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A method is presented in which the ground-state subspace is projected out of a Hamiltonian representation. As a result of this projection, an effective Hamiltonian is constructed where its ground-state coincides with an excited-state of the original problem. Thus, low-lying excited-state energies can be calculated using existing hybrid quantum classical techniques and variational algorithm(s) for determining ground-state. The method as formulated is shown to be fully valid for the $$\hbox{H}_2$$ and LiH molecules. The primary restriction with our technique is the number of terms required in the projection operator, therefore we explore arguments to reduce the number of terms and discuss applicability to different classes of Hamiltonians.

The EAST plasma control system (PCS) undergoes continuous development and upgrade to achieve major goals of EAST steady-state advanced operation. According to the development of computer multi-core processor technology, the four nodes PCS cluster was simplified to one host and one real time computing node structure. Besides, the cluster internal data exchange network Myrinet was replaced by high speed 10 Giga-bit Ethernet for inter machine and shared memory technology for multi-core communication. Such new upgraded system is called standalone PCS which has less hardware but be more efficient and easy to backup. In the new upgraded system, a real time archiving mode using data segment technology of MDSplus was realized which provided the possibility to save all data in segments without increasing the computer memory or reducing the saving frequency in steady–state operation. To reduce the heat flux and surface temperature on the divertor targets, plasma radiation control using divertor inert gas puffing and mid-plane supersonic molecular beam injection (SMBI) was integrated in PCS. In this paper, the control design and experiment results are discussed.

At a typical fusion research site, experimental data is stored using archive technologies that deal with each discharge as an independent set of data. These technologies (e.g. MDSplus or HDF5) are typically supplemented with a database that aggregates metadata for multiple shots to allow for efficient querying of certain predefined quantities. Often, however, a researcher will need to extract information from the archives, possibly for many shots, that is not available in the metadata store or otherwise indexed for quick retrieval. To address this need, a new search tool called TokSearch has been added to the General Atomics TokSys control design and analysis suite. This tool provides the ability to rapidly perform arbitrary, parallelized queries of archived tokamak shot data (both raw and analyzed) over large numbers of shots. The TokSearch query API borrows concepts from SQL, and users can choose to implement queries in either Matlab™ or Python.

ALMA (Anti-symmetric, Large-Moment, Accelerated) is a fast, flexible, and scalable toolkit designed to solve hyperbolic conservation law systems in hybrid supercomputers. This manuscript describes the theoretical background and implementation of ALMA , which uses the anti-symmetric formulation of fluids to obtain simple, robust, and easily paralellizable code. Practical GPU acceleration is realized on entire applications with an overall gain factor of 2 to 4. ALMA also provides a parallel, GPU accelerated sparse solver based on geometric multigrid, capable of diagonalizing linear systems with 239 unknowns. We demonstrate ALMA 's scaling and performance in petascale supercomputers and use standard fluid models to verify the overall approach with canonical benchmark problems.

CGYRO, an Eulerian gyrokinetic solver designed and optimized for collisional, electromagnetic, multiscale fusion plasma simulation, has been ported and benchmarked on a Summit-like Power9-based system equipped with Volta GPUs. We present our experience porting the application and provide benchmark numbers obtained on the Power-based node and compare them with equivalent tests from several leadership class systems. The tested node provided the fastest single-node CGYRO runtimes we’ve measured to date.

Transferring information from observations to models of complex systems may meet impediments when the number of observations at any observation time is not sufficient. This is especially so when chaotic behavior is expressed. We show how to use time-delay embedding, familiar from nonlinear dynamics, to provide the information required to obtain accurate state and parameter estimates. Good estimates of parameters and unobserved states are necessary for good predictions of the future state of a model system. This method may be critical in allowing the understanding of prediction in complex systems as varied as nervous systems and weather prediction where insufficient measurements are typical.

We present a method for using measurements of membrane voltage in individual neurons to estimate the parameters and states of the voltage-gated ion channels underlying the dynamics of the neuron’s behavior. Short injections of a complex time-varying current provide sufficient data to determine the reversal potentials, maximal conductances, and kinetic parameters of a diverse range of channels, representing tens of unknown parameters and many gating variables in a model of the neuron’s behavior. These estimates are used to predict the response of the model at times beyond the observation window. This method of $${{\tt data\, assimilation}}$$ extends to the general problem of determining model parameters and unobserved state variables from a sparse set of observations, and may be applicable to networks of neurons. We describe an exact formulation of the tasks in nonlinear data assimilation when one has noisy data, errors in the models, and incomplete information about the state of the system when observations commence. This is a high dimensional integral along the path of the model state through the observation window. In this article, a stationary path approximation to this integral, using a variational method, is described and tested employing data generated using neuronal models comprising several common channels with Hodgkin–Huxley dynamics. These numerical experiments reveal a number of practical considerations in designing stimulus currents and in determining model consistency. The tools explored here are computationally efficient and have paths to parallelization that should allow large individual neuron and network problems to be addressed.

