133 research outputs found
Equation of state of the neutron star matter, and the nuclear symmetry energy
The nuclear mean-field potentials obtained in the Hartree-Fock method with
different choices of the in-medium nucleon-nucleon (NN) interaction have been
used to study the equation of state (EOS) of the neutron star (NS) matter. The
EOS of the uniform NS core has been calculated for the np composition in
the -equilibrium at zero temperature, using version Sly4 of the Skyrme
interaction as well as two density-dependent versions of the finite-range M3Y
interaction (CDM3Y and M3Y-P), and versions D1S and D1N of the Gogny
interaction. Although the considered effective NN interactions were proven to
be quite realistic in numerous nuclear structure and/or reaction studies, they
give quite different behaviors of the symmetry energy of nuclear matter at
supranuclear densities that lead to the \emph{soft} and \emph{stiff} scenarios
discussed recently in the literature. Different EOS's of the NS core and the
EOS of the NS crust given by the compressible liquid drop model have been used
as input of the Tolman-Oppenheimer-Volkov equations to study how the nuclear
symmetry energy affects the model prediction of different NS properties, like
the cooling process as well as the gravitational mass, radius, and moment of
inertia.Comment: To be published in Physical Review
Clustering-based Identification of Precursors of Extreme Events in Chaotic Systems
Abrupt and rapid high-amplitude changes in a dynamical system's states known
as extreme event appear in many processes occurring in nature, such as drastic
climate patterns, rogue waves, or avalanches. These events often entail
catastrophic effects, therefore their description and prediction is of great
importance. However, because of their chaotic nature, their modelling
represents a great challenge up to this day. The applicability of a data-driven
modularity-based clustering technique to identify precursors of rare and
extreme events in chaotic systems is here explored. The proposed identification
framework based on clustering of system states, probability transition matrices
and state space tessellation was developed and tested on two different chaotic
systems that exhibit extreme events: the Moehliss-Faisst-Eckhardt model of
self-sustained turbulence and the 2D Kolmogorov flow. Both exhibit extreme
events in the form of bursts in kinetic energy and dissipation. It is shown
that the proposed framework provides a way to identify pathways towards extreme
events and predict their occurrence from a probabilistic standpoint. The
clustering algorithm correctly identifies the precursor states leading to
extreme events and allows for a statistical description of the system's states
and its precursors to extreme events
Learning Hidden States in a Chaotic System: A Physics-Informed Echo State Network Approach
International audienceWe extend the Physics-Informed Echo State Network (PI-ESN) framework to reconstruct the evolution of an unmeasured state (hidden state) in a chaotic system. The PI-ESN is trained by using (i) data, which contains no information on the unmeasured state, and (ii) the physical equations of a prototypical chaotic dynamical system. Non-noisy and noisy datasets are considered. First, it is shown that the PI-ESN can accurately reconstruct the unmeasured state. Second, the reconstruction is shown to be robust with respect to noisy data, which means that the PI-ESN acts as a denoiser. This paper opens up new possibilities for leveraging the synergy between physical knowledge and machine learning to enhance the reconstruction and prediction of unmeasured states in chaotic dynamical systems
Modelling spatiotemporal turbulent dynamics with the convolutional autoencoder echo state network
The spatiotemporal dynamics of turbulent flows is chaotic and difficult to
predict. This makes the design of accurate and stable reduced-order models
challenging. The overarching objective of this paper is to propose a nonlinear
decomposition of the turbulent state for a reduced-order representation of the
dynamics. We divide the turbulent flow into a spatial problem and a temporal
problem. First, we compute the latent space, which is the manifold onto which
the turbulent dynamics live (i.e., it is a numerical approximation of the
turbulent attractor). The latent space is found by a series of nonlinear
filtering operations, which are performed by a convolutional autoencoder (CAE).
The CAE provides the decomposition in space. Second, we predict the time
evolution of the turbulent state in the latent space, which is performed by an
echo state network (ESN). The ESN provides the decomposition in time. Third, by
assembling the CAE and the ESN, we obtain an autonomous dynamical system: the
convolutional autoncoder echo state network (CAE-ESN). This is the
reduced-order model of the turbulent flow. We test the CAE-ESN on a
two-dimensional flow. We show that, after training, the CAE-ESN (i) finds a
latent-space representation of the turbulent flow that has less than 1% of the
degrees of freedom than the physical space; (ii) time-accurately and
statistically predicts the flow in both quasiperiodic and turbulent regimes;
(iii) is robust for different flow regimes (Reynolds numbers); and (iv) takes
less than 1% of computational time to predict the turbulent flow than solving
the governing equations. This work opens up new possibilities for nonlinear
decompositions and reduced-order modelling of turbulent flows from data
Asymmetric Hashing for Fast Ranking via Neural Network Measures
Fast item ranking is an important task in recommender systems. In previous
works, graph-based Approximate Nearest Neighbor (ANN) approaches have
demonstrated good performance on item ranking tasks with generic
searching/matching measures (including complex measures such as neural network
measures). However, since these ANN approaches must go through the neural
measures several times during ranking, the computation is not practical if the
neural measure is a large network. On the other hand, fast item ranking using
existing hashing-based approaches, such as Locality Sensitive Hashing (LSH),
only works with a limited set of measures. Previous learning-to-hash approaches
are also not suitable to solve the fast item ranking problem since they can
take a significant amount of time and computation to train the hash functions.
Hashing approaches, however, are attractive because they provide a principle
and efficient way to retrieve candidate items. In this paper, we propose a
simple and effective learning-to-hash approach for the fast item ranking
problem that can be used for any type of measure, including neural network
measures. Specifically, we solve this problem with an asymmetric hashing
framework based on discrete inner product fitting. We learn a pair of related
hash functions that map heterogeneous objects (e.g., users and items) into a
common discrete space where the inner product of their binary codes reveals
their true similarity defined via the original searching measure. The fast
ranking problem is reduced to an ANN search via this asymmetric hashing scheme.
Then, we propose a sampling strategy to efficiently select relevant and
contrastive samples to train the hashing model. We empirically validate the
proposed method against the existing state-of-the-art fast item ranking methods
in several combinations of non-linear searching functions and prominent
datasets
Convolutional autoencoder for the spatiotemporal latent representation of turbulence
Turbulence is characterised by chaotic dynamics and a high-dimensional state
space, which make this phenomenon challenging to predict. However, turbulent
flows are often characterised by coherent spatiotemporal structures, such as
vortices or large-scale modes, which can help obtain a latent description of
turbulent flows. However, current approaches are often limited by either the
need to use some form of thresholding on quantities defining the isosurfaces to
which the flow structures are associated or the linearity of traditional modal
flow decomposition approaches, such as those based on proper orthogonal
decomposition. This problem is exacerbated in flows that exhibit extreme
events, which are rare and sudden changes in a turbulent state. The goal of
this paper is to obtain an efficient and accurate reduced-order latent
representation of a turbulent flow that exhibits extreme events. Specifically,
we employ a three-dimensional multiscale convolutional autoencoder (CAE) to
obtain such latent representation. We apply it to a three-dimensional turbulent
flow. We show that the Multiscale CAE is efficient, requiring less than 10%
degrees of freedom than proper orthogonal decomposition for compressing the
data and is able to accurately reconstruct flow states related to extreme
events. The proposed deep learning architecture opens opportunities for
nonlinear reduced-order modeling of turbulent flows from data
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