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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

The vertical-velocity skewness in the inertial sublayer of turbulent wall flows

Empirical evidence is provided that within the inertial sublayer (i.e. logarithmic region) of adiabatic turbulent flows over smooth walls, the skewness of the vertical-velocity component 𝑆 𝑤 displays universal behaviour, being a positive constant and constrained within the range 𝑆 𝑤 ≈ 0.1–0.16, regardless of flow configuration and Reynolds number. A theoretical model is then proposed to explain this behaviour, including the observed range of variations of 𝑆 𝑤 . The proposed model clarifies why 𝑆 𝑤 cannot be predicted from down-gradient closure approximations routinely employed in large-scale meteorological and climate models. The proposed model also offers an alternative and implementable approach for such large-scale models.

turbulent boundary layers↗
DOE OSTI2022

Application of Recursive Estimation to Heat Tracing for Groundwater/Surface‐Water Exchange

Abstract We present and demonstrate a recursive‐estimation framework to infer groundwater/surface‐water exchange based on temperature time series collected at different vertical depths below the sediment/water interface. We formulate the heat‐transport problem as a state‐space model (SSM), in which the spatial derivatives in the convection/conduction equation are approximated using finite differences. The SSM is calibrated to estimate time‐varying specific discharge using the Extended Kalman Filter (EKF) and Extended Rauch‐Tung‐Striebel Smoother (ERTSS). Whereas the EKF is suited to real‐time (“online”) applications and uses only the past and current measurements for estimation (filtering), the ERTSS is intended for near‐real time or batch‐processing (“offline”) applications and uses a window of data for batch estimation (smoothing). The two algorithms are demonstrated with synthetic and field‐experimental data and are shown to be efficient and rapid for the estimation of time‐varying flux over seasonal periods; further, the recursive approaches are effective in the presence of rapidly changing flux and (or) nonperiodic thermal boundary conditions, both of which are problematic for existing approaches to heat tracing of time‐varying groundwater/surface‐water exchange.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

The second-generation Shifted Boundary Method and its numerical analysis

Recently, the Shifted Boundary Method (SBM) was proposed within the class of unfitted (or immersed, or embedded) finite element methods. By reformulating the original boundary value problem over a surrogate (approximate) computational domain, the SBM avoids integration over cut cells and the associated problematic issues regarding numerical stability and matrix conditioning. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions. Hence the name of the method, that shifts the location and values of the boundary conditions. In this article, we present enhanced variational SBM formulations for the Poisson and Stokes problems with improved flexibility and robustness. These simplified variational forms allow to relax some of the assumptions required by the mathematical proofs of stability and convergence of earlier implementations. First, we show that these new SBM implementations can be proved asymptotically stable and convergent even without the rather restrictive assumption that the inner product between the normals to the true and surrogate boundaries is positive. Second, we show that it is not necessary to introduce a stabilization term involving the tangential derivatives of the solution at Dirichlet boundaries, therefore avoiding the calibration of an additional stabilization parameter. Finally, we prove enhanced L 2 -estimates without the cumbersome assumption – of earlier proofs – that the surrogate domain is convex. Instead we rely on a conventional assumption that the boundary of the true domain is smooth, which can also be replaced by requiring convexity of the true domain. The aforementioned improvements open the way to a more general and efficient implementation of the Shifted Boundary Method, particularly in complex three-dimensional geometries. We complement these theoretical developments with numerical experiments in two and three dimensions.

