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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Classical Simulation of Boson Sampling Based on Graph Structure

Boson sampling is a fundamentally and practically important task that can be used to demonstrate quantum supremacy using noisy intermediate-scale quantum devices. In this Letter, we present classical sampling algorithms for single-photon and Gaussian input states that take advantage of a graph structure of a linear-optical circuit. The algorithms’ complexity grows as so-called treewidth, which is closely related to the connectivity of a given linear-optical circuit. Using the algorithms, we study approximated simulations for local Haar-random linear-optical circuits. For equally spaced initial sources, we show that, when the circuit depth is less than the quadratic in the lattice spacing, the efficient simulation is possible with an exponentially small error. Notably, right after this depth, photons start to interfere each other and the algorithms’ complexity becomes subexponential in the number of sources, implying that there is a sharp transition of its complexity. Finally, when a circuit is sufficiently deep enough for photons to typically propagate to all modes, the complexity becomes exponential as generic sampling algorithms. We numerically implement a likelihood test with a recent Gaussian boson sampling experiment and show that the treewidth-based algorithm with a limited treewidth renders a larger likelihood than the experimental data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Data associated with Quaternary Research manuscript Latest Pleistocene glacial chronology and paleoclimate reconstruction for the East River watershed, Colorado, USA

The data here are associated with Quaternary Research manuscript Latest Pleistocene glacial chronology and paleoclimate reconstruction for the East River watershed, Colorado, USA and include data associated with cosmogenic exposure and depth profile dating as well as glacier-climate numerical modeling. Reconstructing Pleistocene glaciation timing and extent is vital for understanding paleoclimate. While late Pleistocene glaciation has been studied extensively in western North American mountain ranges, the glacial history of the western Elk Range in Colorado remains understudied, particularly in the East River watershed, a site of intense scientific focus. Here we use cosmogenic nuclide exposure and depth–profile dating methods to determine the timing of glaciation in the East River watershed. We use glacier modeling to reconstruct paleoglacier extents and quantify past climate conditions. Our findings indicate that the East River glacier retreated from its maximum position approximately 17–18 ka, moving to recessional positions between 13–15 ka, before experiencing more substantial retreat to high-elevation cirques around 12.9 ka. Glacier modeling suggests that the maximum ice extents at 17–18 ka could have been sustained by temperature depressions of approximately −6.5°C compared to modern conditions, assuming consistent precipitation. Additionally, the ice position at 13–15 ka could have been supported by temperature depressions of around −4.0°C. These results offer insights into the deglaciation timeline in the East River watershed and broader western Elk Range as well as paleoclimate conditions during the late Pleistocene, which may aid future research on critical zone evolution in the East River watershed.The data files include: 1. Table 1 In situ-produced 10Be sample data (.pdf, .csv, .xlsx)2. Table 2 In situ-produced 10Be exposure age results (.pdf, .csv, .xlsx)3. S1_A CRONUS calculator input assuming no erosion (.csv)4. S1_B CRONUS calculator input assuming erosion (.csv)5. S1_C CRONUS calculator results and comparison (.csv)6. S2_A In situ-produced 10Be sample data for depth profile (.csv)7. S2_B In situ-produced 10Be depth profile model input (.csv)8. S2_C In situ-produced 10Be depth profile model results (.csv)9. S3 Monthly cloudiness, rH, and windspeed data used in glacier climate model (.csv)10. S4 Glacier climate model results (.csv)

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Comparing different generations of idealized solar geoengineering simulations in the Geoengineering Model Intercomparison Project (GeoMIP)

Abstract. Solar geoengineering has been receiving increased attention in recent years as a potential temporary solution to offset global warming. One method of approximating global-scale solar geoengineering in climate models is via solar reduction experiments. Two generations of models in the Geoengineering Model Intercomparison Project (GeoMIP) have now simulated offsetting a quadrupling of the CO2 concentration with solar reduction. This simulation is idealized and designed to elicit large responses in the models. Here, we show that energetics, temperature, and hydrological cycle changes in this experiment are statistically indistinguishable between the two ensembles. Of the variables analyzed here, the only major differences involve highly parameterized and uncertain processes, such as cloud forcing or terrestrial net primary productivity. We conclude that despite numerous structural differences and uncertainties in models over the past two generations of models, including an increase in climate sensitivity in the latest generation of models, the models are consistent in their aggregate climate response to global solar dimming.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Nonempirical Range-Separated Hybrid Functional with Spatially Dependent Screened Exchange

