arXiv subjects

Yuan Gao

Publications and source records attributed to Yuan Gao.

At least 469 records · Page 26Linked to original sources

arXiv2020

Regularity and monotonicity for solutions to a continuum model of epitaxial growth with nonlocal elastic effects

We study a nonlocal 4th order degenerate equation deriving from the epitaxial growth on crystalline materials. We first prove the global existence of evolution variational inequality solution with a general initial data using the gradient flow structure. Then with a monotone initial data, we prove the subdifferential of the associated convex functional is indeed single-valued, which gives higher regularities of the global solution. Particularly, higher regularites imply that the strict monotonicity maintains for all time, which provides rigorous justification for global-in time monotone solution to epitaxial growth model with nonlocal elastic effects on vicinal surface.

math.AP↗

arXiv2020

First-Order Methods for Large-Scale Market Equilibrium Computation

Market equilibrium is a solution concept with many applications such as digital ad markets, fair division, and resource sharing. For many classes of utility functions, equilibria can be captured by convex programs. We develop simple first-order methods suitable for solving these convex programs for large-scale markets. We focus on three practically-relevant utility classes: linear, quasilinear, and Leontief utilities. Using structural properties of market equilibria under each utility class, we show that the corresponding convex programs can be reformulated as optimization of a structured smooth convex function over a polyhedral set, for which projected gradient achieves linear convergence. To do so, we utilize recent linear convergence results under weakened strong-convexity conditions, and further refine the relevant constants in existing convergence results. Then, we show that proximal gradient (a generalization of projected gradient) with a practical linesearch scheme achieves linear convergence under the Proximal-PL condition, a recently developed error bound condition for convex composite problems. For quasilinear utilities, we show that Mirror Descent applied to a new convex program achieves sublinear last-iterate convergence and yields a form of Proportional Response dynamics, an elegant, interpretable algorithm for computing market equilibria originally developed for linear utilities. Numerical experiments show that Proportional Response dynamics is highly efficient for computing approximate market equilibria, while projected gradient with linesearch can be much faster when higher-accuracy solutions are needed.

cs.GT↗

arXiv2020

Analysis of a fourth order exponential PDE arising from a crystal surface jump process with Metropolis-type transition rates

We analytically and numerically study a fourth order PDE modeling rough crystal surface diffusion on the macroscopic level. We discuss existence of solutions globally in time and long time dynamics for the PDE model. The PDE, originally derived by the second author, is the continuum limit of a microscopic model of the surface dynamics, given by a Markov jump process with Metropolis type transition rates. We outline the convergence argument, which depends on a simplifying assumption on the local equilibrium measure that is valid in the high temperature regime. We provide numerical evidence for the convergence of the microscopic model to the PDE in this regime.

math.AP↗

arXiv2020

Gradient flow formulation and second order numerical method for motion by mean curvature and contact line dynamics on rough surface

We study the dynamics of a droplet moving on an inclined rough surface in the absence of inertial and viscous stress effects. In this case, the dynamics of the droplet is a purely geometric motion in terms of the wetting domain and the capillary surface. Using a single graph representation, we interpret this geometric motion as a gradient flow on a Hilbert manifold. We propose unconditionally stable first/second order numerical schemes to simulate this geometric motion of the droplet, which is described using motion by mean curvature coupled with moving contact lines. The schemes are based on (i) explicit moving boundaries, which decouple the dynamic updates of the contact lines and the capillary surface, (ii) a semi-Lagrangian method on moving grids and (iii) a predictor-corrector method with a nonlinear elliptic solver upto second order accuracy. For the case of quasi-static dynamics with continuous spatial variable in the numerical schemes, we prove the stability and convergence of the first/second order numerical schemes. To demonstrate the accuracy and long-time validation of the proposed schemes, several challenging computational examples - including breathing droplets, droplets on inhomogeneous rough surfaces and quasi-static Kelvin pendant droplets - are constructed and compared with exact solutions to quasi-static dynamics obtained by desingularized differential-algebraic system of equations (DAEs).

math.NA↗

arXiv2020

Stacking Domain Wall Magnons in Twisted van der Waals Magnets

Using bilayer CrI$_3$ as an example, we demonstrate that stacking domain walls in van der Waals magnets can host one dimensional (1D) magnon channels, which have lower energies than bulk magnons. Interestingly, some magnon channels are hidden in magnetically homogeneous background and can only be inferred with the knowledge of stacking domain walls. Compared to 1D magnons confined in magnetic domain walls, 1D magnons in stacking domain walls are more stable against external perturbations. We show that the relaxed moiré superlattices of small-angle twisted bilayer CrI$_3$ is a natural realization of stacking domain walls and host interconnected moiré magnon network. Our work reveals the importance of stacking domain walls in understanding magnetic properties of van der Waals magnets, and extends the scope of stacking engineering to magnetic dynamics.

