Millions Of Time Steps Research Articles

Sublinear Scaling in Non-Markovian Open Quantum Systems Simulations

While several numerical techniques are available for predicting the dynamics of non-Markovian open quantum systems, most struggle with simulations for very long memory and propagation times, e.g., due to superlinear scaling with the number of time steps n. Here, we introduce a numerically exact algorithm to calculate process tensors—compact representations of environmental influences—which provides a scaling advantage over previous algorithms by leveraging self-similarity of the tensor networks that represent the environment. It is applicable to environments with Gaussian statistics, such as for spin-boson-type open quantum systems. Based on a divide-and-conquer strategy, our approach requires only O(n log n) singular value decompositions for environments with infinite memory. Where the memory can be truncated after nc time steps, a nominal scaling O(nc log nc) is found, which is independent of n. This improved scaling is enabled by identifying process tensors with repeatable blocks. To demonstrate the power and utility of our approach, we provide three examples. (1) We calculate the fluorescence spectra of a quantum dot under both strong driving and strong dot-phonon couplings, a task requiring simulations over millions of time steps, which we are able to perform in minutes. (2) We efficiently find process tensors describing superradiance of multiple emitters. (3) We explore the limits of our algorithm by considering coherence decay with a very strongly coupled environment. The observed computation time is not necessarily proportional to the number of singular value decompositions because the matrix dimensions also depend on the number of time steps. Nevertheless, quasilinear and sublinear scaling of computation time is found in practice for a wide range of parameters. While there are instances where existing methods can achieve comparable nominal scaling by precalculating effective propagators for time-independent or periodic system Hamiltonians, process tensors contain all the information needed to extract arbitrary multitime correlation functions of the system when driven by arbitrary time-dependent system Hamiltonians. The algorithm we present here not only significantly extends the scope of numerically exact techniques to open quantum systems with long memory times, but it also has fundamental implications for the simulation complexity of tensor network approaches. Published by the American Physical Society 2024

Characterization of Transmission Lines in Microelectronic Circuits Using the ARTEMIS Solver

Modeling and characterization of electromagnetic wave interactions with microelectronic devices to derive network parameters has been a widely used practice in the electronic industry. However, as these devices become increasingly miniaturized with finer-scale geometric features, computational tools must make use of manycore/GPU architectures to efficiently resolve length and time scales of interest. This has been the focus of our open-source solver, ARTEMIS (Adaptive mesh Refinement Time-domain ElectrodynaMIcs Solver), which is performant on modern GPU-based supercomputing architectures while being amenable to additional physics coupling. This work demonstrates its use for characterizing network parameters of transmission lines using established techniques. A rigorous verification and validation of the workflow is carried out, followed by its application for analyzing a transmission line on a CMOS chip designed for a photon-detector application. Simulations are performed for millions of timesteps on state-of-the-art GPU resources to resolve nanoscale features at gigahertz frequencies. The network parameters are used to obtain phase delay and characteristic impedance that serve as inputs to SPICE models. The code is demonstrated to exhibit ideal weak scaling efficiency up to 1024 GPUs and 84% efficiency for 2048 GPUs, which underscores its use for network analysis of larger, more complex circuit devices in the future.

Learning to Play Table Tennis From Scratch Using Muscular Robots

Dynamic tasks such as table tennis are relatively easy to learn for humans, but pose significant challenges to robots. Such tasks require accurate control of fast movements and precise timing in the presence of imprecise state estimation of the flying ball and the robot. Reinforcement learning (RL) has shown promise in learning complex control tasks from data. However, applying step-based RL to dynamic tasks on real systems is safety-critical as RL requires exploring and failing safely for millions of time steps in high-speed and high-acceleration regimes. This article demonstrates that using robot arms driven by pneumatic artificial muscles (PAMs) enables safe end-to-end learning of table tennis using model-free RL. In particular, we learn <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">from scratch</i> for thousands of trials while a stochastic policy acts on the low-level controls of the real system. The robot returns and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">smashes</i> real balls with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$5 $</tex-math></inline-formula> ms <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1</sup> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$12 $</tex-math></inline-formula> ms <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1</sup> on average, respectively, to a desired landing point. Additionally, we present hybrid sim and real training (HYSR), a practical procedure that avoids training with real balls by virtually replaying recorded ball trajectories and applying actions to the real robot. To the best of authors’ knowledge, this work pioneers (i) failsafe learning of a safety-critical dynamic task using anthropomorphic robot arms, (ii) learning a precision-demanding problem with a PAM-driven system that is inherently hard to control as well as (iii) train a robot to play table tennis without real balls.