Electronic structure calculations based on density functional theory (DFT) have successfully predicted numerous ground-state properties of a variety of molecules and materials. However, exchange and correlation functionals currently used in the literature, including semilocal and hybrid functionals, are often inaccurate to describe the electronic properties of heterogeneous solids, especially systems composed of building blocks with large dielectric mismatch. Here, in this study, we present a dielectric-dependent range-separated hybrid functional, screened-exchange range-separated hybrid (SE-RSH), for the investigation of heterogeneous materials. We define a spatially dependent fraction of exact exchange inspired by the static Coulomb-hole and screened-exchange (COHSEX) approximation used in many-body perturbation theory, and we show that the proposed functional accurately predicts the electronic structure of several nonmetallic interfaces, three- and two-dimensional, pristine, and defective solids and nanoparticles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

CEBAF Injector for K Long Beam Conditions

The Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab concurrently operates four experimental Halls with distinct bunch charge specifications and repetition rates. Numerous critical beam parameters within CEBAF are configured in the injector, some remaining unchanged throughout the accelerator. Consequently, the injector plays a crucial role in determining final beam characteristics, including bunch structure, beam sizes, bunch lengths, energy spread, and beam transmission. The Jefferson Lab KL experiment is scheduled to take place at CEBAF in Hall D, featuring a much lower bunch repetition rate of 7.80 MHz or 15.59 MHz, below the nominal values of 249.5 MHz or 499 MHz. Although the proposed average current of 5 ?A or 10 ?A is low compared to the maximum CEBAF cur- rent of approximately 180 ?A, the corresponding bunch charge is unusually high for CEBAF injector operation. This study focuses on the behavior of low-repetition-rate, high-bunch- charge (0.32 to 0.64 pC) beams in the CEBAF injector. We investigated the evolution and transmission of low-charge beams to space-charge dominated high-charge beams in the front end of the CEBAF injector for two configurations: the pre-existing CEBAF Phase 1 injector upgrade, operated at 130 kV, and the existing CEBAF Phase 2 injector upgrade, operated at 140 kV, 180 kV, and to be operated at 200 kV. The electron beam through the CEBAF injector is characterized using beam dynamics simulations and comparisons with the available measurements performed at 130 kV. Multi-objective genetic optimizations of the CEBAF injector were performed to determine the operating magnetic elements and RF settings for the evolution and transmission of low, moderate, and high charge beams in the CEBAF injector at 180 kV and 200 kV DC gun voltages. Subsequently, simulations at the same voltages were conducted to obtain the beam characteristics at the front end of the CEBAF injector. The laser spot size and laser pulse length at the cathode were varied to observe their effects on beam transmission in the injector at different voltages (130 kV, 180 kV, and 200 kV). Experimental studies at 130 kV, 140 kV, and 180 kV validate the simulations. Beam study measurements are carried out using EPICS tools, while optimizations and simulations are facilitated by General Particle Tracer. Based on the findings, optimal parameters for the upcoming Jefferson Lab KL experiment are proposed, utilizing a lower repetition rate and higher bunch charge

Pokharel, Sunil↗
DOE OSTI2026

Impact of control signal phase noise on qubit fidelity

As qubit decoherence times are increased and readout technologies are improved, nonidealities in the drive signals, such as phase noise, are going to represent a growing limitation to the fidelity achievable at the end of complex control pulse sequencies. Here we study the impact on fidelity of phase noise affecting reference oscillators with the help of numerical simulations, which allow us to directly take into account the interaction between the phase fluctuations in the control signals and the evolution of the qubit state. Our method is based on the generation of phase noise realizations consistent with a given power spectral density, that are then applied to the pulse carrier in simulations, with Qiskit-Dynamics, of the qubit temporal evolution. By comparing the final state obtained at the end of a noisy pulse sequence with that in the ideal case and averaging over multiple noise realizations, we estimate the resulting degradation in fidelity, and exploiting an approximate analytical representation of a carrier affected by phase fluctuations, we discuss the contributions of the different spectral components of phase noise.

