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Lin, Lin

Publications and source records attributed to Lin, Lin.

At least 37 records · Page 2
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DOE OSTI2024

Finite-size effects in periodic coupled cluster calculations

Here, we provide the first rigorous study of the finite-size error in the simplest and representative coupled cluster theory, namely the coupled cluster doubles (CCD) theory, for gapped periodic systems. Given exact Hartree-Fock orbitals and their corresponding orbital energies, we demonstrate that the correlation energy obtained from the approximate CCD method, after a finite number of fixed-point iterations over the amplitude equation, exhibits a finite-size error scaling as $\mathcal{O}(N^{-\frac{1}{3}}_k)$. Here $N_k$ is the number of discretization points in the Brillouin zone and characterizes the system size. Under additional assumptions ensuring the convergence of the fixed-point iterations, we demonstrate that the CCD correlation energy also exhibits a finite-size error scaling as $\mathcal{O}(N^{-\frac{1}{3}}_k)$. Our analysis shows that the dominant error lies in the coupled cluster amplitude calculation, and the convergence of the finite-size error in energy calculation can be boosted to $\mathcal{O}(N^{-1}_k)$ with accurate amplitudes. This also provides the first proof of the scaling of the finite-size error in the third order Møller-Plesset perturbation theory (MP3) for periodic systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Green's function methods for multiphysics simulations (Final Report)

Green's functions are important tools for analyzing mathematical properties of partial differential equations (PDEs), and for numerically solving PDEs, especially when equations for the same operator but with multiple right hand sides need to be solved simultaneously. This proposal aims at developing efficient and accurate numerical methods for computing Green's functions, which can be used to tackle a challenging question in multiphysics simulation of DOE-mission science problems: how to couple quantum physics with classical physics. The key mathematical difficulty is properly formulate a "boundary condition" for the region described by quantum physics, and conventional approaches often model such boundary conditions in an empirical way. The proposed Green's function methods use the Dirichlet-to-Neumann map to formulate a boundary condition that is non-empirical and can couple the quantum and classical regions in an in principle exact way. The key ingredient of the new methods is to construct the Dirichlet-to-Neumann map in an efficient, accurate and versatile manner. The new methods have provably low complexity and are ideally suited for massively parallel and emerging many-core computational systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Simultaneous estimation of multiple eigenvalues with short-depth quantum circuit on early fault-tolerant quantum computers

We introduce a multi-modal, multi-level quantum complex exponential least squares (MM-QCELS) method to simultaneously estimate multiple eigenvalues of a quantum Hamiltonian on early fault-tolerant quantum computers. Our theoretical analysis demonstrates that the algorithm exhibits Heisenberg-limited scaling in terms of circuit depth and total cost. Notably, the proposed quantum circuit utilizes just one ancilla qubit, and with appropriate initial state conditions, it achieves significantly shorter circuit depths compared to circuits based on quantum phase estimation (QPE). Numerical results suggest that compared to QPE, the circuit depth can be reduced by around two orders of magnitude under several settings for estimating ground-state and excited-state energies of certain quantum systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

The Role of In-Cloud Wet Removal in Simulating Aerosol Vertical Profiles and Cloud Radiative Forcing

Among the physical processes controlling aerosol vertical profiles, in-cloud wet removal is of utmost importance while its representation in global climate models (GCMs) is crude. In this study, we implement into the Community Atmosphere Model version 6 (CAM6) a physically based aerosol wet removal parameterization scheme that explicitly treats aerosol activation, removal and resuspension. Evaluation against in-situ observations shows that the default scheme substantially overestimates the upper tropospheric black carbon (BC) and sea salt mass. Our physically based scheme reduces BC and sea salt mass by a factor of 10 and 1,000, respectively, in better agreement with observations. Also, the new scheme slightly increases number of aerosol particles between 12 nm and 4.8 μm in diameter, thereby mitigating the aerosol number underestimation in the default scheme. Our new scheme reduces the overestimation of coarse-mode aerosol (0.5–4.8 μm) number. Overall, the aerosol property changes (mass decrease and number increase) reduce the cloud condensation nuclei (CCN) concentration at low supersaturation (i.e., 0.02% and 0.1%), and increase CCN at high supersaturations (i.e., 0.5% and 1%). Consequently, the global annual mean cloud liquid water path increases by 1.89 g m -2 and the ice water path increases by 0.51 g m -2 . The global annual mean shortwave, longwave, and net cloud radiative forcing change by -1.06, 0.57, and -0.48 W m -2 , respectively. Further improvement is needed to reflect the real physics that the removal efficiencies for aerosol mass and number are disproportionate and to advect cloud-borne (activated) aerosols for a complete aerosol lifecycle.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Unified analysis of finite-size error for periodic Hartree-Fock and second order Møller-Plesset perturbation theory

