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This is the final report on the project, and describes the main accomplishments in the development of the Shifted Boundary Method (SBM), a new computational framework for embedded/immersed computational mechanics applications.
We illustrate a technique to calculate the gradient of scalar functions that are defined on any arbitrary matrix subspace. It generalizes our earlier work titled “What is the gradient of a scalar function of a symmetric matrix ?”(Indian Journal of Pure and Applied Mathematics (2022), https://doi.org/10.1007/s13226-022-00313-x), in which we considered the special case of the subspace of symmetric matrices. Extant methods to calculate the gradient in such cases have an inherent flaw which leads to spurious results that populate several publications, as well as respected textbooks and handbooks on matrix calculus. Here, we examine these sources and results in a rigorous and concrete mathematical setting of a finite-dimensional inner-product space and discover the inherent flaw and also a remedy. We demonstrate two ways to calculate the derivative/gradient and second derivative for scalar functions of matrices defined over an arbitrary matrix subspace; the first method is by considering any (differentiable) extension to the space of square matrices and projection of its gradient onto the given subspace. The second method utilizes an ordered basis and computes each component of the gradient through evaluation of the directional derivative. All the ideas presented are illustrated by non-trivial examples, namely, considering the subspace of 3 x 3 circulant and Toeplitz matrices and presenting the results of gradient-descent with both the spurious and correct gradients. Moreover, our bibliography makes it clear that a rigorous approach to matrix calculus is not common in practice, and our presentation of matrix calculus in the language of inner-product spaces will be significant and meaningful for applied mathematicians, engineers and researchers working in inter-disciplinary fields to avoid the conceptual pitfalls that exist.
We illustrate a technique to calculate the gradient of scalar functions that are defined on any arbitrary matrix subspace. It generalizes our earlier work titled “What is the gradient of a scalar function of a symmetric matrix ?”(Indian Journal of Pure and Applied Mathematics (2022), doi:10.1007/s13226-022-00313-x), in which we considered the special case of the subspace of symmetric matrices. Extant methods to calculate the gradient in such cases have an inherent flaw which leads to spurious results that populate several publications, as well as respected textbooks and handbooks on matrix calculus. We examine these sources and results in a rigorous and concrete mathematical setting of a finite-dimensional inner-product space and discover the inherent flaw and also a remedy. We demonstrate two ways to calculate the derivative/gradient and second derivative for scalar functions of matrices defined over an arbitrary matrix subspace; the first method is by considering any (differentiable) extension to the space of square matrices and projection of its gradient onto the given subspace. The second method utilizes an ordered basis and computes each component of the gradient through evaluation of the directional derivative. All the ideas presented are illustrated by non-trivial examples, namely, considering the subspace of 3 × 3 circulant and Toeplitz matrices and presenting the results of gradient-descent with both the spurious and correct gradients. Moreover, our bibliography makes it clear that a rigorous approach to matrix calculus is not common in practice, and our presentation of matrix calculus in the language of inner-product spaces will be significant and meaningful for applied mathematicians, engineers and researchers working in inter-disciplinary fields to avoid the conceptual pitfalls that exist.
ABSTRACT The construction of catalogues of a particular type of galaxy can be complicated by interlopers contaminating the sample. In spectroscopic galaxy surveys this can be due to the misclassification of an emission line; for example in the Hobby–Eberly Telescope Dark Energy Experiment (HETDEX) low-redshift [O ii] emitters may make up a few per cent of the observed Ly α emitter (LAE) sample. The presence of contaminants affects the measured correlation functions and power spectra. Previous attempts to deal with this using the cross-correlation function have assumed sources at a fixed redshift, or not modelled evolution within the adopted redshift bins. However, in spectroscopic surveys like HETDEX, where the contamination fraction is likely to be redshift dependent, the observed clustering of misclassified sources will appear to evolve strongly due to projection effects, even if their true clustering does not. We present a practical method for accounting for the presence of contaminants with redshift-dependent contamination fractions and projected clustering. We show using mock catalogues that our method, unlike existing approaches, yields unbiased clustering measurements from the upcoming HETDEX survey in scenarios with redshift-dependent contamination fractions within the redshift bins used. We show our method returns autocorrelation functions with systematic biases much smaller than the statistical noise for samples with at least as high as 7 per cent contamination. We also present and test a method for fitting for the redshift-dependent interloper fraction using the LAE–[O ii] galaxy cross-correlation function, which gives less biased results than assuming a single interloper fraction for the whole sample.