Barsotti, Agata [Pisa U.]↗
DOE OSTI2024

The FRB-searching Pipeline of the Tianlai Cylinder Pathfinder Array

This paper presents the design, calibration, and survey strategy of the Fast Radio Burst (FRB) digital backend and its real-time data processing pipeline employed in the Tianlai Cylinder Pathfinder Array. The array, consisting of three parallel cylindrical reflectors and equipped with 96 dual-polarization feeds, is a radio interferometer array designed for conducting drift scans of the northern celestial semi-sphere. The FRB digital backend enables the formation of 96 digital beams, effectively covering an area of approximately 40 square degrees with the 3 dB beam. Our pipeline demonstrates the capability to conduct an automatic search of FRBs, detecting at quasi-real-time and classifying FRB candidates automatically. The current FRB searching pipeline has an overall recall rate of 88%. During the commissioning phase, we successfully detected signals emitted by four well-known pulsars: PSR B0329+54, B2021+51, B0823+26, and B2020+28. We report the first discovery of an FRB by our array, designated as FRB 20220414A. We also investigate the optimal arrangement for the digitally formed beams to achieve maximum detection rate by numerical simulation.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Computing molecular excited states on a D-Wave quantum annealer

Abstract The possibility of using quantum computers for electronic structure calculations has opened up a promising avenue for computational chemistry. Towards this direction, numerous algorithmic advances have been made in the last five years. The potential of quantum annealers, which are the prototypes of adiabatic quantum computers, is yet to be fully explored. In this work, we demonstrate the use of a D-Wave quantum annealer for the calculation of excited electronic states of molecular systems. These simulations play an important role in a number of areas, such as photovoltaics, semiconductor technology and nanoscience. The excited states are treated using two methods, time-dependent Hartree–Fock (TDHF) and time-dependent density-functional theory (TDDFT), both within a commonly used Tamm–Dancoff approximation (TDA). The resulting TDA eigenvalue equations are solved on a D-Wave quantum annealer using the Quantum Annealer Eigensolver (QAE), developed previously. The method is shown to reproduce a typical basis set convergence on the example $$\hbox {H}_2$$ H 2 molecule and is also applied to several other molecular species. Characteristic properties such as transition dipole moments and oscillator strengths are computed as well. Three potential energy profiles for excited states are computed for $$\hbox {NH}_3$$ NH 3 as a function of the molecular geometry. Similar to previous studies, the accuracy of the method is dependent on the accuracy of the intermediate meta-heuristic software called qbsolv.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Counterdiabatic Driving with Performance Guarantees

Counterdiabatic (CD) driving has the potential to speed up adiabatic quantum state preparation by suppressing unwanted excitations. However, existing approaches either require intractable classical computations or are based on approximations that do not have performance guarantees. We propose and analyze a nonvariational, system-agnostic CD expansion method and analytically show that it converges exponentially quickly in the expansion order. In finite systems, the required resources scale inversely with the spectral gap, which we argue is asymptotically optimal. To extend our method to the thermodynamic limit and suppress errors stemming from high-frequency transitions, we leverage finite-time adiabatic protocols. In particular, we show that a time determined by the quantum speed limit is sufficient to prepare the desired ground state, without the need to optimize the adiabatic trajectory. Numerical tests of our method on the quantum Ising chain show that our method can outperform state-of-the-art variational CD approaches.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Scalable Bayesian Physics-Informed Kolmogorov-Arnold Networks

Uncertainty quantification (UQ) plays a pivotal role in scientific machine learning, especially when surrogate models are used to approximate complex systems. Although multilayer perceptions (MLPs) are commonly employed as surrogates, they often suffer from overfitting due to their large number of parameters. Kolmogorov-Arnold networks (KANs) offer an alternative solution with fewer parameters. However, gradient-based inference methods, such as Hamiltonian Monte Carlo (HMC), may result in computational inefficiency when applied to KANs, especially for large-scale datasets, due to the high cost of back-propagation. To address these challenges, we propose a novel approach, combining the dropout Tikhonov ensemble Kalman inversion (DTEKI) with Chebyshev KANs. This gradient-free method effectively mitigates overfitting and enhances numerical stability. In addition, we incorporate the active subspace method to reduce the parameter-space dimensionality, allowing us to improve the accuracy of predictions and obtain more reliable uncertainty estimates. Extensive experiments demonstrate the efficacy of our approach in various test cases, including scenarios with large datasets and high noise levels. Our results show that the new method achieves comparable or better accuracy, much higher efficiency as well as stability compared to HMC, in addition to scalability. Moreover, by leveraging the low-dimensional parameter subspace, our method preserves prediction accuracy while substantially reducing further the computational cost.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Approximating the linear response of physical chaos