42 ENGINEERING↗
DOE OSTI2025

Sharp front tracking with geometric interface reconstruction

Here, this paper presents a novel sharp front-tracking method designed to address limitations in classical front-tracking approaches, specifically their reliance on smooth interpolation kernels and extended stencils for coupling the front and fluid mesh. In contrast, the proposed method employs exclusively sharp, localized interpolation and spreading kernels, restricting the coupling to the interfacial fluid cells–those containing the interface/front. This localized coupling is achieved by integrating a divergence-preserving velocity interpolation method with a piecewise parabolic interface calculation (PPIC) and a polyhedron intersection algorithm to compute the indicator function and local interface curvature. Surface tension is computed using the Continuum Surface Force (CSF) method, maintaining consistency with the sharp representation. Additionally, we propose an efficient local roughness smoothing implementation to account for surface mesh undulations, which is easily applicable to any triangulated surface mesh. Building on our previous work, the primary innovation of this study lies in the localization of the coupling for both the indicator function and surface tension calculations. By reducing the interface thickness on the fluid mesh to a single cell, as opposed to the 4–5 cell spans typical in classical methods, the proposed sharp front-tracking method achieves a highly localized and accurate representation of the interface. This sharper representation mitigates parasitic currents and improves force balancing, making it particularly suitable for scenarios where the interface plays a critical role, such as microfluidics, fluid-fluid interactions, and fluid-structure interactions. The proposed method is comprehensively validated and tested on canonical interfacial flow problems, including stationary and translating Laplace equilibria, oscillating droplets, and rising bubbles. The presented results demonstrate that the sharp front-tracking method significantly outperforms the classical approach in terms of accuracy, stability, and computational efficiency. Notably, parasitic currents are reduced by approximately two orders of magnitude and stable results are obtained for parameter ranges where classical front tracking fails to converge.

42 ENGINEERING↗
DOE OSTI2022

Comment on Comment on “Anomalous structural recovery in the near glass transition range in a polymer glass: Data revisited in light of temperature variability in vacuum oven‐based experiments”*

Abstract Cangialosi, Alegría, and Colmenero have made a comment on a paper of ours [Polym. Eng. Sci. 2022:1–13], in which we discussed the concern that the enthalpy recovery data reported by Cangialosi and co‐workers [Phys. Rev. Lett. 2013;111(9):095701] for polystyrene aged up to 15 K below glass transition temperature was anomalous and contradicted existing experimental results from the literature over a similar range of aging conditions. Their response shifts the focus away from the raised questions about their experimental results and attempts to invalidate the data that we cited in support of our argument. Here we respond to the comment and add additional analysis that suggests the structural recovery response of glassy materials exhibits smooth behavior over the full range of measurements, up to 7 or 8 logarithmic decades. We do this by referring to the work on the intrinsic isotherm down‐jump and memory responses of poly(vinyl acetate) between 40°C and 15°C over six logarithmic decades by Kovacs [Fortsch. Hochpolym. Fo. 1963;3(1/2):394–508], the small‐strain tensile creep of poly(vinyl chloride) quenched from 90°C to 40°C (approximately 40°C below T g ) over seven logarithmic decades from Struik [Polym Eng. Sci., 1977;17:165–173], and the volume recovery behavior for aging times up to 3 months in a temperature range between 95°C and −50°C by Greiner and Schwarzl [Rheol. Acta. 1984;23(4):378–395]. We also add discussion that an isothermal aging procedure using a vacuum oven is highly vulnerable to temperature errors due to the problem of good temperature control when the heat transfer mechanism is primarily radiative.

Jin, Shuang↗
DOE OSTI2024

Via Machinae 2.0 : Full-sky, model-agnostic search for stellar streams in Gaia DR2

ABSTRACT We present an update to Via Machinae, an automated stellar stream-finding algorithm based on the deep learning anomaly detector ANODE. Via Machinae identifies stellar streams within Gaia, using only angular positions, proper motions, and photometry, without reference to a model of the Milky Way potential for orbit integration or stellar distances. This new version, Via Machinae 2.0, includes many improvements and refinements to nearly every step of the algorithm, that altogether result in more robust and visually distinct stream candidates than our original formulation. In this work, we also provide a quantitative estimate of the false positive rate of Via Machinae 2.0 by applying it to a simulated Gaia-mock catalogue based on galaxia, a smooth model of the Milky Way that does not contain substructure or stellar streams. Finally, we perform the first full-sky search for stellar streams with Via Machinae 2.0, identifying 102 streams at high significance within the Gaia Data Release 2, of which only 10 have been previously identified. While follow-up observations for further confirmation are required, taking into account the false positive rate presented in this work, we expect approximately 90 of these stream candidates to correspond to real stellar structures.