The purpose of this project is to build a fuel cell prototype that demonstrates high temperature proton exchange membrane fuel cell technology (HT PEMFC) commercial readiness. It advances from a technology baseline established in a prior CRADA in which these same Parties collaborated during the years 2020-2024. These efforts are aligned with the intentions of the DOE Hydrogen Fuel Cell Technology Office (HFTO) L’Innovator Pilot Program. Participant observes that its US-based competitive advantage may be improved by further optimizing Laboratory inventions. This CRADA is intended to further improve National Laboratory compositions and to develop commercial HT PEMFC membrane electrode assemblies (MEAs) that perform over a range of operating temperatures and relative humidity, that generate power from both low grade and pure hydrogen, and that are resistant to air impurities. Participant’s goal is to advance the commercial competitiveness of National Laboratory technologies in fuel cell products for heavy-duty truck integrators, for stationary power generation, marine applications, and for emerging interest from commercial aviation. The Parties will collaborate on producing a HT PEMFC MEA that integrates LANL ion pair technology and Brookhaven catalyst technology. The Laboratories plan to research and develop compositions for testing and evaluation. The participant will manufacture multiple MEAs based on the Laboratory compositions and will enable selected customers to validate performance characteristics. The Laboratories will convey to Participant the methods of making the National Laboratory compositions such that Participant may reproduce and then scale Laboratory methods into commercial production. Throughout the project, the Laboratories and Participant will iteratively test and optimize the compositions of materials of the MEAs, intending to optimize characteristics such as power density and lifecycle durability. Participant’s intended customers include fuel cells for large trucks, aviation, power back up, marine, and portable power.
Tungsten and tungsten heavy alloys (WHAs), known for their remarkably high hardness, durability, and corrosion resistance, play a critical role in the thriving development of nuclear fusion reactors in recent years. However, the exploration in tungsten alloys for the nuclear-related applications has been limited by the difficulty of manufacturing and the complexity of experiments to reproduce the environment of nuclear reaction. Therefore, this project aims to utilize nanoscale simulation methods such as density functional theory (DFT) and molecular dynamics (MD) with the help of machine learning techniques to not only understand the mechanisms of tungsten alloys but also allow us to computationally predict their mechanical behaviors under extreme environments. One critical problem of the application of WHAs in nuclear reactors is the surface melting. In the current design of the SPARC reactor, the WHA, W97Ni2.1Fe0.9 or W97NiFe, is chosen to be the first wall components to confine the plasma where the particles are fiercely moving and colliding into each other to create nuclear fusion reaction. This process will generate extremely high heat flux onto these WHA tiles, leaving high surface temperature that could possibly melt the surface of the WHA tiles, As illustrated in Fig. 1(a). a laser experiment previously done illustrates that a rough surface damage would be made after the surface melting where the matrix area mainly composed of nickel and iron as shown in Fig. 1(b), will first melt and then leave vacancies between these tungsten grains. Unfortunately, these kinds of roughness on the first-wall components could be deadly to the plasma inside a Tokmak reactor because the heat that is supposed to dissipate at a designed ratio through the tiles may in turn be excessively absorbed and accumulated on any uneven area of the surface, which will eventually make the whole nuclear reaction fail. In this project, we will introduce a machine learning potential, Allegro, based on DFT calculation and then build a MD model for W-Ni-Fe alloys.
