Simulation Of Large Systems Research Articles

Nonparametric Analysis of Nonequilibrium Simulations.

We extend the nonparametric framework of reaction coordinate optimization to nonequilibrium ensembles of (short) trajectories. For example, we show how, starting from such an ensemble, one can obtain an equilibrium free-energy profile along the committor, which can be used to determine important properties of the dynamics exactly. A new adaptive sampling approach, the transition-state ensemble enrichment, is suggested, which samples the configuration space by "growing" committor segments toward each other starting from the boundary states. This framework is suggested as a general tool, alternative to the Markov state models, for a rigorous and accurate analysis of simulations of large biomolecular systems, as it has the following attractive properties. It is immune to the curse of dimensionality, does not require system-specific information, can approximate arbitrary reaction coordinates with high accuracy, and has sensitive and rigorous criteria to test optimality and convergence. The approaches are illustrated on a 50-dimensional model system and a realistic protein folding trajectory.

Computational Fluid Dynamics Study of NACA 0012 Airfoil Performance with OpenFOAM®

Numerical methodologies have been implemented in most recent years in order to predict the lift and drag coefficients, the flow velocity, and the pressure distributions around the airfoil profiles in order to develop powerful computational tools based on the analysis of the main features, which describe the optimal wing or blade performance and predict a functional aerodynamic profile implemented to obtain the better energy efficiency generated, for different airplane designs. Computational Fluid Dynamics (CFD) analysis, computation, and prediction of inviscid and viscous two-dimensional flows are based on unsteady simulations of large systems with linear equations solved in a reasonable amount of computing resources. In this sense, Reynolds Averaged Navier Stokes (RANS) approach is generally applied for simulating the mean quantities of turbulent flows with high efficiency in the solving of differential equations of fluid flows into the control volume. However, Large Eddy Simulations are widely recognized to capture the main turbulent effects in a free stream influenced by the inertial forces of the airfoil displacement. Therefore, this research presents a CFD study of the NACA 0012 airfoil with the aim of checking the level of prediction and the numerical performance methodologies proposed by recent numerical reviews developed to study the description of turbulent flows analyzed with the Navier Stokes equations for incompressible flows with small temperature differences between the airfoil surface, and the air free stream. Numerical results have been analyzed in order to compare URANS and LES data used to predict physical variables and turbulent quantities that perform the airfoil profile in the virtual environment offered by OpenFOAM software.

AENET-LAMMPS and AENET-TINKER: Interfaces for accurate and efficient molecular dynamics simulations with machine learning potentials.

Machine-learning potentials (MLPs) trained on data from quantum-mechanics based first-principles methods can approach the accuracy of the reference method at a fraction of the computational cost. To facilitate efficient MLP-based molecular dynamics and Monte Carlo simulations, an integration of the MLPs with sampling software is needed. Here, we develop two interfaces that link the atomic energy network (ænet) MLP package with the popular sampling packages TINKER and LAMMPS. The three packages, ænet, TINKER, and LAMMPS, are free and open-source software that enable, in combination, accurate simulations of large and complex systems with low computational cost that scales linearly with the number of atoms. Scaling tests show that the parallel efficiency of the ænet-TINKER interface is nearly optimal but is limited to shared-memory systems. The ænet-LAMMPS interface achieves excellent parallel efficiency on highly parallel distributed-memory systems and benefits from the highly optimized neighbor list implemented in LAMMPS. We demonstrate the utility of the two MLP interfaces for two relevant example applications: the investigation of diffusion phenomena in liquid water and the equilibration of nanostructured amorphous battery materials.

Accelerating Simulations of Large Scale Phased-Array Systems

Next generation wireless communications systems operating at millimeter-wave frequencies are utilizing phased arrays of increasing electrical size to overcome path loss. The size of these arrays can make simulations become infeasible due to the amount of computation and memory required. Here we discuss parallelization and hardware acceleration methods to overcome these obstacles for large scale phased array systems. The acceleration of these methods was quantified using an orthogonal frequency division multiplexing frequency-domain simulator.

