568 research outputs found
Anomalous dissipation in a stochastic inviscid dyadic model
A stochastic version of an inviscid dyadic model of turbulence, with
multiplicative noise, is proved to exhibit energy dissipation in spite of the
formal energy conservation. As a consequence, global regular solutions cannot
exist. After some reductions, the main tool is the escape bahavior at infinity
of a certain birth and death process.Comment: Published in at http://dx.doi.org/10.1214/11-AAP768 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Uniqueness for a Stochastic Inviscid Dyadic Model
For the deterministic dyadic model of turbulence, there are examples of
initial conditions in which have more than one solution. The aim of this
paper is to prove that uniqueness, for all -initial conditions, is
restored when a suitable multiplicative noise is introduced. The noise is
formally energy preserving. Uniqueness is understood in the weak probabilistic
sense.Comment: 13 pages, no figures. Submitted to the Proceedings of the American
Mathematical Societ
Anomalous dissipation in a stochastic inviscid dyadic model
A stochastic version of an inviscid dyadic model of turbulence, with
multiplicative noise, is proved to exhibit energy dissipation in spite of the
formal energy conservation. As a consequence, global regular solutions cannot
exist. After some reductions, the main tool is the escape bahavior at infinity
of a certain birth and death process.Comment: Published in at http://dx.doi.org/10.1214/11-AAP768 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A dyadic model on a tree
We study an infinite system of non-linear differential equations coupled in a
tree-like structure. This system was previously introduced in the literature
and it is the model from which the dyadic shell model of turbulence was
derived. It mimics 3d Euler and Navier-Stokes equations in a rough
approximation of a wavelet decomposition. We prove existence of finite energy
solutions, anomalous dissipation in the inviscid unforced case, existence and
uniqueness of stationary solutions (either conservative or not) in the forced
case
Smooth solutions for the dyadic model
We consider the dyadic model, which is a toy model to test issues of
well-posedness and blow-up for the Navier-Stokes and Euler equations. We prove
well-posedness of positive solutions of the viscous problem in the relevant
scaling range which corresponds to Navier-Stokes. Likewise we prove
well-posedness for the inviscid problem (in a suitable regularity class) when
the parameter corresponds to the strongest transport effect of the
non-linearity
Positive and non-positive solutions for an inviscid dyadic model. Well-posedness and regularity
We improve regolarity and uniqueness results from the literature for the
inviscid dyadic model. We show that positive dyadic is globally well-posed for
every rate of growth of the scaling coefficients k_n = 2^{bn}. Some
regularity results are proved for positive solutions, namely \sup_n n^{-a}
k_n^{1/3} X_n(t) < \infty for a.e. t and \sup_n k_n^{1/3-1/(3b)} X_n(t) \leq C
t^{-1/3}t$. Moreover it is shown that under very general hypothesis,
solutions become positive after a finite time
SAI, a Sensible Artificial Intelligence that plays Go
We propose a multiple-komi modification of the AlphaGo Zero/Leela Zero
paradigm. The winrate as a function of the komi is modeled with a
two-parameters sigmoid function, so that the neural network must predict just
one more variable to assess the winrate for all komi values. A second novel
feature is that training is based on self-play games that occasionally branch
-- with changed komi -- when the position is uneven. With this setting,
reinforcement learning is showed to work on 7x7 Go, obtaining very strong
playing agents. As a useful byproduct, the sigmoid parameters given by the
network allow to estimate the score difference on the board, and to evaluate
how much the game is decided.Comment: Updated for IJCNN 2019 conferenc
GloNets: Globally Connected Neural Networks
Deep learning architectures suffer from depth-related performance
degradation, limiting the effective depth of neural networks. Approaches like
ResNet are able to mitigate this, but they do not completely eliminate the
problem. We introduce Globally Connected Neural Networks (GloNet), a novel
architecture overcoming depth-related issues, designed to be superimposed on
any model, enhancing its depth without increasing complexity or reducing
performance. With GloNet, the network's head uniformly receives information
from all parts of the network, regardless of their level of abstraction. This
enables GloNet to self-regulate information flow during training, reducing the
influence of less effective deeper layers, and allowing for stable training
irrespective of network depth. This paper details GloNet's design, its
theoretical basis, and a comparison with existing similar architectures.
Experiments show GloNet's self-regulation ability and resilience to
depth-related learning challenges, like performance degradation. Our findings
suggest GloNet as a strong alternative to traditional architectures like
ResNets
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