3,630 research outputs found
DOSnet as a Non-Black-Box PDE Solver: When Deep Learning Meets Operator Splitting
Deep neural networks (DNNs) recently emerged as a promising tool for
analyzing and solving complex differential equations arising in science and
engineering applications. Alternative to traditional numerical schemes,
learning-based solvers utilize the representation power of DNNs to approximate
the input-output relations in an automated manner. However, the lack of
physics-in-the-loop often makes it difficult to construct a neural network
solver that simultaneously achieves high accuracy, low computational burden,
and interpretability. In this work, focusing on a class of evolutionary PDEs
characterized by having decomposable operators, we show that the classical
``operator splitting'' numerical scheme of solving these equations can be
exploited to design neural network architectures. This gives rise to a
learning-based PDE solver, which we name Deep Operator-Splitting Network
(DOSnet). Such non-black-box network design is constructed from the physical
rules and operators governing the underlying dynamics contains learnable
parameters, and is thus more flexible than the standard operator splitting
scheme. Once trained, it enables the fast solution of the same type of PDEs. To
validate the special structure inside DOSnet, we take the linear PDEs as the
benchmark and give the mathematical explanation for the weight behavior.
Furthermore, to demonstrate the advantages of our new AI-enhanced PDE solver,
we train and validate it on several types of operator-decomposable differential
equations. We also apply DOSnet to nonlinear Schr\"odinger equations (NLSE)
which have important applications in the signal processing for modern optical
fiber transmission systems, and experimental results show that our model has
better accuracy and lower computational complexity than numerical schemes and
the baseline DNNs
EUCLIA - Exploring the UV/optical continuum lag in active galactic nuclei. I. a model without light echoing
The tight inter-band correlation and the lag-wavelength relation among
UV/optical continua of active galactic nuclei have been firmly established.
They are usually understood within the widespread reprocessing scenario,
however, the implied inter-band lags are generally too small. Furthermore, it
is challenged by new evidences, such as the X-ray reprocessing yields too much
high frequency UV/optical variations as well as it fails to reproduce the
observed timescale-dependent color variations among {\it Swift} lightcurves of
NGC 5548. In a different manner, we demonstrate that an upgraded inhomogeneous
accretion disk model, whose local {\it independent} temperature fluctuations
are subject to a speculated {\it common} large-scale temperature fluctuation,
can intrinsically generate the tight inter-band correlation and lag across
UV/optical, and be in nice agreement with several observational properties of
NGC 5548, including the timescale-dependent color variation. The emergent lag
is a result of the {\it differential regression capability} of local
temperature fluctuations when responding to the large-scale fluctuation. An
average speed of propagations as large as of the speed of light
may be required by this common fluctuation. Several potential physical
mechanisms for such propagations are discussed. Our interesting
phenomenological scenario may shed new light on comprehending the UV/optical
continuum variations of active galactic nuclei.Comment: 18 pages, 8 figures. ApJ accepted. Further comments are very welcome
Topological triply-degenerate point with double Fermi arcs
Unconventional chiral particles have recently been predicted to appear in
certain three dimensional (3D) crystal structures containing three- or
more-fold linear band degeneracy points (BDPs). These BDPs carry topological
charges, but are distinct from the standard twofold Weyl points or fourfold
Dirac points, and cannot be described in terms of an emergent relativistic
field theory. Here, we report on the experimental observation of a topological
threefold BDP in a 3D phononic crystal. Using direct acoustic field mapping, we
demonstrate the existence of the threefold BDP in the bulk bandstructure, as
well as doubled Fermi arcs of surface states consistent with a topological
charge of 2. Another novel BDP, similar to a Dirac point but carrying nonzero
topological charge, is connected to the threefold BDP via the doubled Fermi
arcs. These findings pave the way to using these unconventional particles for
exploring new emergent physical phenomena
The universal "heartbeat" oscillations in black hole systems accross the mass-scale
The hyperluminous X-ray source (HLX-1, the peak X-ray luminosity ) near the spiral galaxy ESO 243-49 is possibly the best
candidate for intermediate mass black hole (IMBH), which underwent recurrent
outbursts with a period of days. The physical reason for this
quasi-periodic variability is still unclear. We explore the possibility of
radiation-pressure instability in accretion disk by modeling the light curve of
HLX-1, and find that it can roughly reproduce the duration, period and
amplitude of the recurrent outbursts HLX-1 with an IMBH of ~10^5Msun. Our
result provides a possible mechanism to explain the recurrent outbursts in
HLX-1. We further find a universal correlation between the outburst duration
and the bolometric luminosity for the BH sources with a very broad mass range
(e.g., X-ray binaries, XRBs, HLX-1 and active galactic nuclei, AGNs), which is
roughly consistent with the prediction of radiation-pressure instability of the
accretion disk. These results imply that "heartbeat" oscillations triggered by
radiation-pressure instability may appears in different-scale BH systems.Comment: ApJ in press; 15 pages, 5 Figure
Heat shock transcription factor 1 preserves cardiac angiogenesis and adaptation during pressure overload
To examine how heat shock transcription factor 1 (HSF1) protects against maladaptive hypertrophy during pressure overload, we subjected HSF1 transgenic (TG), knockout (KO) and wild type (WT) mice to a constriction of transverse aorta (TAC), and found that cardiac hypertrophy, functions and angiogenesis were well preserved in TG mice but were decreased in KO mice compared to WT ones at 4 weeks, which was related to HIF-1 and p53 expression. Inhibition of angiogenesis suppressed cardiac adaptation in TG mice while overexpression of angiogenesis factors improved maladaptive hypertrophy in KO mice. In vitro formation of vasculatures by microvascular endothelial cells was higher in TG mice but lower in KO mice than in WT ones. A siRNA of p53 but not a HIF-1 gene significantly reversed maladaptive hypertrophy in KO mice whereas a siRNA of HIF-1 but not a p53 gene induced maladaptive hypertrophy in TG mice. Heart microRNA analysis showed that miR-378 and miR-379 were differently changed among the three mice after TAC, and miR-378 or siRNA of miR-379 could maintain cardiac adaptation in WT mice. These results indicate that HSF1 preserves cardiac adaptation during pressure overload through p53-HIF-1-associated angiogenesis, which is controlled by miR-378 and miR-379
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