7,180 research outputs found
Domain Decomposition for Stochastic Optimal Control
This work proposes a method for solving linear stochastic optimal control
(SOC) problems using sum of squares and semidefinite programming. Previous work
had used polynomial optimization to approximate the value function, requiring a
high polynomial degree to capture local phenomena. To improve the scalability
of the method to problems of interest, a domain decomposition scheme is
presented. By using local approximations, lower degree polynomials become
sufficient, and both local and global properties of the value function are
captured. The domain of the problem is split into a non-overlapping partition,
with added constraints ensuring continuity. The Alternating Direction
Method of Multipliers (ADMM) is used to optimize over each domain in parallel
and ensure convergence on the boundaries of the partitions. This results in
improved conditioning of the problem and allows for much larger and more
complex problems to be addressed with improved performance.Comment: 8 pages. Accepted to CDC 201
Retrieving highly structured models starting from black-box nonlinear state-space models using polynomial decoupling
Nonlinear state-space modelling is a very powerful black-box modelling
approach. However powerful, the resulting models tend to be complex, described
by a large number of parameters. In many cases interpretability is preferred
over complexity, making too complex models unfit or undesired. In this work,
the complexity of such models is reduced by retrieving a more structured,
parsimonious model from the data, without exploiting physical knowledge.
Essential to the method is a translation of all multivariate nonlinear
functions, typically found in nonlinear state-space models, into sets of
univariate nonlinear functions. The latter is computed from a tensor
decomposition. It is shown that typically an excess of degrees of freedom are
used in the description of the nonlinear system whereas reduced representations
can be found. The method yields highly structured state-space models where the
nonlinearity is contained in as little as a single univariate function, with
limited loss of performance. Results are illustrated on simulations and
experiments for: the forced Duffing oscillator, the forced Van der Pol
oscillator, a Bouc-Wen hysteretic system, and a Li-Ion battery model.Comment: submitted to Mechanical Systems and Signal Processin
JALAD: Joint Accuracy- and Latency-Aware Deep Structure Decoupling for Edge-Cloud Execution
Recent years have witnessed a rapid growth of deep-network based services and
applications. A practical and critical problem thus has emerged: how to
effectively deploy the deep neural network models such that they can be
executed efficiently. Conventional cloud-based approaches usually run the deep
models in data center servers, causing large latency because a significant
amount of data has to be transferred from the edge of network to the data
center. In this paper, we propose JALAD, a joint accuracy- and latency-aware
execution framework, which decouples a deep neural network so that a part of it
will run at edge devices and the other part inside the conventional cloud,
while only a minimum amount of data has to be transferred between them. Though
the idea seems straightforward, we are facing challenges including i) how to
find the best partition of a deep structure; ii) how to deploy the component at
an edge device that only has limited computation power; and iii) how to
minimize the overall execution latency. Our answers to these questions are a
set of strategies in JALAD, including 1) A normalization based in-layer data
compression strategy by jointly considering compression rate and model
accuracy; 2) A latency-aware deep decoupling strategy to minimize the overall
execution latency; and 3) An edge-cloud structure adaptation strategy that
dynamically changes the decoupling for different network conditions.
Experiments demonstrate that our solution can significantly reduce the
execution latency: it speeds up the overall inference execution with a
guaranteed model accuracy loss.Comment: conference, copyright transfered to IEE
Scrambling speed of random quantum circuits
Random transformations are typically good at "scrambling" information.
Specifically, in the quantum setting, scrambling usually refers to the process
of mapping most initial pure product states under a unitary transformation to
states which are macroscopically entangled, in the sense of being close to
completely mixed on most subsystems containing a fraction fn of all n particles
for some constant f. While the term scrambling is used in the context of the
black hole information paradox, scrambling is related to problems involving
decoupling in general, and to the question of how large isolated many-body
systems reach local thermal equilibrium under their own unitary dynamics.
Here, we study the speed at which various notions of scrambling/decoupling
occur in a simplified but natural model of random two-particle interactions:
random quantum circuits. For a circuit representing the dynamics generated by a
local Hamiltonian, the depth of the circuit corresponds to time. Thus, we
consider the depth of these circuits and we are typically interested in what
can be done in a depth that is sublinear or even logarithmic in the size of the
system. We resolve an outstanding conjecture raised in the context of the black
hole information paradox with respect to the depth at which a typical quantum
circuit generates an entanglement assisted encoding against the erasure
channel. In addition, we prove that typical quantum circuits of poly(log n)
depth satisfy a stronger notion of scrambling and can be used to encode alpha n
qubits into n qubits so that up to beta n errors can be corrected, for some
constants alpha, beta > 0.Comment: 24 pages, 2 figures. Superseded by http://arxiv.org/abs/1307.063
Maximally rotating waves in AdS and on spheres
We study the cubic wave equation in AdS_(d+1) (and a closely related cubic
wave equation on S^3) in a weakly nonlinear regime. Via time-averaging, these
systems are accurately described by simplified infinite-dimensional quartic
Hamiltonian systems, whose structure is mandated by the fully resonant spectrum
of linearized perturbations. The maximally rotating sector, comprising only the
modes of maximal angular momentum at each frequency level, consistently
decouples in the weakly nonlinear regime. The Hamiltonian systems obtained by
this decoupling display remarkable periodic return behaviors closely analogous
to what has been demonstrated in recent literature for a few other related
equations (the cubic Szego equation, the conformal flow, the LLL equation).
This suggests a powerful underlying analytic structure, such as integrability.
We comment on the connection of our considerations to the Gross-Pitaevskii
equation for harmonically trapped Bose-Einstein condensates.Comment: 17 page
A discontinuous Galerkin method for a new class of Green-Naghdi equations on simplicial unstructured meshes
In this paper, we introduce a discontinuous Finite Element formulation on
simplicial unstructured meshes for the study of free surface flows based on the
fully nonlinear and weakly dispersive Green-Naghdi equations. Working with a
new class of asymptotically equivalent equations, which have a simplified
analytical structure, we consider a decoupling strategy: we approximate the
solutions of the classical shallow water equations supplemented with a source
term globally accounting for the non-hydrostatic effects and we show that this
source term can be computed through the resolution of scalar elliptic
second-order sub-problems. The assets of the proposed discrete formulation are:
(i) the handling of arbitrary unstructured simplicial meshes, (ii) an arbitrary
order of approximation in space, (iii) the exact preservation of the motionless
steady states, (iv) the preservation of the water height positivity, (v) a
simple way to enhance any numerical code based on the nonlinear shallow water
equations. The resulting numerical model is validated through several
benchmarks involving nonlinear wave transformations and run-up over complex
topographies
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