4,277 research outputs found
Assessing the effects of data compression in simulations using physically motivated metrics
Abstract not provide
How to validate machine-learned interatomic potentials
Machine learning (ML) approaches enable large-scale atomistic simulations
with near-quantum-mechanical accuracy. With the growing availability of these
methods there arises a need for careful validation, particularly for physically
agnostic models - that is, for potentials which extract the nature of atomic
interactions from reference data. Here, we review the basic principles behind
ML potentials and their validation for atomic-scale materials modeling. We
discuss best practice in defining error metrics based on numerical performance
as well as physically guided validation. We give specific recommendations that
we hope will be useful for the wider community, including those researchers who
intend to use ML potentials for materials "off the shelf"
Performance Prediction of Nonbinary Forward Error Correction in Optical Transmission Experiments
In this paper, we compare different metrics to predict the error rate of
optical systems based on nonbinary forward error correction (FEC). It is shown
that the correct metric to predict the performance of coded modulation based on
nonbinary FEC is the mutual information. The accuracy of the prediction is
verified in a detailed example with multiple constellation formats, FEC
overheads in both simulations and optical transmission experiments over a
recirculating loop. It is shown that the employed FEC codes must be universal
if performance prediction based on thresholds is used. A tutorial introduction
into the computation of the threshold from optical transmission measurements is
also given.Comment: submitted to IEEE/OSA Journal of Lightwave Technolog
Geometry of logarithmic strain measures in solid mechanics
We consider the two logarithmic strain measureswhich are isotropic invariants of the
Hencky strain tensor , and show that they can be uniquely characterized
by purely geometric methods based on the geodesic distance on the general
linear group . Here, is the deformation gradient,
is the right Biot-stretch tensor, denotes the principal
matrix logarithm, is the Frobenius matrix norm, is the
trace operator and is the -dimensional deviator of
. This characterization identifies the Hencky (or
true) strain tensor as the natural nonlinear extension of the linear
(infinitesimal) strain tensor , which is the
symmetric part of the displacement gradient , and reveals a close
geometric relation between the classical quadratic isotropic energy potential
in
linear elasticity and the geometrically nonlinear quadratic isotropic Hencky
energywhere
is the shear modulus and denotes the bulk modulus. Our deduction
involves a new fundamental logarithmic minimization property of the orthogonal
polar factor , where is the polar decomposition of . We also
contrast our approach with prior attempts to establish the logarithmic Hencky
strain tensor directly as the preferred strain tensor in nonlinear isotropic
elasticity
Challenges in imaging and predictive modeling of rhizosphere processes
Background Plant-soil interaction is central to human food production and ecosystem function. Thus, it is essential to not only understand, but also to develop predictive mathematical models which can be used to assess how climate and soil management practices will affect these interactions. Scope In this paper we review the current developments in structural and chemical imaging of rhizosphere processes within the context of multiscale mathematical image based modeling. We outline areas that need more research and areas which would benefit from more detailed understanding. Conclusions We conclude that the combination of structural and chemical imaging with modeling is an incredibly powerful tool which is fundamental for understanding how plant roots interact with soil. We emphasize the need for more researchers to be attracted to this area that is so fertile for future discoveries. Finally, model building must go hand in hand with experiments. In particular, there is a real need to integrate rhizosphere structural and chemical imaging with modeling for better understanding of the rhizosphere processes leading to models which explicitly account for pore scale processes
Wavelet correlations to reveal multiscale coupling in geophysical systems
The interactions between climate and the environment are highly complex. Due
to this complexity, process-based models are often preferred to estimate the
net magnitude and directionality of interactions in the Earth System. However,
these models are based on simplifications of our understanding of nature, thus
are unavoidably imperfect. Conversely, observation-based data of climatic and
environmental variables are becoming increasingly accessible over large scales
due to the progress of space-borne sensing technologies and data-assimilation
techniques. Albeit uncertain, these data enable the possibility to start
unraveling complex multivariable, multiscale relationships if the appropriate
statistical methods are applied.
Here, we investigate the potential of the wavelet cross-correlation method as
a tool for identifying multiscale interactions, feedback and regime shifts in
geophysical systems. The ability of wavelet cross-correlation to resolve the
fast and slow components of coupled systems is tested on synthetic data of
known directionality, and then applied to observations to study one of the most
critical interactions between land and atmosphere: the coupling between soil
moisture and near-ground air temperature. Results show that our method is not
only able to capture the dynamics of the soil moisture-temperature coupling
over a wide range of temporal scales (from days to several months) and climatic
regimes (from wet to dry), but also to consistently identify the magnitude and
directionality of the coupling. Consequently, wavelet cross-correlations are
presented as a promising tool for the study of multiscale interactions, with
the potential of being extended to the analysis of causal relationships in the
Earth system.Comment: Submitted to Journal of Geophysical Research - Atmospher
- …