Abstract Parametric derivatives of statistics are highly desired quantities in prediction, design optimization and uncertainty quantification. In the presence of chaos, the rigorous computation of these quantities is certainly possible, but mathematically complicated and computationally expensive. Based on Ruelle’s formalism, this paper shows that the sophisticated linear response algorithm can be dramatically simplified in higher-dimensional systems featuring statistical homogeneity in the physical space. We argue that the contribution of the SRB (Sinai–Ruelle–Bowen) measure gradient, which is an integral yet the most cumbersome part of the full algorithm, is negligible if the objective function is appropriately aligned with unstable manifolds. This abstract condition could potentially be satisfied by a vast family of real-world chaotic systems, regardless of the physical meaning and mathematical form of the objective function and perturbed parameter. We demonstrate several numerical examples that support these conclusions and that present the use and performance of a simplified linear response algorithm. In the numerical experiments, we consider physical models described by differential equations, including Lorenz 96 and Kuramoto–Sivashinsky.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

A Fast Time-Stepping Strategy for Dynamical Systems Equipped with a Surrogate Model

Simulation of complex dynamical systems arising in many applications is computationally challenging due to their size and complexity. Model order reduction, machine learning, and other types of surrogate modeling techniques offer cheaper and simpler ways to describe the dynamics of these systems but are inexact and introduce additional approximation errors. In order to overcome the computational difficulties of the full complex models, on one hand, and the limitations of surrogate models, on the other, this work proposes a new accelerated time-stepping strategy that combines information from both. This approach is based on the multirate infinitesimal general-structure additive Runge--Kutta framework. The inexpensive surrogate model is integrated with a small time step to guide the solution trajectory, and the full model is treated with a large time step to occasionally correct for the surrogate model error and ensure convergence. Here, we provide a theoretical error analysis, and several numerical experiments, to show that this approach can be significantly more efficient than using only the full or only the surrogate model for the integration.

Surrogate models↗
DOE OSTI2024

On a Spectral Method for β -particle Bound Excitation Collisions in Kilonovae

The interaction of β-particles with the weakly ionized plasma background is an important mechanism for powering the kilonova (KN) transient signal from neutron star mergers. For this purpose, we present an implementation of the approximate fast-particle collision kernel, described by Inokuti following the seminal formulation of Bethe, in a spectral solver of the Vlasov–Maxwell–Boltzmann equation. In particular, we expand the fast-particle plane-wave atomic excitation kernel into coefficients of the Hermite basis, and derive the relevant discrete spectral system. In this fast-particle limit, the approach permits the direct use of atomic data, including optical oscillator strengths, normally applied to photon–matter interaction. The resulting spectral matrix is implemented in the MASS-APP spectral solver framework, in a way that avoids full matrix storage per spatial zone. We numerically verify aspects of the matrix construction, and present a proof-of-principle 3D simulation of a 2D axisymmetric KN ejecta snapshot. Our preliminary numerical results indicate that a reasonable choice of Hermite basis parameters for β-particles in the KN is a bulk velocity parameter u = 0, a thermal velocity parameter α = 0.5c, and a 9 × 9 × 9 mode velocity basis set (Hermite orders of 0–8 in each dimension). For interior-ejecta sample zones, we estimate that the ratio of thermalization from large-angle (≳2fdg5) bound excitation scattering to total thermalization is ~0.002–0.003.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Predicting the Slowing of Stellar Differential Rotation by Instability-driven Turbulence

