23,148 research outputs found
Differential Evolution with Reversible Linear Transformations
Differential evolution (DE) is a well-known type of evolutionary algorithms
(EA). Similarly to other EA variants it can suffer from small populations and
loose diversity too quickly. This paper presents a new approach to mitigate
this issue: We propose to generate new candidate solutions by utilizing
reversible linear transformation applied to a triplet of solutions from the
population. In other words, the population is enlarged by using newly generated
individuals without evaluating their fitness. We assess our methods on three
problems: (i) benchmark function optimization, (ii) discovering parameter
values of the gene repressilator system, (iii) learning neural networks. The
empirical results indicate that the proposed approach outperforms vanilla DE
and a version of DE with applying differential mutation three times on all
testbeds.Comment: Code: https://github.com/jmtomcza
Differential Evolution with Reversible Linear Transformations
Differential evolution (DE) is a well-known type of evolutionary algorithms (EA). Similarly to other EA variants it can suffer from small populations and loose diversity too quickly. This paper presents a new approach to mitigate this issue: We propose to generate new candidate solutions by utilizing reversible linear transformations applied to a triplet of solutions from the population. In other words, the population is enlarged by using newly generated individuals without evaluating their fitness. We assess our methods on three problems: (i) benchmark function optimization, (ii) discovering parameter values of the gene repressilator system, (iii) learning neural networks. The empirical results indicate that the proposed approach outperforms vanilla DE and a version of DE with applying differential mutation three times on all testbeds
Discrete Nonholonomic Lagrangian Systems on Lie Groupoids
This paper studies the construction of geometric integrators for nonholonomic
systems. We derive the nonholonomic discrete Euler-Lagrange equations in a
setting which permits to deduce geometric integrators for continuous
nonholonomic systems (reduced or not). The formalism is given in terms of Lie
groupoids, specifying a discrete Lagrangian and a constraint submanifold on it.
Additionally, it is necessary to fix a vector subbundle of the Lie algebroid
associated to the Lie groupoid. We also discuss the existence of nonholonomic
evolution operators in terms of the discrete nonholonomic Legendre
transformations and in terms of adequate decompositions of the prolongation of
the Lie groupoid. The characterization of the reversibility of the evolution
operator and the discrete nonholonomic momentum equation are also considered.
Finally, we illustrate with several classical examples the wide range of
application of the theory (the discrete nonholonomic constrained particle, the
Suslov system, the Chaplygin sleigh, the Veselova system, the rolling ball on a
rotating table and the two wheeled planar mobile robot).Comment: 45 page
Lie groups in nonequilibrium thermodynamics: Geometric structure behind viscoplasticity
Poisson brackets provide the mathematical structure required to identify the
reversible contribution to dynamic phenomena in nonequilibrium thermodynamics.
This mathematical structure is deeply linked to Lie groups and their Lie
algebras. From the characterization of all the Lie groups associated with a
given Lie algebra as quotients of a universal covering group, we obtain a
natural classification of rheological models based on the concept of discrete
reference states and, in particular, we find a clear-cut and deep distinction
between viscoplasticity and viscoelasticity. The abstract ideas are illustrated
by a naive toy model of crystal viscoplasticity, but similar kinetic models are
also used for modeling the viscoplastic behavior of glasses. We discuss some
implications for coarse graining and statistical mechanics.Comment: 11 pages, 1 figure, accepted for publication in J. Non-Newtonian
Fluid Mech. Keywords: Elastic-viscoplastic materials, Nonequilibrium
thermodynamics, GENERIC, Lie groups, Reference state
Robust learning with implicit residual networks
In this effort, we propose a new deep architecture utilizing residual blocks
inspired by implicit discretization schemes. As opposed to the standard
feed-forward networks, the outputs of the proposed implicit residual blocks are
defined as the fixed points of the appropriately chosen nonlinear
transformations. We show that this choice leads to the improved stability of
both forward and backward propagations, has a favorable impact on the
generalization power and allows to control the robustness of the network with
only a few hyperparameters. In addition, the proposed reformulation of ResNet
does not introduce new parameters and can potentially lead to a reduction in
the number of required layers due to improved forward stability. Finally, we
derive the memory-efficient training algorithm, propose a stochastic
regularization technique and provide numerical results in support of our
findings
Moving gap solitons in periodic potentials
We address existence of moving gap solitons (traveling localized solutions)
in the Gross-Pitaevskii equation with a small periodic potential. Moving gap
solitons are approximated by the explicit localized solutions of the
coupled-mode system. We show however that exponentially decaying traveling
solutions of the Gross-Pitaevskii equation do not generally exist in the
presence of a periodic potential due to bounded oscillatory tails ahead and
behind the moving solitary waves. The oscillatory tails are not accounted in
the coupled-mode formalism and are estimated by using techniques of spatial
dynamics and local center-stable manifold reductions. Existence of bounded
traveling solutions of the Gross--Pitaevskii equation with a single bump
surrounded by oscillatory tails on a finite large interval of the spatial scale
is proven by using these technique. We also show generality of oscillatory
tails in other nonlinear equations with a periodic potential.Comment: 22 pages, 2 figure
Microscopic derivation of an adiabatic thermodynamic transformation
We obtain macroscopic adiabatic thermodynamic transformations by space-time
scalings of a microscopic Hamiltonian dynamics subject to random collisions
with the environment. The microscopic dynamics is given by a chain of
oscillators subject to a varying tension (external force) and to collisions
with external independent particles of "infinite mass". The effect of each
collision is to change the sign of the velocity without changing the modulus.
This way the energy is conserved by the resulting dynamics. After a diffusive
space-time scaling and cross-graining, the profiles of volume and energy
converge to the solution of a deterministic diffusive system of equations with
boundary conditions given by the applied tension. This defines an irreversible
thermodynamic transformation from an initial equilibrium to a new equilibrium
given by the final tension applied. Quasi-static reversible adiabatic
transformations are then obtained by a further time scaling. Then we prove that
the relations between the limit work, internal energy and thermodynamic entropy
agree with the first and second principle of thermodynamics.Comment: New version accepted for the publication in Brazilian Journal of
Probability and Statistic
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