Despite decades of practice, finite-size errors in many widely used electronic structure theories for periodic systems remain poorly understood. For periodic systems using a general Monkhorst-Pack grid, there has been no comprehensive and rigorous analysis of the finite-size error in the Hartree-Fock theory (HF) and the second order Møller-Plesset perturbation theory (MP2), which are the simplest wavefunction based method, and the simplest post-Hartree-Fock method, respectively. Such calculations can be viewed as a multi-dimensional integral discretized with certain trapezoidal rules. Due to the Coulomb singularity, the integrand has many points of discontinuity in general, and standard error analysis based on the Euler-Maclaurin formula gives overly pessimistic results. The lack of analytic understanding of finite-size errors also impedes the development of effective finite-size correction schemes. We propose a unified analysis to obtain sharp convergence rates of finite-size errors for the periodic HF and MP2 theories. Our main technical advancement is a generalization of the result of Lyness [Math. Comp. 30 (1976), pp. 1–23] for obtaining sharp convergence rates of the trapezoidal rule for a class of non-smooth integrands. Our result is applicable to three-dimensional bulk systems as well as low dimensional systems (such as nanowires and 2D materials). Our unified analysis also allows us to prove the effectiveness of the Madelung-constant correction to the Fock exchange energy, and the effectiveness of a recently proposed staggered mesh method for periodic MP2 calculations (see X. Xing, X. Li, and L. Lin [J. Chem. Theory Comput. 17 (2021), pp. 4733–4745]). In conclusion, our analysis connects the effectiveness of the staggered mesh method with integrands with removable singularities, and suggests a new staggered mesh method for reducing finite-size errors of periodic HF calculations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Orographic Cirrus and Its Radiative Forcing in NCAR CAM6

Cirrus clouds play an important role in the Earth's radiative energy budget, thereby affecting the climate state and climate change. Orographic gravity wave (OGW)-induced sub-grid scale vertical velocity (i.e., cooling rate) is not resolved by large-scale models and its impact on ice formation in cirrus clouds is not well quantified. In this study, one sub-grid scale OGW scheme (e.g., McFarlane) is used in the Community Atmosphere Model version 6 (CAM6) to generate vertical velocity variance (σw) for cirrus formation. Results from the default model and simulations with the OGW-induced σw are evaluated against the DOE ARM Small Particles in Cirrus (SPARTICUS) campaign observations. The OGW based on the McFarlane scheme increases the sub-grid scale σw over mountains compared to the default model and improves the model agreement with the SPARTICUS observations. Larger σ w due to OGWs can trigger more frequent homogeneous nucleation in orographic cirrus and generates a higher number concentration of ice crystals observed during the SPARTICUS campaign. Moreover, our evaluation of the model simulations against satellite observations indicates that the McFarlane scheme generates high in-cloud ice number concentrations (>200 L -1 ) in the upper troposphere over mountains and high plateaus at mid- and high-latitudes of the winter hemisphere as shown in the observations. More ice crystals with smaller sizes absorb more infrared radiation (+0.523 ± 0.125 W m -2 ). The net radiative cloud forcing change at the top of the atmosphere is +0.330 W m -2 due to the orographic cirrus.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Climate Impacts of Convective Cloud Microphysics in NCAR CAM5