Abstract Differentially rotating stars and planets transport angular momentum (AM) internally due to turbulence at rates that have long been a challenge to predict reliably. We develop a self-consistent saturation theory, using a statistical closure approximation, for hydrodynamic turbulence driven by the axisymmetric Goldreich–Schubert–Fricke instability at the stellar equator with radial differential rotation. This instability arises when fast thermal diffusion eliminates the stabilizing effects of buoyancy forces in a system where a stabilizing entropy gradient dominates over the destabilizing AM gradient. Our turbulence closure invokes a dominant three-wave coupling between pairs of linearly unstable eigenmodes and a near-zero frequency, viscously damped eigenmode that features latitudinal jets. We derive turbulent transport rates of momentum and heat and provide them in analytic forms. Such formulae, free of tunable model parameters, are tested against direct numerical simulations; the comparison shows good agreement. They improve upon prior quasi-linear or “parasitic saturation” models containing a free parameter. Given model correspondences, we also extend this theory to heat and compositional transport for axisymmetric thermohaline-instability-driven turbulence in certain regimes.

Astronomy & Astrophysics↗
DOE OSTI2020

Update to the Performance Assessment for the Savannah River Site Saltstone Disposal Facility - 20124

In 2019, Savannah River Remediation developed a revision to the performance assessment (PA) on behalf of the U.S. Department of Energy (DOE) Savannah River Operations Office (SR) for the near-surface disposal of low-level waste at the Savannah River Site (SRS) Saltstone Disposal Facility (SDF). Soluble waste from SRS Tank Farms undergoes salt processing to remove cesium and other high activity constituents. The low-activity decontaminated salt solution (DSS) is then immobilized by mixing it into a cementitious waste form known as saltstone. After mixing, the saltstone is poured into leak-tight concrete vaults, known as saltstone disposal units (SDUs), where the waste form cures. By the time of facility closure, the SDF is expected to consist of 15 SDUs with a combined capacity of 1.06 E+09 L (280 Mgal) of cured saltstone. The facility operates under a Disposal Authorization Statement (DAS) from DOE and a permit from the South Carolina Department of Health and Environmental Control (SCDHEC). Since the start of operations in 1990, the SDF has received almost 6.7 E+07 L (18 Mgal) of DSS, resulting in the safe disposal of 2.7 E+16 Bq (7.3 E+05 Ci) of activity. Due to the radioactive decay of short-lived contaminants, the total remaining activity in the disposed waste is estimated to be approximately 1.4 E+16 Bq (3.9 E+05 Ci), as of September 2018. The Disposal Authorization Statement requires a demonstration that the system of engineered and natural features of the disposal facility will limit releases from the facility and be protective of human health and the environment for at least the next 1,000 years. The long-term performance of the facility was evaluated under the requirements of the DoE's Radioactive Waste Management Manual (US DOE Manual 435.1-1). Simulations were performed to demonstrate that the disposal facility would meet performance objectives specified in the manual. The evaluation was based on numerical models that simulate the releases of contaminants from the saltstone waste form. Contaminants were transported through groundwater and air pathways to points of assessment to evaluate compliance. In addition, the potential consequences of an inadvertent human intrusion (IHI) were also evaluated. In accordance with the guidance and recommendations in US DoE's technical standard for DAS, deterministic and probabilistic analyses were performed to demonstrate the SDF system, which includes the engineered cover system, the SDUs, the waste form, and the natural features of the site, provides a reasonable expectation that saltstone disposal will meet performance objectives. Post-closure doses to future members of the public (MOP) were evaluated; dose estimates from the air pathway were well below the 1.0 E-04 Sv/yr (10 mrem/yr) performance objective within 1,000 years, and the calculated doses to the MOP from all exposure pathways, including the groundwater and air pathways, were well below the 2.5 E-04 Sv/yr (25 mrem/yr) performance objective within 1,000 years. Doses following an assumed intrusion event within the facility boundaries were well below the IHI performance objectives, where the acute IHI dose was below the acute IHI dose performance objective of 5.0 E-03 Sv (500 mrem) and the chronic IHI dose was below the chronic IHI dose performance objective of 1.0 E-03 Sv/yr (100 mrem/yr) within 1,000 years. (author)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

Issue Resolution During the Development of the Performance Assessment for the Savannah River Site Saltstone Disposal Facility - 20125