Impulse Response Functions for Nonlinear, Nonstationary, and Heterogeneous Systems, Estimated by Deconvolution and Demixing of Noisy Time Series.

Impulse response functions (IRFs) are useful for characterizing systems’ dynamic behavior and gaining insight into their underlying processes, based on sensor data streams of their inputs and outputs. However, current IRF estimation methods typically require restrictive assumptions that are rarely met in practice, including that the underlying system is homogeneous, linear, and stationary, and that any noise is well behaved. Here, I present data-driven, model-independent, nonparametric IRF estimation methods that relax these assumptions, and thus expand the applicability of IRFs in real-world systems. These methods can accurately and efficiently deconvolve IRFs from signals that are substantially contaminated by autoregressive moving average (ARMA) noise or nonstationary ARIMA noise. They can also simultaneously deconvolve and demix the impulse responses of individual components of heterogeneous systems, based on their combined output (without needing to know the outputs of the individual components). This deconvolution–demixing approach can be extended to characterize nonstationary coupling between inputs and outputs, even if the system’s impulse response changes so rapidly that different impulse responses overlap one another. These techniques can also be extended to estimate IRFs for nonlinear systems in which different input intensities yield impulse responses with different shapes and amplitudes, which are then overprinted on one another in the output. I further show how one can efficiently quantify multiscale impulse responses using piecewise linear IRFs defined at unevenly spaced lags. All of these methods are implemented in an R script that can efficiently estimate IRFs over hundreds of lags, from noisy time series of thousands or even millions of time steps.

Implementation of Strangely Behaving Intelligent Agents to Determine Human Intervention During Reinforcement Learning

Intrinsic motivation helps autonomous exploring agents traverse a larger portion of their environments. However, simulations of different learning environments in previous research show that after millions of timesteps of successful training, an intrinsically motivated agent may learn to act in ways unintended by the designer. This potential for unintended actions of autonomous exploring agents poses threats to the environment and humans if operated in the real world. We investigated this topic by using <i>Unity’s Machine Learning Agent Toolkit</i> (<i>ML-Agents</i>) implementation of the Proximal Policy Optimization (PPO) algorithm with the Intrinsic Curiosity Module (ICM) to train autonomous exploring agents in three learning environments. We demonstrate that ICM, although designed to assist agent navigation in environments with sparse reward generation, increasing gradually as a tool for purposely training misbehaving agent in significantly less than 1 million timesteps. We present the following achievements: 1) experiments designed to cause agents to act undesirably, 2) a metric for gauging how well an agent achieves its goal without collisions, and 3) validation of PPO best practices. Then, we used optimized methods to improve the agent’s performance and reduce collisions within the same environments. These achievements help further our understanding of the significance of monitoring training statistics during reinforcement learning for determining how humans can intervene to improve agent safety and performance.

Visual Analysis of Large‐Scale Protein‐Ligand Interaction Data

AbstractWhen studying protein‐ligand interactions, many different factors can influence the behaviour of the protein as well as the ligands. Molecular visualisation tools typically concentrate on the movement of single ligand molecules; however, viewing only one molecule can merely provide a hint of the overall behaviour of the system. To tackle this issue, we do not focus on the visualisation of the local actions of individual ligand molecules but on the influence of a protein and their overall movement. Since the simulations required to study these problems can have millions of time steps, our presented system decouples visualisation and data preprocessing: our preprocessing pipeline aggregates the movement of ligand molecules relative to a receptor protein. For data analysis, we present a web‐based visualisation application that combines multiple linked 2D and 3D views that display the previously calculated data The central view, a novel enhanced sequence diagram that shows the calculated values, is linked to a traditional surface visualisation of the protein. This results in an interactive visualisation that is independent of the size of the underlying data, since the memory footprint of the aggregated data for visualisation is constant and very low, even if the raw input consisted of several terabytes.

High temperature pure carbon nanoparticle formation: Validation of AIREBO and ReaxFF reactive molecular dynamics

Molecular dynamics with reactive interatomic potentials is the only computationally feasible approach for modeling at the atomistic level the formation of carbon nanoparticles from gas state. Such models require thousands of atoms and millions of time steps that is beyond the current capabilities of first principles electronic structure calculations. A continuously growing variety of available reactive interatomic potentials for carbon requires their careful validation for a particular molecular system and pressure-temperature conditions. In this work we consider a generic example process of carbon nanoparticle formation at cooling of the gas phase and compare different AIREBO and ReaxFF reactive models. Three main processes of clusterization, change of hybridization and graphitization are analysed and used for comparison of potentials. Ab initio density functional theory and parameterized density functional tight-binding calculations together with experimental data available are used for validation of the reactive models considered. We highlight the detected problems of some well-known reactive potentials and conclude with three models that can be selected as the best options for molecular dynamics simulations of pure carbon nanoparticle formation.