Simulation of Large Aggregate Particles System With a New Morphological Model

For the development of a new porous material such as catalytic carrier, the control of the textural properties is of fundamental importance. In order to move towards rational synthesis, it is necessary to better understand the physical phenomena that generate a defined solid structure. A contribute to this purpose can be achieved by studying the aggregation process inside colloidal suspensions, leading to porosity generation: this phenomenon can be described with a Brownian dynamics model that, for any set of chemical parameters, gives access to the mass distribution and the fractal dimension of colloidal aggregates. However, this model cannot be used for the simulation of large colloidal systems, due to its high computational time, limiting comparison with analytical methods, which probe the whole multi-scale system. This problem is solved by developing a new aggregation morphological model, wherein the fractal dimension is tuned with two compactness parameters. An efficient simulation algorithm is proposed in case of spheres, for which the fractal dimension of the generated aggregates varies between 1.2 and 3. Brownian dynamics results are used to parametrize this purely geometric model, in order to constrain the size and the morphology of the aggregates created. The large numerical solid will be representative of the textural properties of a real solid and will give more information on the porous network. It could be used, for example, to simulate diffusive transport coupled with chemical reaction and to study the impact of the geometry of the porous system on the catalytic performance.

The study of the optical phonon frequency of 3C-SiC by molecular dynamics simulations with deep neural network potential

In this work, we implement molecular dynamics (MD) simulations with deep neural network (DNN) potential trained with the datasets from ab initio calculations to determine the dielectric spectra of crystal. The fluctuations of the total dipole moment of crystal, which are obtained from MD, can be directly related to the frequency-dependent permittivity according to the work of Neumann and Steinhauser [Chem. Phys. Lett. 102, 508–513 (1983)]. We generalize their theoretical work to express the permittivity in the form of a tensor and perform MD simulations for cubic silicon carbide (3C-SiC) with 8000 atoms to assess the accuracy. The infrared resonance frequency and the phonon linewidth obtained by the DNN potential are compared with those obtained by the empirical Vashishta potential and experiments. The results of the DNN potential are in good agreement with the experimental measurements. It shows that we can carry out MD simulations for large systems with the accuracy of ab initio calculations to obtain dielectric properties.

Projector-Free Capped-Fragment Scheme within Density Functional Embedding Theory for Covalent and Ionic Compounds.

Quantum-mechanics-(QM)-based simulations now routinely aid in understanding and even discovering new chemistries involving molecules and materials exhibiting desired functionalities. Ab initio correlated wavefunction (CW) theories systematically improve QM methods, with many exhibiting high accuracy. However, execution of CW methods requires expensive computations that typically scale poorly with system size. Divide-and-conquer approaches partition large systems into smaller fragments; a lower level of theory treats fragment interactions while a preferred higher level of theory describes the important fragment. These methods offer ways to incorporate CWs into chemical simulations of large systems, e.g., biomolecules, surfaces, large inorganic clusters, bulk crystals, etc. Here we propose a partitioning protocol that utilizes capping atoms to saturate severed covalent bonds at fragment interfaces and density functional embedding theory (DFET) to describe fragment interactions. The capping groups in each fragment provide an ad-hoc potential that approximates the effects of the environment. An embedding potential optimized via DFET then serves as an augmentation of the capping group to simulate the effects of the environment. We concurrently use an auxiliary fragment (a separate system comprised of only the combined capping groups) to account for, and thereby correct, the electron density contributions of all the capping groups added to all of the fragments. This method depends only on the capped-subsystem and auxiliary-fragment electron densities, forgoing, as with the original DFET developed for metallic systems, orbital-based projector approaches that determine a nonlocal action of the embedding potential onto the fragment electrons. By using an auxiliary fragment, the method maintains a purely electron-density-dependent embedding potential, substantially lessening the cost and leading to simpler implementation. Here, we demonstrate the utility of our capped-DFET and ensuing capped embedded CW method in two contrasting systems, namely, an organic molecule and an ionic metal oxide cluster.

Linear embedding of nonlinear dynamical systems and prospects for efficient quantum algorithms

The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic computational plasma physics. This motivates exploring whether a future error-corrected quantum computer could perform these simulations more efficiently than any classical computer. We describe a method for mapping any finite nonlinear dynamical system to an infinite linear dynamical system (embedding) and detail three specific cases of this method that correspond to previously studied mappings. Then we explore an approach for approximating the resulting infinite linear system with finite linear systems (truncation). Using a number of qubits only logarithmic in the number of variables of the nonlinear system, a quantum computer could simulate truncated systems to approximate output quantities if the nonlinearity is sufficiently weak. Other aspects of the computational efficiency of the three detailed embedding strategies are also discussed.