Here we improved the treatments of convective cloud microphysics in the NCAR Community Atmosphere Model version 5.3 (CAM5.3) by 1) implementing new terminal velocity parameterizations for convective ice and snow particles, 2) adding graupel microphysics, 3) considering convective snow detrainment, and 4) enhancing rain initiation and generation rate in warm clouds. Furthermore, we evaluated the impacts of improved microphysics on simulated global climate, focusing on simulated cloud radiative forcing, graupel microphysics, convective cloud ice amount, and tropical precipitation. Compared to CAM5.3 with the default convective microphysics, the too-strong cloud shortwave radiative forcing due primarily to excessive convective cloud liquid is largely alleviated over the tropics and midlatitudes after rain initiation and generation rate is enhanced, in better agreement with the CERES-EBAF estimates. Geographic distributions of graupel occurrence are reasonably simulated over continents; whereas the graupel occurrence remains highly uncertain over the oceanic storm-track regions. When evaluated against the CloudSat–CALIPSO estimates, the overestimation of convective ice mass is alleviated with the improved convective ice microphysics, among which adding graupel microphysics and the accompanying increase in hydrometeor fall speed play the most important role. The probability distribution function (PDF) of rainfall intensity is sensitive to warm rain processes in convective clouds, and enhancement in warm rain production shifts the PDF toward heavier precipitation, which agrees better with the TRMM observations. Common biases of overestimating the light rain frequency and underestimating the heavy rain frequency in GCMs are mitigated.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Evaluating the evidence for exponential quantum advantage in ground-state quantum chemistry

Due to intense interest in the potential applications of quantum computing, it is critical to understand the basis for potential exponential quantum advantage in quantum chemistry. Here we gather the evidence for this case in the most common task in quantum chemistry, namely, ground-state energy estimation, for generic chemical problems where heuristic quantum state preparation might be assumed to be efficient. The availability of exponential quantum advantage then centers on whether features of the physical problem that enable efficient heuristic quantum state preparation also enable efficient solution by classical heuristics. Through numerical studies of quantum state preparation and empirical complexity analysis (including the error scaling) of classical heuristics, in both ab initio and model Hamiltonian settings, we conclude that evidence for such an exponential advantage across chemical space has yet to be found. While quantum computers may still prove useful for ground-state quantum chemistry through polynomial speedups, it may be prudent to assume exponential speedups are not generically available for this problem.

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

The 2022 High-energy Outburst and Radio Disappearing Act of the Magnetar 1E 1547.0–5408

We report the radio and high-energy properties of a new outburst from the radio-loud magnetar 1E 1547.0–5408. Following the detection of a short burst from the source with Swift-BAT on 2022 April 7, observations by NICER detected an increased flux peaking at (6.0 ± 0.4) × 10 –11 erg s –1 cm –2 in the soft X-ray band, falling to a baseline level of 1.7 × 10 –11 erg s –1 cm –2 over a 17 day period. Joint spectroscopic measurements by NICER and NuSTAR indicated no change in the hard nonthermal tail despite the prominent increase in soft X-rays. Observations at radio wavelengths with Murriyang, the 64 m Parkes radio telescope, revealed that the persistent radio emission from the magnetar disappeared at least 22 days prior to the initial Swift-BAT detection and was redetected two weeks later. Such behavior is unprecedented in a radio-loud magnetar, and may point to an unnoticed slow rise in the high-energy activity prior to the detected short bursts. Finally, our combined radio and X-ray timing revealed the outburst coincided with a spin-up glitch, where the spin frequency and spin-down rate increased by 0.2 ± 0.1 μHz and (–2.4 ± 0.1) × 10 –12 s –2 , respectively. A linear increase in the spin-down rate of (–2.0 ± 0.1) × 10 –19 s –3 was also observed over 147 days of postoutburst timing. Our results suggest that the outburst may have been associated with a reconfiguration of the quasi-polar field lines, likely signaling a changing twist, accompanied by spatially broader heating of the surface and a brief quenching of the radio signal, yet without any measurable impact on the hard X-ray properties.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Robust analytic continuation of Green's functions via projection, pole estimation, and semidefinite relaxation

Green's functions of fermions are described by matrix-valued Herglotz-Nevanlinna functions. Since analytic continuation is fundamentally an ill-posed problem, the causal space described by the matrix-valued Herglotz-Nevanlinna structure can be instrumental in improving the accuracy and in enhancing the robustness with respect to noise. We demonstrate a three-pronged procedure for robust analytic continuation called PES: (1) projection of data to the causal space; (2) estimation of pole locations; and (3) semidefinite relaxation within the causal space. We compare the performance of PES with the recently developed Nevanlinna and Carathéodory continuation methods and find that PES is more robust in the presence of noise and does not require the usage of extended precision arithmetics. We also demonstrate that a causal projection improves the performance of the Nevanlinna and Carathéodory methods. The PES method is generalized to bosonic response functions, for which the Nevanlinna and Carathéodory continuation methods have not yet been developed. Furthermore, it is particularly useful for studying spectra with sharp features, as they occur in the study of molecules and band structures in solids.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Explicitly antisymmetrized neural network layers for variational Monte Carlo simulation