Model description of a two-dimensional electrostatic particle-in-cell simulation parallelized with a graphics processing unit for plasma discharges

Many key aspects of low-temperature plasmas include nonlinear, transient, and kinetic effects related to the spatio-temporal variation of electron energy distribution function (EEDF) which cannot be treated in a fluid simulation model. The particle-in-cell (PIC) simulation calculates kinetic effects through the statistical representation of the EEDF using many particles and thus gives accurate results. However, the computational cost is very expensive to resolve all aspects in a plasma discharge with millions of computational particles as well as hundreds of thousands of grids during millions of time steps. Additionally, the simulation of discharge plasmas should handle the collision processes and the rapid increase in the total number of simulation particles. In this presentation, details of a two-dimensional PIC simulation parallelized with graphics processing units (GPUs) are explained for the improvement of computation speed. The resulting GPU-PIC code executes aggregate time steps in two-dimensional geometry from 80 to 140 times faster than a conventional single CPU-PIC code with the same numerical scheme modelling a standard capacitively coupled plasma (CCP) reactor.

Transferable Kinetic Monte Carlo Models with Thousands of Reactions Learned from Molecular Dynamics Simulations.

Molecular dynamics (MD) simulation of complex chemistry typically involves thousands of atoms propagating over millions of time steps, generating a wealth of data. Traditionally these data are used to calculate some aggregate properties of the system and then discarded, but we propose that these data can be reused to study related chemical systems. Using approximate chemical kinetic models and methods from statistical learning, we study hydrocarbon chemistries under extreme thermodynamic conditions. We discover that a single MD simulation can contain sufficient information about reactions and rates to predict the dynamics of related yet different chemical systems using kinetic Monte Carlo (KMC) simulation. Our learned KMC models identify thousands of reactions and run 4 orders of magnitude faster than MD. The transferability of these models suggests that we can viably reuse data from existing MD simulations to accelerate future simulation studies and reduce the number of new MD simulations required.

Transient Moisture Distribution and Hygrothermal Stress Analysis of Composite Laminates Using Equivalent Diffusion Methods

It often takes several decades to reach moisture equilibrium state in composite laminates. Therefore, hourly varying fluctuating boundary moisture and temperature conditions require several millions of time steps to reach a state of equilibrium. A new transient analysis method is proposed to efficiently solve moisture distribution of composite laminates with rapidly fluctuating moisture and temperature boundary conditions. First, effective constant diffusivity and maximum moisture content were obtained by averaging transient temperature-dependent moisture diffusivity. In this way, a simple analytic solution can be effectively used to determine the transient moisture distribution under hourly fluctuating boundary conditions. Its efficiencies are demonstrated in three different conditions by comparing this method with a conventional finite difference method. Hygrothermal stress and material degradation were consequently discussed to demonstrate that we must avoid a simple knock-down factor or 40% devastating penalty and use more rational simulation and supporting data.

Parallel algorithm for spin and spin-lattice dynamics simulations

To control numerical errors accumulated over tens of millions of time steps during the integration of a set of highly coupled equations of motion is not a trivial task. In this paper, we propose a parallel algorithm for spin dynamics and the newly developed spin-lattice dynamics simulation [P. W. Ma, Phys. Rev. B 78, 024434 (2008)]. The algorithm is successfully tested in both types of dynamic calculations involving a million spins. It shows good stability and numerical accuracy over millions of time steps (approximately 1 ns) . The scheme is based on the second-order Suzuki-Trotter decomposition (STD). The usage can avoid numerical energy dissipation despite the trajectory and machine errors. The mathematical base of the symplecticity, for properly decomposed evolution operators, is presented. Due to the noncommutative nature of the spin in the present STD scheme, a unique parallel algorithm is needed. The efficiency and stability are tested. It can attain six to seven times speed up when eight threads are used. The run time per time step is linearly proportional to the system size.