Parallel quantum simulation of large systems on small NISQ computers

Tensor networks permit computational and entanglement resources to be concentrated in interesting regions of Hilbert space. Implemented on NISQ machines they allow simulation of quantum systems that are much larger than the computational machine itself. This is achieved by parallelising the quantum simulation. Here, we demonstrate this in the simplest case; an infinite, translationally invariant quantum spin chain. We provide Cirq and Qiskit code that translates infinite, translationally invariant matrix product state (iMPS) algorithms to finite-depth quantum circuit machines, allowing the representation, optimisation and evolution of arbitrary one-dimensional systems. The illustrative simulated output of these codes for achievable circuit sizes is given.

Structure determination of an amorphous drug through large-scale NMR predictions

Knowledge of the structure of amorphous solids can direct, for example, the optimization of pharmaceutical formulations, but atomic-level structure determination in amorphous molecular solids has so far not been possible. Solid-state nuclear magnetic resonance (NMR) is among the most popular methods to characterize amorphous materials, and molecular dynamics (MD) simulations can help describe the structure of disordered materials. However, directly relating MD to NMR experiments in molecular solids has been out of reach until now because of the large size of these simulations. Here, using a machine learning model of chemical shifts, we determine the atomic-level structure of the hydrated amorphous drug AZD5718 by combining dynamic nuclear polarization-enhanced solid-state NMR experiments with predicted chemical shifts for MD simulations of large systems. From these amorphous structures we then identify H-bonding motifs and relate them to local intermolecular complex formation energies.

Stable iPEPO Tensor-Network Algorithm for Dynamics of Two-Dimensional Open Quantum Lattice Models

Being able to describe accurately the dynamics and steady-states of driven and/or dissipative but quantum correlated lattice models is of fundamental importance in many areas of science: from quantum information to biology. An efficient numerical simulation of large open systems in two spatial dimensions is a challenge. In this work, we develop a tensor network method, based on an infinite Projected Entangled Pair Operator (iPEPO) ansatz, applicable directly in the thermodynamic limit. We incorporate techniques of finding optimal truncations of enlarged network bonds by optimising an objective function appropriate for open systems. Comparisons with numerically exact calculations, both for the dynamics and the steady-state, demonstrate the power of the method. In particular, we consider dissipative transverse quantum Ising and driven-dissipative hard core boson models in non-mean field limits, proving able to capture substantial entanglement in the presence of dissipation. Our method enables to study regimes which are accessible to current experiments but lie well beyond the applicability of existing techniques.

Coarse-grained model of a nanoscale-segregated ionic liquid for simulations of low-temperature structure and dynamics

We perform molecular dynamics simulations to study the structure and dynamics of the ionic liquid [Omim][TFSI] in a broad temperature range. A particular focus is the progressing nanoscale segregation into polar and nonpolar regions upon cooling. As this analysis requires simulations of large systems for long times, we use the iterative Boltzmann inversion method to develop a new coarse-grained (CG) model from a successful all-atom (AA) model. We show that the properties are similar for both levels of description at room temperature, while the CG model shows stronger nanoscale segregation and faster diffusion dynamics than its AA counterpart at low temperatures. Exploiting these features of the CG model, we find that the characteristic length scale of the structural inhomogeneity nearly doubles to ∼3 nm when the temperature is decreased to about 200 K. Moreover, we observe that the nanoscale segregation is characterized by a bicontinuous morphology. In worm-like nonpolar regions, the ends of the octyl rests of the cations preferentially aggregate in the centers, while the other parts of the alkyl chains tend to be aligned parallel on a next-neighbor level and point outward, allowing for an integration of the imidazolium head groups of the cations into polar regions together with the anions, resembling to some degree the molecular arrangement in cylindrical micelles.