The combination of neural networks and quantum Monte Carlo methods has arisen as a promising path forward for highly accurate electronic structure calculations. Previous proposals have combined equivariant neural network layers with a final antisymmetric layer in order to satisfy the antisymmetry requirements of the electronic wavefunction. However, to date it is unclear if one can represent antisymmetric functions of physical interest, and it is difficult to precisely measure the expressiveness of the antisymmetric layer. Here, this work attempts to address this problem by introducing explicitly antisymmetrized universal neural network layers. This approach has a computational cost which increases factorially with respect to the system size, but we are nonetheless able to apply it to small systems to better understand how the structure of the antisymmetric layer affects its performance. We first introduce a generic antisymmetric (GA) neural network layer, which we use to replace the entire antisymmetric layer of the highly accurate ansatz known as the FermiNet. We demonstrate that the resulting FermiNet-GA architecture can yield effectively the exact ground state energy for small atoms and molecules. We then consider a factorized antisymmetric (FA) layer which more directly generalizes the FermiNet by replacing the products of determinants with products of antisymmetrized neural networks. We find, interestingly, that the resulting FermiNet-FA architecture does not significantly outperform the FermiNet. This strongly suggests that the sum of products of antisymmetries is a key limiting aspect of the FermiNet architecture. To explore this further, we investigate a slight modification of the FermiNet, called the full determinant mode, which replaces each product of determinants with a single combined determinant. We find that the full single-determinant FermiNet closes a large part of the gap between the standard single-determinant FermiNet and FermiNet-GA on small atomic and molecular problems. Surprisingly, on the nitrogen molecule at a dissociating bond length of 4.0 Bohr, the full single-determinant FermiNet can outperform the largest standard FermiNet calculation with 64 determinants.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A quantum hamiltonian simulation benchmark

Hamiltonian simulation is one of the most important problems in quantum computation, and quantum singular value transformation (QSVT) is an efficient way to simulate a general class of Hamiltonians. However, the QSVT circuit typically involves multiple ancilla qubits and multi-qubit control gates. In order to simulate a certain class of n-qubit random Hamiltonians, we propose a drastically simplified quantum circuit that we refer to as the minimal QSVT circuit, which uses only one ancilla qubit and no multi-qubit controlled gates. We formulate a simple metric called the quantum unitary evolution score (QUES), which is a scalable quantum benchmark and can be verified without any need for classical computation. Under the globally depolarized noise model, we demonstrate that QUES is directly related to the circuit fidelity, and the potential classical hardness of an associated quantum circuit sampling problem. Under the same assumption, theoretical analysis suggests there exists an ‘optimal’ simulation time t opt ≈ 4.81, at which even a noisy quantum device may be sufficient to demonstrate the potential classical hardness.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

On the energy landscape of symmetric quantum signal processing

Symmetric quantum signal processing provides a parameterized representation of a real polynomial, which can be translated into an efficient quantum circuit for performing a wide range of computational tasks on quantum computers. For a given polynomial f , the parameters (called phase factors) can be obtained by solving an optimization problem. However, the cost function is non-convex, and has a very complex energy landscape with numerous global and local minima. It is therefore surprising that the solution can be robustly obtained in practice, starting from a fixed initial guess Φ 0 that contains no information of the input polynomial. To investigate this phenomenon, we first explicitly characterize all the global minima of the cost function. We then prove that one particular global minimum (called the maximal solution) belongs to a neighborhood of Φ 0 , on which the cost function is strongly convex under the condition ‖ f ‖ ∞ = O ( d − 1 ) with d = d e g ( f ) . Our result provides a partial explanation of the aforementioned success of optimization algorithms.