Optimization Techniques for Parallel Biophysical Simulations Generated by insilicoIDE

Recent work in biophysical science increasingly focuses on modeling and simulating human biophysical systems to better understand the human physiome. One program to generate such models is insilicoIDE. These models may consist of thousands or millions of components with complex relations. Simulations of such models can require millions of time steps and take hours or days to run on a single machine. To improve the speed of biophysical simulations generated by insilicoIDE, we propose techniques for augmenting the simulations to support parallel execution in an MPI-enabled environment. In this paper we discuss the methods involved in efficient parallelization of such simulations, including classification and identification of model component relationships and work division among multiple machines. We demonstrate the effectiveness of the augmented simulation code in a parallel computing environment by performing simulations of large scale neuron and cardiac models.

Parallel TREE code for two-component ultracold plasma analysis

The TREE method has been widely used for long-range interaction N-body problems. We have developed a parallel TREE code for two-component classical plasmas with open boundary conditions and highly non-uniform charge distributions. The program efficiently handles millions of particles evolved over long relaxation times requiring millions of time steps. Appropriate domain decomposition and dynamic data management were employed, and large-scale parallel processing was achieved using an intermediate level of granularity of domain decomposition and ghost TREE communication. Even though the computational load is not fully distributed in fine grains, high parallel efficiency was achieved for ultracold plasma systems of charged particles. As an application, we performed simulations of an ultracold neutral plasma with a half million particles and a half million time steps. For the long temporal trajectories of relaxation between heavy ions and light electrons, large configurations of ultracold plasmas can now be investigated, which was not possible in past studies.

High resolution Godunov‐type schemes with small stencils

AbstractHigher‐order Godunov‐type schemes have to cope with the following two problems: (i) the increase in the size of the stencil that make the scheme computationally expensive, and (ii) the monotony‐preserving treatments (limiters) that must be implemented to avoid oscillations, leading to strong damping of the solution, in particular linear waves (e.g. acoustic waves). When too compressive, limiting procedures may also trigger the instability of oscillatory numerical solutions (e.g. in advection–dispersion phenomena) via the artificial amplification of the shorter modes. The present paper proposes a new approach to carry out the reconstruction. In this approach, the values of the flow variable at the edges of the computational cells are obtained directly from the reconstruction within these cells. This method is applied to the MUSCL and DPM schemes for the solution of the linear advection equation. The modified DPM scheme can capture contact discontinuities within one computational cell, even after millions of time steps at Courant numbers ranging from 1 to values as low as 10‐4. Linear waves are subject to negligible damping. Application of the method to the DPM for one‐dimensional advection–dispersion problems shows that the numerical instability of oscillatory solutions caused by the over compressive, original DPM limiter is eliminated. One‐ and two‐dimensional shallow water simulations show an improvement over classical methods, in particular for two‐dimensional problems with strongly distorted meshes. The quality of the computational solution in the two‐dimensional case remains acceptable even for mesh aspect ratios Δx/Δy as large as 10. The method can be extend to the discretization of higher‐order PDEs, allowing third‐order space derivatives to be discretized using only two cells in space. Copyright © 2004 John Wiley &amp; Sons, Ltd.

A Comparison Between Elastic Network Interpolation and MD Simulation of 16S Ribosomal RNA

In this paper a coarse-grained method called elastic network interpolation (ENI) is used to generate feasible transition pathways between two given conformations of the core central domain of 16S Ribosomal RNA (16S rRNA). The two given conformations are the extremes generated by a molecular dynamics (MD) simulation, which differ from each other by 10Å in root-mean-square deviation (RMSD). It takes only several hours to build an ENI pathway on a 1.5GHz Pentium with 512 MB memory, while the MD takes several weeks on high-performance multi-processor servers such as the SGI ORIGIN 2000/2100. It is shown that multiple ENI pathways capture the essential anharmonic motions of millions of timesteps in a particular MD simulation. A coarse-grained normal mode analysis (NMA) is performed on each intermediate ENI conformation, and the lowest 1% of the normal modes (representing about 40 degrees of freedom (DOF)) are used to parameterize fluctuations. This combined ENI/NMA method captures all intermediate conformations in the MD run with 1.5Å RMSD on average. In addition, if we restrict attention to the time interval of the MD run between the two extreme conformations, the RMSD between the closest ENI/NMA pathway and the MD results is about 1Å. These results may serve as a paradigm for reducedDOF dynamic simulations of large biological macromolecules as well as a method for the reduced-parameter interpretation of massive amounts of MD data.