In 2019, Savannah River Remediation developed a revision to the performance assessment (PA) on behalf of the U.S. Department of Energy (DOE) Savannah River Operations Office (SR) for the near-surface disposal of low-level waste at the Savannah River Site (SRS) Saltstone Disposal Facility (SDF). Soluble waste from SRS Tank Farms undergoes salt processing to remove cesium and other high-activity constituents. The low-activity decontaminated salt solution (DSS) is then immobilized by mixing it into a cementitious waste form known as saltstone. After mixing, the saltstone is poured into leak-tight concrete vaults, known as saltstone disposal units (SDUs), where the waste form cures. By the time of facility closure, the SDF is expected to consist of 15 SDUs with a combined capacity of 1.06 E+09 L (280 Mgal) of cured saltstone. The facility operates under a Disposal Authorization Statement from DOE and a permit from the South Carolina Department of Health and Environmental Control (SCDHEC). Since the start of operations in 1990, the SDF has received almost 6.7 E+07 L (18 Mgal) of DSS, resulting in the safe disposal of 2.7 E+16 Bq (7.3 E+05 Ci) of activity. Due to the radioactive decay of short-lived contaminants, the total remaining activity in the disposed waste is estimated to be approximately 1.4 E+16 Bq (3.9 E+05 Ci), as of September 2018. The Disposal Authorization Statement requires a demonstration that the system of engineered and natural features of the disposal facility will limit releases from the facility and be protective of human health and the environment for at least the next 1,000 years. The long-term performance of the facility was evaluated under the requirements of the DoE's Radioactive Waste Management Manual (US DOE Manual 435.1-1). Simulations were performed to demonstrate that the disposal facility would meet performance objectives specified in the manual. The evaluation was based on numerical models that simulate the releases of contaminants from the saltstone waste form. Contaminants were transported through groundwater and air pathways to points of assessment to evaluate compliance (i.e., 100 m from the SDUs). In addition, the potential consequences of an inadvertent human intrusion (IHI) were also evaluated. A number of issues were overcome during the development of these simulations. These issues were identified as part of internal technical reviews. Simulations are developed by people and people make mistakes, so the internal technical review process is a vital step in PA development. Specific examples of resolved issues include a unit-conversion error, an inappropriate definition for a model boundary condition, a model time-stepping issue, and an error in the calculation for the buildup of contaminants in soil. Actions taken to address these issues resulted in an improved product with a better supported technical basis and more defensible results. The identification and correction of these issues are discussed. By understanding these issues, model developers and technical reviewers working on PAs in the future may avoid repeating these types of mistakes. Transparency with respect to these mistakes builds trust between waste management sites, regulators, and stakeholders. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2025

Strong Correlation DMRG and DFT

This project developed new ways to improve computer simulations of materials where electrons interact strongly with each other, a challenge for today’s most widely used method, density functional theory (DFT). We used an exact numerical method, the density matrix renormalization group (DMRG), to create highly accurate reference results for simple model systems, and used these to test DFT, prove when it will converge, and even train machine-learned functionals. We also invented new kinds of localized basis functions (“gausslets” and “multi-sliced gausslets”) and a “sliced-basis” approach that make high-accuracy simulations faster and more practical. These methods were applied to extended hydrogen systems, enabling the direct derivation of accurate low-energy models from first-principles calculations. We also introduced a new formalism, Conditional-Probability DFT, which could bypass traditional approximations. The tools and results from this work, including open-source software releases, will help scientists design and understand complex quantum materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Probabilistic partition of unity networks for high–dimensional regression problems

We explore the probabilistic partition of unity network (PPOU-Net) model in the context of high-dimensional regression problems and propose a general framework focusing on adaptive dimensionality reduction. With the proposed framework, the target function is approximated by a mixture of experts model on a low-dimensional manifold, where each cluster is associated with a fixed-degree polynomial. We present a training strategy that leverages the expectation maximization (EM) algorithm. During the training, we alternate between (i) applying gradient descent to update the DNN coefficients; and (ii) using closed-form formulae derived from the EM algorithm to update the mixture of experts model parameters. Under the probabilistic formulation, step (ii) admits the form of embarrassingly paralleliazable weighted least-squares solves. The PPOU-Nets consistently outperform the baseline fully-connected neural networks of comparable sizes in numerical experiments of various data dimensions. Here, we also explore the proposed model in applications of quantum computing, where the PPOU-Nets act as surrogate models for cost landscapes associated with variational quantum circuits.

97 MATHEMATICS AND COMPUTING↗