A bin and hash method for analyzing reference data and descriptors in machine learning potentials

In recent years the development of machine learning potentials (MLPs) has become a very active field of research. Numerous approaches have been proposed, which allow one to perform extended simulations of large systems at a small fraction of the computational costs of electronic structure calculations. The key to the success of modern MLPs is the close-to first principles quality description of the atomic interactions. This accuracy is reached by using very flexible functional forms in combination with high-level reference data from electronic structure calculations. These data sets can include up to hundreds of thousands of structures covering millions of atomic environments to ensure that all relevant features of the potential energy surface are well represented. The handling of such large data sets is nowadays becoming one of the main challenges in the construction of MLPs. In this paper we present a method, the bin-and-hash (BAH) algorithm, to overcome this problem by enabling the efficient identification and comparison of large numbers of multidimensional vectors. Such vectors emerge in multiple contexts in the construction of MLPs. Examples are the comparison of local atomic environments to identify and avoid unnecessary redundant information in the reference data sets that is costly in terms of both the electronic structure calculations as well as the training process, the assessment of the quality of the descriptors used as structural fingerprints in many types of MLPs, and the detection of possibly unreliable data points. The BAH algorithm is illustrated for the example of high-dimensional neural network potentials using atom-centered symmetry functions for the geometrical description of the atomic environments, but the method is general and can be combined with any current type of MLP.

Four Generations of High-Dimensional Neural Network Potentials.

Since their introduction about 25 years ago, machine learning (ML) potentials have become an important tool in the field of atomistic simulations. After the initial decade, in which neural networks were successfully used to construct potentials for rather small molecular systems, the development of high-dimensional neural network potentials (HDNNPs) in 2007 opened the way for the application of ML potentials in simulations of large systems containing thousands of atoms. To date, many other types of ML potentials have been proposed continuously increasing the range of problems that can be studied. In this review, the methodology of the family of HDNNPs including new recent developments will be discussed using a classification scheme into four generations of potentials, which is also applicable to many other types of ML potentials. The first generation is formed by early neural network potentials designed for low-dimensional systems. High-dimensional neural network potentials established the second generation and are based on three key steps: first, the expression of the total energy as a sum of environment-dependent atomic energy contributions; second, the description of the atomic environments by atom-centered symmetry functions as descriptors fulfilling the requirements of rotational, translational, and permutation invariance; and third, the iterative construction of the reference electronic structure data sets by active learning. In third-generation HDNNPs, in addition, long-range interactions are included employing environment-dependent partial charges expressed by atomic neural networks. In fourth-generation HDNNPs, which are just emerging, in addition, nonlocal phenomena such as long-range charge transfer can be included. The applicability and remaining limitations of HDNNPs are discussed along with an outlook at possible future developments.

Simulation methods for open quantum many-body systems

This article reviews theoretical methods to deal with interacting quantum particles that are in contact with their environment and are thus described by a master equation rather than a Schr\"odinger equation. The similarities and differences are discussed between the pursuit of pure many-body ground states and mixed steady states by different methods, and an outlook is provided on the advances toward simulation of large open many-body system.

Compact sparse symbolic Jacobian computation in large systems of ODEs

This work introduces a novel algorithm that automatically produces computer code for the calculation of sparse symbolical Jacobian matrices. More precisely, given the code for computing a function f depending on a set of state (independent) variables x, where the code makes use of intermediate algebraic (auxiliary) variables a(x), the algorithm automatically produces the code for the symbolic computation of the matrix J=∂f/∂x in sparse representation.A remarkable feature of the algorithm developed is that it can deal with iterative definitions of the functions preserving the iterative representation during the whole process up to the final Jacobian computation code. That way, in presence of arrays of functions and variables, the computational cost of the code generation and the length of the generated code does not depend on the size of those arrays. This feature is achieved making use of Set–Based Graph representation.The main application of the algorithm is the simulation of large scale dynamical systems with implicit Ordinary Differential Equation (ODE) solvers like CVODE-BDF, whose performance are greatly improved when they are invoked using a sparse Jacobian matrix. However, the algorithm can be used in a more general context for solving large systems of nonlinear equations.The paper, besides introducing the algorithm, discusses some aspects of its implementation in a general purpose ODE solver front-end and analyzes some results obtained.