Deep learning (DL) models have enjoyed increased attention in recent years because of their powerful predictive capabilities. While many successes have been achieved, standard deep learning methods suffer from a lack of uncertainty quantification (UQ). While the development of methods for producing UQ from DL models is an active area of current research, little attention has been given to the quality of the UQ produced by such methods. In order to deploy DL models to high-consequence applications, high-quality UQ is necessary. This report details the research and development conducted as part of a Laboratory Directed Research and Development (LDRD) project at Sandia National Laboratories. The focus of this project is to develop a framework of methods and metrics for the principled assessment of UQ quality in DL models. This report presents an overview of UQ quality assessment in traditional statistical modeling and describes why this approach is difficult to apply in DL contexts. An assessment on relatively simple simulated data is presented to demonstrate that UQ quality can differ greatly between DL models trained on the same data. A method for simulating image data that can then be used for UQ quality assessment is described. A general method for simulating realistic data for the purpose of assessing a model’s UQ quality is also presented. A Bayesian uncertainty framework for understanding uncertainty and existing metrics is described. Research that came out of collaborations with two university partners are discussed along with a software toolkit that is currently being developed to implement the UQ quality assessment framework as well as serve as a general guide to incorporating UQ into DL applications.
Starting from a general wave-function described on a set of spins or qubits, we propose several quantum algorithms to extract the components of this state on eigenstates of total spin S 2 and its z component S z . The method plays the role of total spin projection and gives access to the amplitudes of the initial state on a total spin basis. Here, the different algorithms have various degrees of sophistication depending on the requested tasks. They can either solely project onto the subspace with good total spin or completely uplift the degeneracy in this subspace. In the former case, when the projection on the total spin j is made, we show that the number of operations for the projection can be reduced from a quadratic to a linear dependence in j. After each measurement, the state collapses to one of the spin eigenstates that could be used for postprocessing. For this reason, we call the method total quantum spin filtering.
The goal of the project was to devise and implement a method of accurately qualifying any noble gas emitted during fuel drying operations (part of the dry fuel storage process) in order to provide the data needed to validate the off-site dose calculations. The imputes of the project was the NRC publishing Information Notice 18-01, 'Noble Fission Gas Releases During Spent Fuel Cask Loading Operations' in February 2018. The information notice describes some industry events that occurred during vacuum drying operations as part of a dry fuel campaign. The solution was devised by Fort Calhoun Station staff in partnership with Mirion Technologies technical staff. The monitoring was accomplished by directing all the effluent from the fuel storage cask vacuum drying machine through a sample chamber containing a compact ISOCS characterized CZT based gamma spectrometer connected to a Mirion Data Analyst. This resulted near real-time quantification of the radionuclides of concern. (authors)
This project aimed at enhancing the quantitative analysis capabilities of electrospray ionization mass spectrometry (ESI-MS) by developing advanced computational methods. The primary focus was to integrate continuum and molecular dynamics simulations to study the behavior of microdroplets in the ESI process, from formation to evaporation. Through this research, we sought to bridge significant length and time scales to provide a comprehensive understanding of how analyte concentrations evolve from bulk solutions into gas-phase ions. This understanding is crucial for addressing challenges such as ionization efficiency, solvent effects, and ion suppression, which currently limit the accuracy of quantitative ESI-MS.
The main scientific contributions of this project are the following novel concepts for multidimensional arrays: shape-based similarity join (SIGMOD 2016), incremental view maintenance (SIGMOD 2017), user-defined stencil functions (HPDC 2017), and distributed caching for in-situ processing (SSDBM 2018). Building on our collaboration with the astrophysics group at LBNL, we applied these techniques to the data generated in the Palomar Transient Factory (PTF) astronomical survey. They played a pivotal role in the first-ever observation of a neutron star merger, which produces gravitational waves and turns out to be the origin of heavy elements, including gold. This has lead to a Science magazine article that has received extensive media coverage on ACM TechNews, Slashdot, FiveThirtyEight, and Quanta Magazine, among others. Additionally, two other articles detailing related aspects of the same discovery have been published in the Astrophysical Journal Letters journal. These publications have more than 3,000 citations according to Google Scholar (as of February 2022). This cross-disciplinary collaboration provided very good opportunities to apply database techniques to real-life scientific problems. The fact that they facilitated major discoveries in astrophysics proves the importance of our research. In addition to the work on multidimensional array databases, this project has also developed stochastic gradient descent (SGD) optimization algorithms for training large scale machine learning models, methods for querying in-situ data, and a database query optimizer based on sketch synopses.