Wang, Jiasu↗
DOE OSTI2022

Microbe-iron interactions control lignin decomposition in soil

Lignin decomposition is critically linked to terrestrial carbon (C) cycle due to the enormous C mass of lignin and its importance in controlling overall rates of litter decomposition. Interactions between lignin and iron (Fe) minerals have been increasingly recognized as key mediators of lignin decomposition in experimental studies. However, we still lack a quantitative understanding of how Fe minerals interact with microbes to control lignin decomposition. Here, we leveraged experimental results from an incubation of Fe-rich soil, in which lignin decomposition rates were measured at aerobic conditions after four levels of pre-treated O2 availability, to examine microbe-Fe (MiFe) interactions in lignin decomposition with a MiFe model. We quantified how Fe redox cycling interacted with microbial activities to control lignin decomposition via data-model integration. Our results showed that the MiFe model with time-dependent growth and mortality functions better represented CO2 release from lignin decomposition (R2 ranging from 0.96 to 0.97) than models assuming either first-order or Michaelis-Menten kinetics. Reduction of Fe(III) to Fe(II) after pre-treatments with lower O2 availability stimu-lated the Fenton reaction to break down macro-molecular lignin into small molecules available to microbes. The small molecules of lignin and necromass bounded with oxidized Fe and were protected from decomposition. After 1-year incubation, the model implied that most of C stabilized with Fe minerals was derived from small molecular lignin C. Our quantitative analysis of microbe-Fe interactions sheds new light on lignin decomposition and preservation and helps improve model prediction of soil C persistence under global change.

Liao, Cuijuan↗
DOE OSTI2022

Towards sharp error analysis of extended Lagrangian molecular dynamics

The extended Lagrangian molecular dynamics (XLMD) method provides a useful framework for reducing the computational cost of a class of molecular dynamics simulations with constrained latent variables. The XLMD method relaxes the constraints by introducing a fictitious mass ε for the latent variables and solving a set of singularly perturbed ordinary differential equations. While favorable numerical performance of XLMD has been demonstrated in several different contexts in the past decade, mathematical analysis of the method remains scarce. Here, we propose the first error analysis of the XLMD method in the context of a classical polarizable force field model. While the dynamics with respect to the atomic degrees of freedom are general and nonlinear, the key mathematical simplification of the polarizable force field model is that the constraints on the latent variables are given by a linear system of equations. We prove that when the initial value of the latent variables is compatible in a sense that we define, XLMD converges as the fictitious mass ε is made small with $\mathscr{O}$(ε) error for the atomic degrees of freedom and with $\mathscr{O}$($\sqrt{ε}$) error for the latent variables, when the dimension of the latent variable d' is 1. Furthermore, when the initial value of the latent variables is improved to be optimally compatible in a certain sense, we prove that the convergence rate can be improved to $\mathscr{O}$(ε) for the latent variables as well. Numerical results verify that both estimates are sharp not only for d'=1, but also for arbitrary d'. In the setting of general d', we do obtain convergence, but with the non-sharp rate of $\mathscr{O}$($\sqrt{ε}$) for both the atomic and latent variables.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

KSSOLV 2.0: An efficient MATLAB toolbox for solving the Kohn-Sham equations with plane-wave basis set

KSSOLV (Kohn-Sham Solver) is a MATLAB toolbox for performing Kohn-Sham density functional theory (DFT) calculations with a plane-wave basis set. KSSOLV 2.0 preserves the design features of the original KSSOLV software to allow users and developers to easily set up a problem and perform ground-state calculations as well as to prototype and test new algorithms. Furthermore, it includes new functionalities such as new iterative diagonalization algorithms, k-point sampling for electron band structures, geometry optimization and advanced algorithms for performing DFT calculations with local, semi-local, and hybrid exchange-correlation functionals. It can be used to study the electronic structures of both molecules and solids. So, we describe these new capabilities in this work through a few use cases. We also demonstrate the numerical accuracy and computational efficiency of KSSOLV on a variety of examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Universal approximation of symmetric and anti-symmetric functions

In this work, we consider universal approximations of symmetric and anti-symmetric functions, which are important for applications in quantum physics, as well as other scientific and engineering computations. We give constructive approximations with explicit bounds on the number of parameters with respect to the dimension and the target accuracy ϵ. While the approximation still suffers from the curse of dimensionality, to the best of our knowledge, these are the first results in the literature with explicit error bounds for functions with symmetry or anti-symmetry constraints

97 MATHEMATICS AND COMPUTING↗