the computation of the number of master integrals based on the connection to algebraic statistics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