109,659 research outputs found
Data-Driven Approximation of Transfer Operators: Naturally Structured Dynamic Mode Decomposition
In this paper, we provide a new algorithm for the finite dimensional
approximation of the linear transfer Koopman and Perron-Frobenius operator from
time series data. We argue that existing approach for the finite dimensional
approximation of these transfer operators such as Dynamic Mode Decomposition
(DMD) and Extended Dynamic Mode Decomposition (EDMD) do not capture two
important properties of these operators, namely positivity and Markov property.
The algorithm we propose in this paper preserve these two properties. We call
the proposed algorithm as naturally structured DMD since it retains the
inherent properties of these operators. Naturally structured DMD algorithm
leads to a better approximation of the steady-state dynamics of the system
regarding computing Koopman and Perron- Frobenius operator eigenfunctions and
eigenvalues. However preserving positivity properties is critical for capturing
the real transient dynamics of the system. This positivity of the transfer
operators and it's finite dimensional approximation also has an important
implication on the application of the transfer operator methods for controller
and estimator design for nonlinear systems from time series data
Numerical product design: Springback prediction, compensation and optimization
Numerical simulations are being deployed widely for product design. However, the accuracy of the numerical tools is not yet always sufficiently accurate and reliable. This article focuses on the current state and recent developments in different stages of product design: springback prediction, springback compensation and optimization by finite element (FE) analysis. To improve the springback prediction by FE analysis, guidelines regarding the mesh discretization are provided and a new through-thickness integration scheme for shell elements is launched. In the next stage of virtual product design the product is compensated for springback. Currently, deformations due to springback are manually compensated in the industry. Here, a procedure to automatically compensate the tool geometry, including the CAD description, is presented and it is successfully applied to an industrial automotive part. The last stage in virtual product design comprises optimization. This article presents an optimization scheme which is capable of designing optimal and robust metal forming processes efficiently
Combined Global and Local Search for the Falsification of Hybrid Systems
In this paper we solve the problem of finding a trajectory that shows that a
given hybrid dynamical system with deterministic evolution leaves a given set
of states considered to be safe. The algorithm combines local with global
search for achieving both efficiency and global convergence. In local search,
it exploits derivatives for efficient computation. Unlike other methods for
falsification of hybrid systems with deterministic evolution, we do not
restrict our search to trajectories of a certain bounded length but search for
error trajectories of arbitrary length
Quantum Annealing and Analog Quantum Computation
We review here the recent success in quantum annealing, i.e., optimization of
the cost or energy functions of complex systems utilizing quantum fluctuations.
The concept is introduced in successive steps through the studies of mapping of
such computationally hard problems to the classical spin glass problems. The
quantum spin glass problems arise with the introduction of quantum
fluctuations, and the annealing behavior of the systems as these fluctuations
are reduced slowly to zero. This provides a general framework for realizing
analog quantum computation.Comment: 22 pages, 7 figs (color online); new References Added. Reviews of
Modern Physics (in press
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