A new computational diagnostic method for pressure-induced compressibility is proposed by projecting its local contribution to the chemical explosive mode (CEM) in the chemical explosive mode analysis (CEMA) framework. The new method is validated for the study of detonation development during the deflagration-to-detonation transition (DDT) process. The flame characteristics are identified through the quantification of individual CEM contributions of chemical reaction, diffusion, and pressure-induced compressibility. Numerical simulations are performed to investigate the DDT processes in a stoichiometric hydrogen-air mixture. A Godunov algorithm, fifth-order in space, and third-order in time are used to solve the fully compressible Navier-Stokes equations on a dynamically adapting mesh. A single-step, calibrated chemical diffusive model (CDM) described by Arrhenius kinetics is used for energy release and conservation between the fuel and the product. The new diagnostic method is first applied to onedimensional (1D) canonical flame configurations followed by two-dimensional (2D) simulations of DDT in an obstructed channel where different detonation initiation scenarios are examined using the new CEMA projection formulation. Detailed examinations of the idealized configuration of detonation initiation through shock focusing mechanism at a flame front are also studied using the new formulation. A comparison of the currently proposed CEMA projection and the original formulation by the authors suggests that including the pressure-induced compressibility is essential for the use of CEMA in DDT process. The results also show that the new formulation of CEMA projection can successively capture the detonation initiation through either a gradient mechanism or a direct initiation mechanism, and therefore can be used as an effective local analytical tool for the computational diagnostics of detonation initiation in a DDT process. It was found that detonation development is characterized by a strong contribution of chemistry role to the CEM which is pivotal to the initiation of detonation. The role of compressibility is found enhanced at the edge of the detonation front where diffusion was found to have minimal effects on detonation development.
Between August 2012 and September 2014, about 114,000 metric tonnes of CO 2 was captured from the coal-fired Plant Barry Power Station at Bucks Alabama and injected into the Paluxy Formation above the oil pool in the southeast unit of the Citronelle Oilfield. Various monitoring methods were deployed at land surface and in project wells to measure system performance, comply with permit requirements and test new and innovative monitoring tools. The monitoring program relied heavily on active seismic methods for subsurface imaging of geologic structure and time-lapse seismic techniques to track the CO 2 migration in the injection interval. Both conventional geophone/hydrophone and fiber-optic based Distributed Acoustic Sensing (DAS) arrays were deployed and tested, allowing a side by side comparison of the equipment and techniques. Geophysical imaging of the subsurface was successful using DAS in the offset vertical seismic profile (OVSP) survey configuration. A high resolution OVSP image of the subsurface was obtained in 2014 with DAS, which exceeded project expectations in comparison to a lower resolution image obtained in 2012 using a conventional 80-level geophone array. A time-lapse image of the redistribution of CO 2 after injection ended in September 2014 was obtained with two DAS OVSP surveys from June 2014 and December 2015, thus successfully demonstrating its proof-of-concept. Unfortunately, a pre-injection baseline survey with DAS, which was in its initial stage of technology development in 2012, did not have sufficient quality for use, making it difficult to interpret the acquired DAS time-lapse difference. Additional research in this area has since demonstrated the utility of time-lapse DAS OVSP. DAS data were also acquired during a cross-well seismic survey conducted in 2014. Unfortunately, the DAS technique was not success in the cross-well survey configuration because the system noise level was too high in the crosswell frequency output range (100–1200 Hz) of the piezoelectric source (increasing by a factor of ten compared to VSP frequency band). Additionally, the cross-well geometry causes sub-horizontal (broadside) incidence on the vertical DAS fiber cable, which is known to be problematic. Current research is focused on improving the DAS cable response to broadside acoustic energy. Time-lapse seismic surveys using commercially available conventional arrays were also acquired. In contrast to the DAS acquired data, the cross-well seismic results obtained with the conventional array was highly successful and clearly showed the CO 2 remained in zone at the end of injection. Time-lapse differencing of the OSVP surveys acquired with the conventional arrays proved to be inconclusive. Finally, changes in wellbore conditions between surveys and unavoidable changes in equipment (the array used for the baseline survey was retired) affected data quality, making it difficult to interpret the OVSP results.
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.