Astronomy & Astrophysics↗
DOE OSTI2021

Optimal Protocols in Quantum Annealing and Quantum Approximate Optimization Algorithm Problems

Quantum annealing (QA) and the quantum approximate optimization algorithm (QAOA) are two special cases of the following control problem: apply a combination of two Hamiltonians to minimize the energy of a quantum state. Which is more effective has remained unclear. Here we analytically apply the framework of optimal control theory to show that generically, given a fixed amount of time, the optimal procedure has the pulsed (or “bang-bang”) structure of QAOA at the beginning and end but can have a smooth annealing structure in between. This is in contrast to previous works which have suggested that bang-bang (i.e., QAOA) protocols are ideal. To support this theoretical work, we carry out simulations of various transverse field Ising models, demonstrating that bang-anneal-bang protocols are more common. Futher, the general features identified here provide guideposts for the nascent experimental implementations of quantum optimization algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Enabling probabilistic learning on manifolds through double diffusion maps

Here, we present a generative learning framework for probabilistic sampling that extends Probabilistic Learning on Manifolds (PLoM), which is designed to generate statistically consistent realizations of a random vector in a finite-dimensional Euclidean space, informed by a (representative) set of observations. In its original form, PLoM constructs a reduced-order probabilistic model by combining three main components: (a) kernel density estimation to approximate the underlying probability measure, (b) Diffusion Maps to characterize the manifold of the data, and (c) a reduced-order Itô Stochastic Differential Equation (ISDE) to sample from the learned distribution. However, its sampling dynamics are posed in the ambient space and the retained number of reduced coordinates is chosen by projection-reconstruction error. In practice, this often (i) requires more coordinates than the data’s intrinsic dimension to achieve stable sampling and (ii) lacks a smooth, basis-independent lifting back to the data domain; moreover, standard Diffusion Maps emphasize harmonic eigenfunctions and can miss non-harmonic latent structure. We address these limitations by decoupling geometry learning from sampling: a first Diffusion Maps pass identifies non-harmonic coordinates on which we formulate a full-order ISDE directly in the latent space, while Double Diffusion Maps captures multiscale geometric features and Geometric Harmonics (GH) learns a smooth lifting map to the ambient variables that is independent of the particular diffusion basis. This hybrid design preserves the system’s dynamical richness with a compact geometric representation and enables principled out-of-sample inference. The effectiveness and robustness of the proposed method are illustrated through two numerical studies: one based on data generated from two-dimensional Hermite polynomial functions and another based on high-fidelity simulations of a detonation wave in a reactive flow.

Double diffusion maps↗
DOE OSTI2022

Computational study of inertial migration of prolate particles in a straight rectangular channel

Inertial migration of spherical particles has been investigated extensively using experiments, theory, and computational modeling. Yet, a systematic investigation of the effect of particle shape on inertial migration is still lacking. Herein, we numerically mapped the migration dynamics of a prolate particle in a straight rectangular microchannel using smoothed particle hydrodynamics at moderate Reynolds number flows. After validation, we applied our model to 2:1 and 3:1 shape aspect ratio particles at multiple confinement ratios. Their effects on the final focusing position, rotational behavior, and transitional dynamics were studied. In addition to the commonly reported tumbling motion, for the first time, we identified a new logrolling behavior of a prolate ellipsoidal particle in the confined channel. This new behavior occurs when the confinement ratio is above an approximate threshold value of K = 0.72. Our microfluidic experiments using cell aggregates with similar shape aspect ratio and confinement ratio confirmed this new predicted logrolling motion. In this study, we also found that the same particle can undergo different rotational modes, including kayaking behavior, depending on its initial cross-sectional position and orientation. Furthermore, we examined the migration speed, angular velocity, and rotation period as well as their dependence on both particle shape aspect ratio and confinement ratio. Our findings are especially relevant to the applications where particle shape and alignment are used for sorting and analysis, such as the use of barcoded particles for biochemical assays through optical reading, or the shape-based enrichment of microalgae, bacteria, and chromosomes.

42 ENGINEERING↗
DOE OSTI2025

Coal to Carbon Fiber (C2CF) Continuous Processing for High Value Composites (Final Report)

