53,849 research outputs found
Inverse Design Based on Nonlinear Thermoelastic Material Models Applied to Injection Molding
This paper describes an inverse shape design method for thermoelastic bodies.
With a known equilibrium shape as input, the focus of this paper is the
determination of the corresponding initial shape of a body undergoing thermal
expansion or contraction, as well as nonlinear elastic deformations. A
distinguishing feature of the described method lies in its capability to
approximately prescribe an initial heterogeneous temperature distribution as
well as an initial stress field even though the initial shape is unknown. At
the core of the method, there is a system of nonlinear partial differential
equations. They are discretized and solved with the finite element method or
isogeometric analysis. In order to better integrate the method with
application-oriented simulations, an iterative procedure is described that
allows fine-tuning of the results. The method was motivated by an inverse
cavity design problem in injection molding applications. Its use in this field
is specifically highlighted, but the general description is kept independent of
the application to simplify its adaptation to a wider range of use cases.Comment: 22 pages, 13 figure
An improved Belief Propagation algorithm finds many Bethe states in the random field Ising model on random graphs
We first present an empirical study of the Belief Propagation (BP) algorithm,
when run on the random field Ising model defined on random regular graphs in
the zero temperature limit. We introduce the notion of maximal solutions for
the BP equations and we use them to fix a fraction of spins in their ground
state configuration. At the phase transition point the fraction of
unconstrained spins percolates and their number diverges with the system size.
This in turn makes the associated optimization problem highly non trivial in
the critical region. Using the bounds on the BP messages provided by the
maximal solutions we design a new and very easy to implement BP scheme which is
able to output a large number of stable fixed points. On one side this new
algorithm is able to provide the minimum energy configuration with high
probability in a competitive time. On the other side we found that the number
of fixed points of the BP algorithm grows with the system size in the critical
region. This unexpected feature poses new relevant questions on the physics of
this class of models.Comment: 20 pages, 8 figure
Online Convex Optimization for Sequential Decision Processes and Extensive-Form Games
Regret minimization is a powerful tool for solving large-scale extensive-form
games. State-of-the-art methods rely on minimizing regret locally at each
decision point. In this work we derive a new framework for regret minimization
on sequential decision problems and extensive-form games with general compact
convex sets at each decision point and general convex losses, as opposed to
prior work which has been for simplex decision points and linear losses. We
call our framework laminar regret decomposition. It generalizes the CFR
algorithm to this more general setting. Furthermore, our framework enables a
new proof of CFR even in the known setting, which is derived from a perspective
of decomposing polytope regret, thereby leading to an arguably simpler
interpretation of the algorithm. Our generalization to convex compact sets and
convex losses allows us to develop new algorithms for several problems:
regularized sequential decision making, regularized Nash equilibria in
extensive-form games, and computing approximate extensive-form perfect
equilibria. Our generalization also leads to the first regret-minimization
algorithm for computing reduced-normal-form quantal response equilibria based
on minimizing local regrets. Experiments show that our framework leads to
algorithms that scale at a rate comparable to the fastest variants of
counterfactual regret minimization for computing Nash equilibrium, and
therefore our approach leads to the first algorithm for computing quantal
response equilibria in extremely large games. Finally we show that our
framework enables a new kind of scalable opponent exploitation approach
On the Virtual Element Method for Topology Optimization on polygonal meshes: a numerical study
It is well known that the solution of topology optimization problems may be
affected both by the geometric properties of the computational mesh, which can
steer the minimization process towards local (and non-physical) minima, and by
the accuracy of the method employed to discretize the underlying differential
problem, which may not be able to correctly capture the physics of the problem.
In light of the above remarks, in this paper we consider polygonal meshes and
employ the virtual element method (VEM) to solve two classes of paradigmatic
topology optimization problems, one governed by nearly-incompressible and
compressible linear elasticity and the other by Stokes equations. Several
numerical results show the virtues of our polygonal VEM based approach with
respect to more standard methods
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