Simulation of large molecular systems with electronically-derived forces

Many-body electronic responses such as dispersion and polarization (at and beyond dipole order) present fundamental challenges in the simulation of materials at the molecular scale. To address these, an emerging strategy employing embedded quantum oscillators as a coarse-grained representation of such responses has been effective in predicting material properties with remarkable accuracy. However, applications have so far been limited to relatively small system sizes. Here we introduce strategies enabling efficient implementation of this framework on high-performance, heterogeneous CPU–GPU (with multiple Graphic Processing Units) computing platforms thereby increasing significantly the scale of accessible problems. Physical properties are reported for a benchmark system of 104 water molecules — to our knowledge, the largest system yet simulated using molecular dynamics with electronically-derived forces.

A Multifidelity Aero-Thermal Design Approach for Secondary Air Systems

Abstract The paper presents a multidisciplinary approach for aero-thermal and heat transfer analysis for internal flows. The versatility and potential benefit offered by the approach are described through the application to a realistic low pressure turbine assembly. The computational method is based on a run time code-coupling architecture that allows mixed models and simulations to be integrated together for the prediction of the subsystem aero-thermal performance. In this specific application, the model is consisting of two rotor blades, the embedded vanes, the interstage cavity, and the solid parts. The geometry represents a real engine situation. The key element of the approach is the use of a fully modular coupling strategy that aims to combine (1) flexibility for design needs, (2) variable level of modeling for better accuracy, and (3) in memory code coupling for preserving computational efficiency in large system and subsystem simulations. For this particular example, Reynolds averaged Navier–Stokes (RANS) equations are solved for the fluid regions and thermal coupling is enforced with the metal (conjugate heat transfer, CHT). Fluid–fluid interfaces use mixing planes between the rotating parts while overlapping regions are exploited to link the cavity flow to the main annulus flow as well as in the cavity itself for mapping of the metal parts and leakages. Metal temperatures predicted by the simulation are compared to those retrieved from a thermal model of the engine, and the results are discussed with reference to the underlying flow physics.

Efficient exponential time integration for simulating nonlinear coupled oscillators

In this paper, we propose an advanced time integration technique associated with explicit exponential Rosenbrock-based methods for the simulation of large stiff systems of nonlinear coupled oscillators. In particular, a novel reformulation of these systems is introduced and a general family of efficient exponential Rosenbrock schemes for simulating the reformulated system is derived. Moreover, we show the required regularity conditions and prove the convergence of these schemes for the system of coupled oscillators. We present an efficient implementation of this new approach and discuss several applications in scientific and visual computing. The accuracy and efficiency of our approach are demonstrated through a broad spectrum of numerical examples, including a nonlinear Fermi–Pasta–Ulam–Tsingou model, elastic and nonelastic deformations as well as collision scenarios focusing on relevant aspects such as stability and energy conservation, large numerical stiffness, high fidelity, and visual accuracy.

A general implementation of time-dependent vibrational coupled-cluster theory.

The first general excitation level implementation of the time-dependent vibrational coupled cluster (TDVCC) method introduced in a recent publication [J. Chem. Phys. 151, 154116 (2019)] is presented. The general framework developed for time-independent vibrational coupled cluster (VCC) calculations has been extended to the time-dependent context. This results in an efficient implementation of TDVCC with general coupling levels in the cluster operator and Hamiltonian. Thus, the convergence of the TDVCC[k] hierarchy toward the complete-space limit can be studied for any sum-of-product Hamiltonian. Furthermore, a scheme for including selected higher-order excitations for a subset of modes is introduced and studied numerically. Three different definitions of the TDVCC autocorrelation function (ACF) are introduced and analyzed in both theory and numerical experiments. Example calculations are presented for an array of systems including imidazole, formyl fluoride, formaldehyde, and a reduced-dimensionality bithiophene model. The results show that the TDVCC[k] hierarchy converges systematically toward the full-TDVCC limit and that the implementation allows accurate quantum-dynamics simulations of large systems to be performed. Specifically, the intramolecular vibrational-energy redistribution of the 21-dimensional imidazole molecule is studied in terms of the decay of the ACF. Furthermore, the importance of product separability in the definition of the ACF is highlighted when studying non-interacting subsystems.