Coal tar is a condensed and recovered by-product of the coking of metallurgical coal for steel production. The heaviest fraction of distilled coal tar is an isotropic pitch largely used as a binder in the manufacturing of carbonaceous electrodes for primary aluminum smelting and in electric arc furnaces. Coal tar pitch offers high carbon yield upon carbonization. In this project, a process to convert the domestically sourced isotropic coal tar pitch, containing very low particulates (QI = 0.32 wt.%), to form flow-domain mesophase pitch amenable for melt spinning into precursor (green) fibers for carbon fiber, was developed and optimized. The final reproducible processing developed is reviewed in this report, along with several characterizations of the mesophase pitch. A final definition of the characteristics of a ‘spinnable’ mesophase pitch is presented. With this mesophase pitch, reproducible and stable multifilament melt spinning was developed, producing green fiber tows with filament diameters of approximately 20 m. The multifilament melt spinning was the most challenging aspect of the project and required the most effort. The best practices learned from this project for melt spinning are reviewed in this report. Once spun, the green fibers were oxidatively stabilized, carbonized and graphitized under inert gas atmosphere to form the final carbon fibers. Given the relatively high softening point of the mesophase pitch, no issues of interfilament fusion were observed during batch oxidation, and subsequent batch carbonization and graphitization went smoothly in all cases. An ~ 80 wt.% conversion of the green fiber mass to final carbon fiber was achieved. After graphitization, the carbon fibers showed high tensile moduli (most were ~ 600 GPa, or 87 Msi) consistent with commercially-available high-performance pitch-based carbon fiber. However, tensile strength and strain to failure were comparatively low. Further work to reduce defects in and on the fiber surfaces would increase these properties. SEM imaging of the graphitic fiber textures is presented herein. Rudimentary composites were fabricated from the carbon fibers and characterized showing similar modulus to baseline composites fabricated with commercial carbon fiber. Finally, a basic economic analysis was done showing the potential to increase the value of the isotropic coal tar pitch by up to 13.6 to 136 times based on a carbon fiber value of $\$$5/lb to $\$$50/lb, respectively. Moreover, the site case study suggests that the coal tar from the single integrated steel mill could supply production of up to 16 kt/yr of carbon fiber. Finally, a technological gap analysis was done which shed light on remaining technical challenges. These challenges included: recovery and utilization of condensates from the mesophase pitch processing, further advancing and increasing stability of the multifilament melt spinning processing, optimization of the oxidation processing, defect reduction for increased carbon fiber strength, and the development of a weaving process towards carbon fiber fabrics. To maximize the coal value chain, the primary objectives of this project were to (a) develop and scale efficient processing technology for producing melt-spinnable mesophase pitch from isotropic coal tar pitch, (b) clarify and simplify tedious continuous fiber processing technologies (particularly multifilament melt spinning of mesophase pitch) towards the efficient production of high performance carbon fiber, and (c) demonstrate and characterize representative composite parts derived from the final carbon fiber. Immense progress was made on all 3 objectives and is detailed in this report.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2022

FSISPH: An SPH formulation for impacts between dissimilar materials

Here, we present an SPH formulation with several new features designed to better model the fully-compressible interaction of dissimilar materials. We developed the new method to simulate the atmospheric entry and break-up of small celestial bodies in planetary atmospheres. The formulation uses a unity-based, density-energy discretization of the hydrodynamic conservation laws with linear-corrected kernel gradients. To account for variations in compressibility, we use an HLLC approximate Riemann solver to adjust the velocity gradient at material interfaces. To handle large transverse velocity discontinuities, we introduce a simple slip interface model that limits the artificial viscosity at material interfaces. Diffusion is optionally applied through the velocity gradient and this allows the density and specific thermal energy to evolve in a manner more consistent with the first law of thermodynamics in comparison to other more direct diffusion schemes. We also introduce a material-local second-order artificial conduction scheme used to smooth the specific thermal energy field. Material damage fits neatly under this framework by treating the damage front as a material interface. The method has been implemented as a solver, FSISPH, within the code, Spheral++, and is publicly available on github. We test our new solver on a number of classic shock, mixing, and multi-material problem. The components we outline can significantly improve accuracy of SPH for problems with sharp contact discontinuities.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Projections of two-particle correlations onto transverse rapidity in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV at STAR

Two-particle correlation measurements projected onto two-dimensional, transverse rapidity coordinates (y T1 ,y T2 ), allow access to dynamical properties of the QCD medium produced in relativistic heavy-ion collisions that angular correlation measurements are not sensitive to. Here, we report non-identified charged-particle correlations for Au + Au minimum-bias collisions at $\sqrt{s_{NN}}$ = 200 GeV taken by the STAR experiment at the Relativistic Heavy-Ion Collider (RHIC). Correlations are presented as 2D functions of transverse rapidity for like-sign, unlike-sign and all charged-particle pairs, as well as for particle pairs whose relative azimuthal angles lie on the near-side, the away-side, or at all relative azimuth. The correlations are constructed using charged particles with transverse momentum p T ≥ 0.15 GeV/c, pseudorapidity from –1 to 1, and azimuthal angles from –π to π. The significant correlation structures that are observed evolve smoothly with collision centrality. The major correlation features include a saddle shape plus a broad peak with maximum near y T ≈ 3, corresponding to p T ≈ 1.5 GeV/c. The broad peak is observed in both like- and unlike-sign charge combinations and in near- and away-side relative azimuthal angles. The all-charge, all-azimuth correlation measurements are compared with the theoretical predictions of HIJING and EPOS. The results indicate that the correlations for peripheral to mid-central collisions can be approximately described as a superposition of nucleon + nucleon collisions with minimal effects from the QCD medium. Strong medium effects are indicated in mid- to most-central collisions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Coordinate-Based Seismic Interpolation in Irregular Land Survey: A Deep Internal Learning Approach

