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 $\gtrsim 15\%$ 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 $\sim 10^{42}\rm erg\ s^{-1}$) 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 $\sim 400$ 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