Control of Complex Dynamic Systems by Neural Networks

This paper considers the use of neural networks (NN's) in controlling a nonlinear, stochastic system with unknown process equations. The NN is used to model the resulting unknown control law. The approach here is based on using the output error of the system to train the NN controller without the need to construct a separate model (NN or other type) for the unknown process dynamics. To implement such a direct adaptive control approach, it is required that connection weights in the NN be estimated while the system is being controlled. As a result of the feedback of the unknown process dynamics, however, it is not possible to determine the gradient of the loss function for use in standard (back-propagation-type) weight estimation algorithms. Therefore, this paper considers the use of a new stochastic approximation algorithm for this weight estimation, which is based on a 'simultaneous perturbation' gradient approximation that only requires the system output error. It is shown that this algorithm can greatly enhance the efficiency over more standard stochastic approximation algorithms based on finite-difference gradient approximations

Intrinsic adaptation in autonomous recurrent neural networks

A massively recurrent neural network responds on one side to input stimuli and is autonomously active, on the other side, in the absence of sensory inputs. Stimuli and information processing depends crucially on the qualia of the autonomous-state dynamics of the ongoing neural activity. This default neural activity may be dynamically structured in time and space, showing regular, synchronized, bursting or chaotic activity patterns. We study the influence of non-synaptic plasticity on the default dynamical state of recurrent neural networks. The non-synaptic adaption considered acts on intrinsic neural parameters, such as the threshold and the gain, and is driven by the optimization of the information entropy. We observe, in the presence of the intrinsic adaptation processes, three distinct and globally attracting dynamical regimes, a regular synchronized, an overall chaotic and an intermittent bursting regime. The intermittent bursting regime is characterized by intervals of regular flows, which are quite insensitive to external stimuli, interseeded by chaotic bursts which respond sensitively to input signals. We discuss these finding in the context of self-organized information processing and critical brain dynamics.Comment: 24 pages, 8 figure

On a criterion for vortex breakdown

A criterion for the onset of vortex breakdown is proposed. Based upon previous experimental, computational, and theoretical studies, an appropriately defined local Rossby number is used to delineate the region where breakdown occurs. In addition, new numerical results are presented which further validate this criterion. A number of previous theoretical studies concentrating on inviscid standing-wave analyses for trailing wing-tip vortices are reviewed and reinterpreted in terms of the Rossby number criterion. Consistent with previous studies, the physical basis for the onset of breakdown is identified as the ability of the flow to sustain such waves. Previous computational results are reviewed and re-evaluated in terms of the proposed breakdown criterion. As a result, the cause of breakdown occurring near the inflow computational boundary, common to several numerical studies, is identified. Finally, previous experimental studies of vortex breakdown for both leading edge and trailing wing-tip vortices are reviewed and quantified in terms of the Rossby number criterion

Optimal random perturbations for stochastic approximation using a simultaneous perturbation gradient approximation

The simultaneous perturbation stochastic approximation (SPSA) algorithm has recently attracted considerable attention for optimization problems where it is di cult or impossible to obtain a direct gradient of the objective (say, loss) function. The approach is based on a highly e cient simultaneous perturbation approximation to the gradient based on loss function measurements. SPSA is based on picking a simultaneous perturbation (random) vector in a Monte Carlo fashion as part of generating the approximation to the gradient. This paper derives the optimal distribution for the Monte Carlo process. The objective is to minimize the mean square error of the estimate. We also consider maximization of the likelihood that the estimate be con ned within a bounded symmetric region of the true parameter. The optimal distribution for the components of the simultaneous perturbation vector is found to be a symmetric Bernoulli in both cases. We end the paper with a numerical study related to the area of experiment design. 1

Permutation-invariant distance between atomic configurations

We present a permutation-invariant distance between atomic configurations, defined through a functional representation of atomic positions. This distance enables to directly compare different atomic environments with an arbitrary number of particles, without going through a space of reduced dimensionality (i.e. fingerprints) as an intermediate step. Moreover, this distance is naturally invariant through permutations of atoms, avoiding the time consuming associated minimization required by other common criteria (like the Root Mean Square Distance). Finally, the invariance through global rotations is accounted for by a minimization procedure in the space of rotations solved by Monte Carlo simulated annealing. A formal framework is also introduced, showing that the distance we propose verifies the property of a metric on the space of atomic configurations. Two examples of applications are proposed. The first one consists in evaluating faithfulness of some fingerprints (or descriptors), i.e. their capacity to represent the structural information of a configuration. The second application concerns structural analysis, where our distance proves to be efficient in discriminating different local structures and even classifying their degree of similarity

Variational quantum Monte Carlo simulations with tensor-network states

We show that the formalism of tensor-network states, such as the matrix product states (MPS), can be used as a basis for variational quantum Monte Carlo simulations. Using a stochastic optimization method, we demonstrate the potential of this approach by explicit MPS calculations for the transverse Ising chain with up to N=256 spins at criticality, using periodic boundary conditions and D*D matrices with D up to 48. The computational cost of our scheme formally scales as ND^3, whereas standard MPS approaches and the related density matrix renromalization group method scale as ND^5 and ND^6, respectively, for periodic systems.Comment: 4+ pages, 2 figures. v2: improved data, comparisons with exact results, to appear in Phys Rev Let