Physical and budget constraints often result in irregular sampling, which complicates accurate subsurface imaging. Preprocessing approaches, such as missing trace or shot interpolation, are typically employed to enhance seismic data in such cases. Recently, deep learning has been used to address the trace interpolation problem at the expense of large amounts of training data to adequately represent typical seismic events. Nonetheless, most research in this area has focused on trace reconstruction, with little attention having been devoted to shot interpolation. Furthermore, existing methods assume regularly spaced receivers/sources failing in approximating seismic data from real (irregular) surveys. This work presents a novel shot gather interpolation approach which uses a continuous coordinate-based representation of the acquired seismic wavefield parameterized by a neural network. The proposed unsupervised approach, which we call coordinate-based seismic interpolation (CoBSI), enables the prediction of specific seismic characteristics in irregular land surveys without using external data during neural network training. Importantly, experimental results on real and synthetic 3-D data validate the ability of the proposed method to estimate continuous smooth seismic events in the time-space and frequency-wavenumber domains, improving sparsity or low-rank-based interpolation methods.

58 GEOSCIENCES↗
DOE OSTI2021

Compositional patterning in irradiated alloys: Effective potentials and effective interfacial energy

Compositional patterning (CP) in binary alloys during energetic particle irradiation is studied using a kinetic model that considers two competing kinetic processes, a thermally activated one promoting macroscopic phase separation (MPS) of the concentration field c(r,t) and a forced one resulting in finite-range random atomic mixing. The forced mixing is modeled by a Gaussian relocation distribution with a characteristic distance R. A series of approximate kinetic models are introduced by expanding the mixing function into a series of n terms, thus replacing the non-local evaluations of the concentration field c(r'-r,t) by local derivatives of c(r,t). This approach makes it possible to obtain exact effective potentials and build steady-state diagrams for each order-n model. Phase field (PF) simulations using these order-n models reveal that near the onset of patterning, phase evolution is accurately described using an order-3 model, which changes smoothly from an extended Cahn-Hilliard free energy in the MPS regime to a one-mode Swift-Hohenberg functional in the CP regime. Deeper into the patterning regime, higher-order models are required to achieve convergence, yielding square-like concentration profiles characteristic of a strong segregation regime. These higher-order effective free energies are analogous to multimodal Swift-Hohenberg functionals. Here, a new definition for the effective interfacial energy is proposed in the CP regime, since the interfacial area is no longer an excess quantity in that regime, precluding the use of the standard thermodynamic definition of interfacial energy.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Meshfree Methods

Meshfree methods have undergone substantial development and have received much attention in the last two decades. This new family of numerical methods is designed to inherit the main advantages of the finite element method such as compact supports of shape functions and good approximation properties while, at the same time, overcome the main disadvantages of the finite element method caused by the mesh dependence. The meshfree methods share a common feature that no mesh is needed and shape functions are constructed from sets of points, thus eliminating the need for time consuming mesh generation. The most significant advantage of meshfree methods is the flexibility in customizing approximation functions for desired regularity and for capturing essential physics and features of the particular problems of interest. Adaptivity formulation and multiple-scale solution strategies also can be implemented with relative ease. It has become clear that the meshfree methods provide considerable advantages over the conventional finite element methods in solving problems involving moving discontinuities, evolving material interfaces, multiple-scale phenomena, large material distortion and structural deformation, and fracture and damage processes. This Chapter gives an overview of many classes of meshfree methods, with more detailed discussions on Smoothed Particle Hydrodynamics (SPH), the Reproducing Kernel Particle Method (RKPM), Peridynamics (PD), the Material Point Method (MPM), as well as their applications in various challenging engineering problems.2