Modular chemical process intensification (MCPI) is an emerging field where chemical processing is performed using small-scale modular equipment instead of conventional large centralized chemical plants. Conventional chemical plants benefit from economies of scale that encourage scale-up to ever larger plants. A goal of MCPI is to develop technology that intensifies processing so that equipment can be dramatically smaller and integrated into modular systems. Scale-up occurs by adding more modules in parallel rather than making the equipment larger. A key concept is that equipment and modules can ultimately be cheaper by leveraging economies of mass production, analogous to the automotive industry, in manufacturing the equipment. This project made significant progress toward this outcome by meeting the RAPID institute metric to reduce equipment cost by 20% for each doubling in manufacturing volume. The MCPI application was thermochemical technology that is being commercialized by STARS Technology Corporation, one of the CRADA partners. The technology converts solar and renewable power to chemical energy to produce renewable hydrogen, fuels, and chemicals. The benefit to the public is reduction in greenhouse gases that are contributing to climate change. The project transitioned the steam methane reforming (SMR) reactor from conventional fabrication methods to additive manufacturing (AM) direct metal laser sintering (DMLS) process. This is projected to reduce the cost of making a reactor by 58% when producing 100 reactors per year. Innovations in the DMLS process produced a patented design that reduces reactor weight by 60%. Reductions in material costs and processing time extend the DMLS advantage to higher production volumes. The new design promises to be 38% cheaper than the conventional processes at 1000 units per year. The resulting 87% reduction in the steam methane reforming (SMR) module cost in scaling from current costs meets the RAPID metric. The project was successful in producing and testing the first ever additively manufactured SMR reactors. A reactor achieved over 82% efficiency in converting electric power to chemical energy, which is a world record for an inductively heated SMR. The project has contributed to the design and assembly of a first demonstration plant that is headed to a hydrogen bus filling station in Thousand Palms, CA.
This project aims to evaluate RSA as a method for public-key encryption for cyber-physical systems (CPS). As technology advances, cyber attacks are increasing, and with them, the need for cybersecurity advances; the average cost for cybercrime in the world was estimated at $6 trillion in 2021. A public-key cryptosystem that has been around since 1977, RSA has recently garnered some critiques for its fragility, computational cost, and lazy implementation. In this project I will review the mathematical derivation of RSA, analyze the practical implications of such mathematical framework for the security of RSA, and propose a formal methods based approach to verify encryption schemes for CPS.
In this work, a novel approach is introduced for accelerating the solution of structural dynamics problems in the presence of localised phenomena, such as cracks. For this category of problems, conventional projection-based Model Order Reduction (MOR) methods are either limited with respect to the range of system configurations that can be represented or require frequent solutions of the Full Order Model (FOM) to update the low-dimensional spaces, in which solutions are represented. In the proposed approach, low-dimensional spaces, constructed for the healthy structure, are enriched with appropriately selected columns of the flexibility matrix of the system. It can be shown that these spaces contain the solution to the original problem for the static case, while their dimension is much smaller. In order to allow their online construction for arbitrary localised features, the full flexibility matrix of the system should be available. To this end, a hierarchical representation is used for the matrices involved, allowing to compute the flexibility matrix efficiently and with reduced memory requirements. The resulting method offers significant speedups, without sacrificing the flexibility and accuracy of the full order model. The performance and limitations of the approach are studied through a series of examples in structural dynamics.
We propose a domain decomposition method for the efficient simulation of nonlocal problems. Our approach is based on a multi-domain formulation of a nonlocal diffusion problem where the subdomains share “nonlocal” interfaces of the size of the nonlocal horizon. This system of nonlocal equations is first rewritten in terms of minimization of a nonlocal energy, then discretized with a meshfree approximation and finally solved via a Lagrange multiplier approach in a way that resembles the finite element tearing and interconnect method. Specifically, we propose a distributed projected gradient algorithm for the solution of the Lagrange multiplier system, whose unknowns determine the nonlocal interface conditions between subdomains. Several two-dimensional numerical tests on problems as large as 191 million unknowns illustrate the strong and the weak scalability of our algorithm, which outperforms the standard approach to the distributed numerical solution of the problem. Finally, this work is the first rigorous numerical study in a two-dimensional multi-domain setting for nonlocal operators with finite horizon and, as such, it is a fundamental step towards increasing the use of nonlocal models in large scale simulations.