Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userScaling advantage of nonrelaxational dynamics for high-performance combinatorial optimization
65
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The development of physical simulators, called Ising machines, that sample from low energy states of the Ising Hamiltonian has the potential to drastically transform our ability to understand and control complex systems. However, most of the physical implementations of such machines have been based on a similar concept that is closely related to relaxational dynamics such as in simulated, mean-field, chaotic, and quantum annealing. We show that nonrelaxational dynamics that is associated with broken detailed balance and positive entropy production rate can accelerate the sampling of low energy states compared to that of conventional methods. By implementing such dynamics on field programmable gate array, we show that the nonrelaxational dynamics that we propose, called chaotic amplitude control, exhibits a scaling with problem size of the time to finding optimal solutions and its variance that is significantly smaller than that of relaxational schemes recently implemented on Ising machines.
rate research
Read More
[Devito] is an open-source Python project based on domain-specific language and compiler technology. Driven by the requirements of rapid HPC applications development in exploration seismology, the language and compiler have evolved significantly since inception. Sophisticated boundary conditions, tensor contractions, sparse operations and features such as staggered grids and sub-domains are all supported; operators of essentially arbitrary complexity can be generated. To accommodate this flexibility whilst ensuring performance, data dependency analysis is utilized to schedule loops and detect computational-properties such as parallelism. In this article, the generation and simulation of MPI-parallel propagators (along with their adjoints) for the pseudo-acoustic wave-equation in tilted transverse isotropic media and the elastic wave-equation are presented. Simulations are carried out on industry scale synthetic models in a HPC Cloud system and reach a performance of 28TFLOP/s, hence demonstrating Devitos suitability for production-grade seismic inversion problems.
We describe a computational method for constructing a coarse combinatorial model of some dynamical system in which the macroscopic states are given by elementary cycling motions of the system. Our method is in particular applicable to time series data. We illustrate the construction by a perturbed double well Hamiltonian as well as the Lorenz system.
We investigate the computational performance of various numerical methods for the integration of the equations of motion and the variational equations for some typical classical many-body models of condensed matter physics: the Fermi-Pasta-Ulam-Tsingou (FPUT) chain and the one- and two-dimensional disordered, discrete nonlinear Schrodinger equations (DDNLS). In our analysis we consider methods based on Taylor series expansion, Runge-Kutta discretization and symplectic transformations. The latter have the ability to exactly preserve the symplectic structure of Hamiltonian systems, which results in keeping bounded the error of the systems computed total energy. We perform extensive numerical simulations for several initial conditions of the studied models and compare the numerical efficiency of the used integrators by testing their ability to accurately reproduce characteristics of the systems dynamics and quantify their chaoticity through the computation of the maximum Lyapunov exponent. We also report the expressions of the implemented symplectic schemes and provide the explicit forms of the used differential operators. Among the tested numerical schemes the symplectic integrators $ABA864$ and $SRKN^a_{14}$ exhibit the best performance, respectively for moderate and high accuracy levels in the case of the FPUT chain, while for the DDNLS models $s9mathcal{ABC}6$ and $s11mathcal{ABC}6$ (moderate accuracy), along with $s17mathcal{ABC}8$ and $s19mathcal{ABC}8$ (high accuracy) proved to be the most efficient schemes.
Relativistic jets are intrinsic phenomena of active galactic nuclei (AGN) and quasars. They have been observed to also emanate from systems containing compact objects, such as white dwarfs, neutron stars and black hole candidates. The corresponding Lorentz factors, $Gamma$, were found to correlate with the compactness of the central objects. In the case of quasars and AGNs, plasmas with $Gamma$-factors larger than $8$ were detected. However, numerically consistent modelling of propagating shock-fronts with $Gamma geq 4$ is a difficult issue, as the non-linearities underlying the transport operators increase dramatically with $Gamma$, thereby giving rise to a numerical stagnation of the time-advancement procedure or alternatively they may diverge completely. In this paper, we present a unified numerical solver for modelling the propagation of one-dimensional shock fronts with high Lorentz factors. The numerical scheme is based on the finite-volume formulation with adaptive mesh refinement (AMR) and domain decomposition for parallel computation. It unifies both time-explicit and time-implicit numerical schemes within the framework of the pre-conditioned defect-correction iteration solution procedure. We find that time-implicit solution procedures are remarkably superior over their time-explicit counterparts in the very high $Gamma$-regime and therefore most suitable for consistent modelling of relativistic outflows in AGNs and micro-quasars.
We demonstrate an efficient algorithm for inverse problems in time-dependent quantum dynamics based on feedback loops between Hamiltonian parameters and the solutions of the Schr{o}dinger equation. Our approach formulates the inverse problem as a target vector estimation problem and uses Bayesian surrogate models of the Schr{o}dinger equation solutions to direct the optimization of feedback loops. For the surrogate models, we use Gaussian processes with vector outputs and composite kernels built by an iterative algorithm with Bayesian information criterion (BIC) as a kernel selection metric. The outputs of the Gaussian processes are designed to model an observable simultaneously at different time instances. We show that the use of Gaussian processes with vector outputs and the BIC-directed kernel construction reduce the number of iterations in the feedback loops by, at least, a factor of 3. We also demonstrate an application of Bayesian optimization for inverse problems with noisy data. To demonstrate the algorithm, we consider the orientation and alignment of polyatomic molecules SO$_2$ and chiral propylene oxide (PPO) induced by strong laser pulses. We use simulated time evolutions of the orientation or alignment signals to determine the relevant components of the molecular polarizability tensors to within 1% accuracy. We show that, for the five independent components of the polarizability tensor of PPO, this can be achieved with as few as 30 quantum dynamics calculations.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