Chen, Jiun-Shyan↗
DOE OSTI2024

Self-Cleaning Highly Porous TiO 2 Coating Designed by Swelling-Assisted Sequential Infiltration Synthesis (SIS) of a Block Copolymer Template

Photocatalytic self-cleaning coatings with a high surface area are important for a wide range of applications, including optical coatings, solar panels, mirrors, etc. Here, we designed a highly porous TiO 2 coating with photoinduced self-cleaning characteristics and very high hydrophilicity. This was achieved using the swelling-assisted sequential infiltration synthesis (SIS) of a block copolymer (BCP) template, which was followed by polymer removal via oxidative thermal annealing. The quartz crystal microbalance (QCM) was employed to optimize the infiltration process by estimating the mass of material infiltrated into the polymer template as a function of the number of SIS cycles. This adopted swelling-assisted SIS approach resulted in a smooth uniform TiO 2 film with an interconnected network of pores. The synthesized film exhibited good crystallinity in the anatase phase. The resulting nanoporous TiO 2 coatings were tested for their functional characteristics. Exposure to UV irradiation for 1 h induced an improvement in the hydrophilicity of coatings with wetting angle reducing to unmeasurable values upon contact with water droplets. Furthermore, their self-cleaning characteristics were tested by measuring the photocatalytic degradation of methylene blue (MB). The synthesized porous TiO 2 nanostructures displayed promising photocatalytic activity, demonstrating the degradation of approximately 92% of MB after 180 min under ultraviolet (UV) light irradiation. Thus, the level of performance was comparable to the photoactivity of commercial anatase TiO 2 nanoparticles of the same quantity. Our results highlight a new robust approach for designing hydrophilic self-cleaning coatings with controlled porosity and composition.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Implicit shock tracking for unsteady flows by the method of lines

Here, a recently developed high-order implicit shock tracking (HOIST) framework for resolving discontinuous solutions of inviscid, steady conservation laws is extended to the unsteady case. Central to the framework is an optimization problem which simultaneously computes a discontinuity-aligned mesh and the corresponding high-order approximation to the flow, which provides nonlinear stabilization and a high-order approximation to the solution. This work extends the implicit shock tracking framework to the case of unsteady conservation laws using a method of lines discretization via a diagonally implicit Runge-Kutta method by “solving a steady problem at each timestep”. We formulate and solve an optimization problem that produces a feature-aligned mesh and solution at each Runge-Kutta stage of each timestep, and advance this solution in time by standard Runge-Kutta update formulas. A Rankine-Hugoniot based prediction of the shock location together with a high-order, untangling mesh smoothing procedure provides a high-quality initial guess for the optimization problem at each time, which results in rapid convergence of the sequential quadratic programing (SQP) optimization solver. This method is shown to deliver highly accurate solutions on coarse, high-order discretizations without nonlinear stabilization and recover the design accuracy of the Runge-Kutta scheme. We demonstrate this framework on a series of inviscid, unsteady conservation laws in both one- and two- dimensions. We also verify that our method is able to recover the design order of accuracy of our time integrator in the presence of a strong discontinuity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

A deep potential model with long-range electrostatic interactions

Machine learning models for the potential energy of multi-atomic systems, such as the deep potential (DP) model, make molecular simulations with the accuracy of quantum mechanical density functional theory possible at a cost only moderately higher than that of empirical force fields. However, the majority of these models lack explicit long-range interactions and fail to describe properties that derive from the Coulombic tail of the forces. To overcome this limitation, we extend the DP model by approximating the long-range electrostatic interaction between ions (nuclei + core electrons) and valence electrons with that of distributions of spherical Gaussian charges located at ionic and electronic sites. The latter are rigorously defined in terms of the centers of the maximally localized Wannier distributions, whose dependence on the local atomic environment is modeled accurately by a deep neural network. In the DP long-range (DPLR) model, the electrostatic energy of the Gaussian charge system is added to short-range interactions that are represented as in the standard DP model. The resulting potential energy surface is smooth and possesses analytical forces and virial. Missing effects in the standard DP scheme are recovered, improving on accuracy and predictive power. By including long-range electrostatics, DPLR correctly extrapolates to large systems the potential energy surface learned from quantum mechanical calculations on smaller systems. We illustrate the approach with three examples: the potential energy profile of the water dimer, the free energy of interaction of a water molecule with a liquid water slab, and the phonon dispersion curves of the NaCl crystal.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