80,110 research outputs found
Quantum dynamics in transverse-field Ising models from classical networks
The efficient representation of quantum many-body states with classical
resources is a key challenge in quantum many-body theory. In this work we
analytically construct classical networks for the description of the quantum
dynamics in transverse-field Ising models that can be solved efficiently using
Monte Carlo techniques. Our perturbative construction encodes time-evolved
quantum states of spin-1/2 systems in a network of classical spins with local
couplings and can be directly generalized to other spin systems and higher
spins. Using this construction we compute the transient dynamics in one, two,
and three dimensions including local observables, entanglement production, and
Loschmidt amplitudes using Monte Carlo algorithms and demonstrate the accuracy
of this approach by comparisons to exact results. We include a mapping to
equivalent artificial neural networks, which were recently introduced to
provide a universal structure for classical network wave functions
Over-parameterisation, a major obstacle to the use of artificial neural networks in hydrology?
International audienceRecently Feed-Forward Artificial Neural Networks (FNN) have been gaining popularity for stream flow forecasting. However, despite the promising results presented in recent papers, their use is questionable. In theory, their "universal approximator? property guarantees that, if a sufficient number of neurons is selected, good performance of the models for interpolation purposes can be achieved. But the choice of a more complex model does not ensure a better prediction. Models with many parameters have a high capacity to fit the noise and the particularities of the calibration dataset, at the cost of diminishing their generalisation capacity. In support of the principle of model parsimony, a model selection method based on the validation performance of the models, "traditionally" used in the context of conceptual rainfall-runoff modelling, was adapted to the choice of a FFN structure. This method was applied to two different case studies: river flow prediction based on knowledge of upstream flows, and rainfall-runoff modelling. The predictive powers of the neural networks selected are compared to the results obtained with a linear model and a conceptual model (GR4j). In both case studies, the method leads to the selection of neural network structures with a limited number of neurons in the hidden layer (two or three). Moreover, the validation results of the selected FNN and of the linear model are very close. The conceptual model, specifically dedicated to rainfall-runoff modelling, appears to outperform the other two approaches. These conclusions, drawn on specific case studies using a particular evaluation method, add to the debate on the usefulness of Artificial Neural Networks in hydrology. Keywords: forecasting; stream-flow; rainfall-runoff; Artificial Neural Network
Large statistical learning models effectively forecast diverse chaotic systems
Chaos and unpredictability are traditionally synonymous, yet recent advances
in statistical forecasting suggest that large machine learning models can
derive unexpected insight from extended observation of complex systems. Here,
we study the forecasting of chaos at scale, by performing a large-scale
comparison of 24 representative state-of-the-art multivariate forecasting
methods on a crowdsourced database of 135 distinct low-dimensional chaotic
systems. We find that large, domain-agnostic time series forecasting methods
based on artificial neural networks consistently exhibit strong forecasting
performance, in some cases producing accurate predictions lasting for dozens of
Lyapunov times. Best-in-class results for forecasting chaos are achieved by
recently-introduced hierarchical neural basis function models, though even
generic transformers and recurrent neural networks perform strongly. However,
physics-inspired hybrid methods like neural ordinary equations and reservoir
computers contain inductive biases conferring greater data efficiency and lower
training times in data-limited settings. We observe consistent correlation
across all methods despite their widely-varying architectures, as well as
universal structure in how predictions decay over long time intervals. Our
results suggest that a key advantage of modern forecasting methods stems not
from their architectural details, but rather from their capacity to learn the
large-scale structure of chaotic attractors.Comment: 5 pages, 3 figure
Machine Learning for the Prediction of Converged Energies from Ab Initio Nuclear Structure Calculations
The prediction of nuclear observables beyond the finite model spaces that are
accessible through modern ab initio methods, such as the no-core shell model,
pose a challenging task in nuclear structure theory. It requires reliable tools
for the extrapolation of observables to infinite many-body Hilbert spaces along
with reliable uncertainty estimates. In this work we present a universal
machine learning tool capable of capturing observable-specific convergence
patterns independent of nucleus and interaction. We show that, once trained on
few-body systems, artificial neural networks can produce accurate predictions
for a broad range of light nuclei. In particular, we discuss neural-network
predictions of ground-state energies from no-core shell model calculations for
6Li, 12C and 16O based on training data for 2H, 3H and 4He and compare them to
classical extrapolations.Comment: 7 pages, 5 figures, 1 tabl
MI-NODES multiscale models of metabolic reactions, brain connectome, ecological, epidemic, world trade, and legal-social networks
[Abstract] Complex systems and networks appear in almost all areas of reality. We find then from proteins residue networks to Protein Interaction Networks (PINs). Chemical reactions form Metabolic Reactions Networks (MRNs) in living beings or Atmospheric reaction networks in planets and moons. Network of neurons appear in the worm C. elegans, in Human brain connectome, or in Artificial Neural Networks (ANNs). Infection spreading networks exist for contagious outbreaks networks in humans and in malware epidemiology for infection with viral software in internet or wireless networks. Social-legal networks with different rules evolved from swarm intelligence, to hunter-gathered societies, or citation networks of U.S. Supreme Court. In all these cases, we can see the same question. Can we predict the links based on structural information? We propose to solve the problem using Quantitative Structure-Property Relationship (QSPR) techniques commonly used in chemo-informatics. In so doing, we need software able to transform all types of networks/graphs like drug structure, drug-target interactions, protein structure, protein interactions, metabolic reactions, brain connectome, or social networks into numerical parameters. Consequently, we need to process in alignment-free mode multitarget, multiscale, and multiplexing, information. Later, we have to seek the QSPR model with Machine Learning techniques. MI-NODES is this type of software. Here we review the evolution of the software from chemoinformatics to bioinformatics and systems biology. This is an effort to develop a universal tool to study structure-property relationships in complex systems
Artificial Neural Network in Cosmic Landscape
In this paper we propose that artificial neural network, the basis of machine
learning, is useful to generate the inflationary landscape from a cosmological
point of view. Traditional numerical simulations of a global cosmic landscape
typically need an exponential complexity when the number of fields is large.
However, a basic application of artificial neural network could solve the
problem based on the universal approximation theorem of the multilayer
perceptron. A toy model in inflation with multiple light fields is investigated
numerically as an example of such an application.Comment: v2, add some new content
Morphological Network: How Far Can We Go with Morphological Neurons?
In recent years, the idea of using morphological operations as networks has
received much attention. Mathematical morphology provides very efficient and
useful image processing and image analysis tools based on basic operators like
dilation and erosion, defined in terms of kernels. Many other morphological
operations are built up using the dilation and erosion operations. Although the
learning of structuring elements such as dilation or erosion using the
backpropagation algorithm is not new, the order and the way these morphological
operations are used is not standard. In this paper, we have theoretically
analyzed the use of morphological operations for processing 1D feature vectors
and shown that this gets extended to the 2D case in a simple manner. Our
theoretical results show that a morphological block represents a sum of hinge
functions. Hinge functions are used in many places for classification and
regression tasks (Breiman (1993)). We have also proved a universal
approximation theorem -- a stack of two morphological blocks can approximate
any continuous function over arbitrary compact sets. To experimentally validate
the efficacy of this network in real-life applications, we have evaluated its
performance on satellite image classification datasets since morphological
operations are very sensitive to geometrical shapes and structures. We have
also shown results on a few tasks like segmentation of blood vessels from
fundus images, segmentation of lungs from chest x-ray and image dehazing. The
results are encouraging and further establishes the potential of morphological
networks.Comment: 35 pages, 19 figures, 7 table
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