Dynamical and Statistical Mechanical Characterization of Temperature Coupling Algorithms

In this article, we investigate molecular dynamics (MD) trajectories of a butane molecule, as obtained using different types of thermostats. Results show that at low temperature, where the harmonic approximation holds, the Nose'−Hoover (NH) thermostat fails to reproduce the statistical mechanical behavior, even using simulation lengths of millions of time steps, whereas the Gaussian isokinetic (IG) thermostat reproduces quite well the expected statistical mechanical values. The Berendsen's coupling (BC) provides good results for basic properties such as the average potential and kinetic energies but fails in reproducing the canonical fluctuations. Moreover, using the speed of divergence of initially nearby trajectories in phase space as a measure of the dynamical chaoticity, we found that the NH thermostat provides very slow divergence for the physical phase space degrees of freedom, concentrating most of its chaoticity in the dynamics of the thermostat virtual degree of freedom. On the contrary, the IG thermostat provides always highly diverging trajectories in phase space, characterized by a high chaoticity of each degree of freedom. Finally, the BC thermostat provides a moderate chaotic behavior for all of the degrees of freedom. Such results suggest that even assuming for both the “rigorous” algorithms (NH and IG) a full ergodic behavior the NH thermostat could require an extremely long time to achieve convergence of the time averaged properties.

Predicting channel function from channel structure using Brownian dynamics simulations.

1. The transport process of ions across the potassium channel is studied using computer simulations. The shape of the model channel corresponds closely to that deduced from crystallography. 2. We first give an intuitive account of how the motion of ions experiencing an applied electric force and interacting with a dielectric boundary and charge residues on the channel wall can be simulated accurately by using a powerful supercomputer. 3. We then show how some of the salient features of ion channels can be deduced by following the positions of ions at each discrete step over many millions of time steps.

Crush Simulation of Cars with FEA

This article illustrates that while crash analyses have been carried out with success, a crush analysis is much more difficult to achieve. In a crash analysis, the inertia effects smooth out the nonlinearities and deficiencies in the solution algorithms. In a crush test, it takes about 10 to 30 seconds to crush the car to the required maximum displacement of the steel plate. Since the critical time step for explicit time integration in a crash code is on the order of microseconds, millions of time steps must be used to perform the analysis in a physically correct manner. With sufficient numerical experimentation, involving changes to the load application speed and perhaps to other parameters, LSDYNA results can be obtained that would match laboratory test results, but such experimentation requires a lot of time and computational effort. A solution that corresponds to the actual physical conditions and is computationally efficient is much more desirable. Such a computed solution is given above for a Ford Taurus model. The calculated crush results obtained with ADINA using implicit integration compare favorably with the laboratory test results.

An eficient time scaling technique for coupled geochemical and transport models

In earlier work using coupled geochemical and transport models such as CHEQMATE, HYDROGEOCHEM, PHREEQM and other codes, we have found that, when the mass of mineral phases in the system is large compared with the solubilities of the minerals in the water, computing times become prohibitively large. These problems have been found for several systems of interest for radionuclide migration. In a study of the coupled formation and movement of redox fronts, hydrolysis fronts and dissolving and precipitating secondary minerals, scaling of the amounts of the minerals could be made without influencing the results. This is not possible in general. In these circumstances the computations would typically need millions or many millions of time steps to have the fronts move through one “cell” in a finite difference based code. It has been noted, however, that this also leads to stationary states, developing in the system. This has been pointed out and utilised by Lichtner. We have developed a code, CHEMFRONTS, which utilises this property. The drawback is that it is not easy to incorporate diffusion/dispersion using this approach. It can only handle advection dominated transport. For such cases however it is extremely fast compared with conventional codes. We have now developed a technique whereby the stationary state approximation can be superimposed on and incorporated in finite difference and finite element codes. This speeds up the computations considerably. So far we have used it successfully in CHEQMATE, HYDROGEOCHEM and PHREEQM. In this paper we show the method and give some examples of its application using previously addressed problems.

The two-dimensional Navier-Stokes-Kuramoto-Sivashinsky equation on the Connection Machine

The two-dimensional Navier-Stokes equations with a large scale instability of the Kuramoto-Sivashinsky type, describing marginally negative eddy viscosity situations, is simulated on a Connection Machine CM-2. Up to millions of time steps at the resolution 256 2 and tens of thousands at the resolution 1024 2 are performed. A linear growth phase, a disorganized inverse cascade phase and a structured vortical phase are successively observed. In the vortical phase monopolar and multipolar structures are proliferating and display strongly depleted nonlinearities.