We discuss the problem of determining unknown fixed parameters and unobserved state variables in nonlinear models of a dynamical system using observed time series data from that system. In dynamica...

Most data based state and parameter estimation methods require suitable initial values or guesses to achieve convergence to the desired solution, which typically is a global minimum of some cost function. Unfortunately, however, other stable solutions (e.g., local minima) may exist and provide suboptimal or even wrong estimates. Here we demonstrate for a 9-dimensional Lorenz-96 model how to characterize the basin size of the global minimum when applying some particular optimization based estimation algorithm. We compare three different strategies for generating suitable initial guesses and we investigate the dependence of the solution on the given trajectory segment (underlying the measured time series). To address the question of how many state variables have to be measured for optimal performance, different types of multivariate time series are considered consisting of 1, 2, or 3 variables. Based on these time series the local observability of state variables and parameters of the Lorenz-96 model is investigated and confirmed using delay coordinates. This result is in good agreement with the observation that correct state and parameter estimation results are obtained if the optimization algorithm is initialized with initial guesses close to the true solution. In contrast, initialization with other exact solutions of the model equations (different from the true solution used to generate the time series) typically fails, i.e. the optimization procedure ends up in local minima different from the true solution. Initialization using random values in a box around the attractor exhibits success rates depending on the number of observables and the available time series (trajectory segment)., 15 pages, 2 figures

Recent results demonstrate techniques for fully quantitative, statistical inference of the dynamics of individual neurons under the Hodgkin---Huxley framework of voltage-gated conductances. Using a variational approximation, this approach has been successfully applied to simulated data from model neurons. Here, we use this method to analyze a population of real neurons recorded in a slice preparation of the zebra finch forebrain nucleus HVC. Our results demonstrate that using only 1,500 ms of voltage recorded while injecting a complex current waveform, we can estimate the values of 12 state variables and 72 parameters in a dynamical model, such that the model accurately predicts the responses of the neuron to novel injected currents. A less complex model produced consistently worse predictions, indicating that the additional currents contribute significantly to the dynamics of these neurons. Preliminary results indicate some differences in the channel complement of the models for different classes of HVC neurons, which accords with expectations from the biology. Whereas the model for each cell is incomplete (representing only the somatic compartment, and likely to be missing classes of channels that the real neurons possess), our approach opens the possibility to investigate in modeling the plausibility of additional classes of channels the cell might possess, thus improving the models over time. These results provide an important foundational basis for building biologically realistic network models, such as the one in HVC that contributes to the process of song production and developmental vocal learning in songbirds.

Hodgkin–Huxley (HH) models of neuronal membrane dynamics consist of a set of nonlinear differential equations that describe the time-varying conductance of various ion channels. Using observations of voltage alone we show how to estimate the unknown parameters and unobserved state variables of an HH model in the expected circumstance that the measurements are noisy, the model has errors, and the state of the neuron is not known when observations commence. The joint probability distribution of the observed membrane voltage and the unobserved state variables and parameters of these models is a path integral through the model state space. The solution to this integral allows estimation of the parameters and thus a characterization of many biological properties of interest, including channel complement and density, that give rise to a neuron’s electrophysiological behavior. This paper describes a method for directly evaluating the path integral using a Monte Carlo numerical approach. This provides estimates not only of the expected values of model parameters but also of their posterior uncertainty. Using test data simulated from neuronal models comprising several common channels, we show that short (

In variational formulations of data assimilation, the estimation of parameters or initial state values by a search for a minimum of a cost function can be hindered by the numerous local minima in the dependence of the cost function on those quantities. We argue that this is a result of instability on the synchronization manifold where the observations are required to match the model outputs in the situation where the data and the model are chaotic. The solution to this impediment to estimation is given as controls moving the positive conditional Lyapunov exponents on the synchronization manifold to negative values and adding to the cost function a penalty that drives those controls to zero as a result of the optimization process implementing the assimilation. This is seen as the solution to the proper size of ‘nudging’ terms: they are zero once the estimation has been completed, leaving only the physics of the problem to govern forecasts after the assimilation window. We show how this procedure, called Dynamical State and Parameter Estimation (DSPE), works in the case of the Lorenz96 model with nine dynamical variables. Using DSPE, we are able to accurately estimate the fixed parameter of this model and all of the state variables, observed and unobserved, over an assimilation time interval [0, T]. Using the state variables at T and the estimated fixed parameter, we are able to accurately forecast the state of the model for t > T to those times where the chaotic behaviour of the system interferes with forecast accuracy. Copyright © 2010 Royal Meteorological Society