cond-mat.mtrl-sci↗

arXiv2020

Lagrangian correspondences and the generalized Viterbo restriction functor

We study two kinds of functors of wrapped Fukaya categories: 1) the Viterbo restriction functor for an inclusion of a Liouville sub-domain; 2) the Lagrangian correspondence functor associated to the graph of the completion of the inclusion of the sub-domain, named the graph correspondence functor. We prove that these two functors agree on the sub-category where the Viterbo restriction functor is defined. We also extend the Viterbo restriction functor to the case of non-strongly-exact restrictions of Lagrangian submanifolds, which yields a natural object-wise deformation of the wrapped Fukaya category, constructed using another theory - linearized Legendrian homology. On the other hand, the graph correspondence functor is naturally defined on the whole wrapped Fukaya category, a priori taking values in a suitable enlargement of the wrapped Fukaya category having certain Lagrangian immersions as objects. We prove that the graph correspondence functor agrees with the extension of the Viterbo restriction functor.

math.SG↗

arXiv2020

WeChat Neural Machine Translation Systems for WMT20

We participate in the WMT 2020 shared news translation task on Chinese to English. Our system is based on the Transformer (Vaswani et al., 2017a) with effective variants and the DTMT (Meng and Zhang, 2019) architecture. In our experiments, we employ data selection, several synthetic data generation approaches (i.e., back-translation, knowledge distillation, and iterative in-domain knowledge transfer), advanced finetuning approaches and self-bleu based model ensemble. Our constrained Chinese to English system achieves 36.9 case-sensitive BLEU score, which is the highest among all submissions.

cs.CL↗

arXiv2020

Grid-Forming Converters control based on DC voltage feedback

The renewable energy is connected to the power grid through power electronic converters, which are lack of make the inertia of synchronous generator/machine (SM) be lost. The increasing penetration of renewable energy in power system weakens the frequency and voltage stability. The Grid-Forming Converters (GFCs) simulate the function of synchronous motor through control method in order to improve the stability of power grid by providing inertia and stability regulation mechanism. This kind of converter control methods include virtual synchronous machine, schedulable virtual oscillator control and so on. These control method mainly use AC side state feedback and do not monitor the DC side state. This paper analyzes the control strategy of GFC considering power grid stability, including Frequency Droop Control, Virtual Synchronous Machine Control and dispatchable Virtual Oscillator Control. The DC side voltage collapse problem is found when a large load disturbance occurs. The control methods of GFC considering DC side voltage feedback are proposed, which can ensure the synchronization characteristics of grid connection and solve the problem of DC side voltage collapse. The proposed method is verified by IEEE-9 bus system, which shows the effectiveness of the proposed method.

eess.SY↗

arXiv2020

CAD-PU: A Curvature-Adaptive Deep Learning Solution for Point Set Upsampling

Point set is arguably the most direct approximation of an object or scene surface, yet its practical acquisition often suffers from the shortcoming of being noisy, sparse, and possibly incomplete, which restricts its use for a high-quality surface recovery. Point set upsampling aims to increase its density and regularity such that a better surface recovery could be achieved. The problem is severely ill-posed and challenging, considering that the upsampling target itself is only an approximation of the underlying surface. Motivated to improve the surface approximation via point set upsampling, we identify the factors that are critical to the objective, by pairing the surface approximation error bounds of the input and output point sets. It suggests that given a fixed budget of points in the upsampling result, more points should be distributed onto the surface regions where local curvatures are relatively high. To implement the motivation, we propose a novel design of Curvature-ADaptive Point set Upsampling network (CAD-PU), the core of which is a module of curvature-adaptive feature expansion. To train CAD-PU, we follow the same motivation and propose geometrically intuitive surrogates that approximate discrete notions of surface curvature for the upsampled point set. We further integrate the proposed surrogates into an adversarial learning based curvature minimization objective, which gives a practically effective learning of CAD-PU. We conduct thorough experiments that show the efficacy of our contributions and the advantages of our method over existing ones. Our implementation codes are publicly available at https://github.com/JiehongLin/CAD-PU.

cs.CV↗

arXiv2020

Pion production and absorption in heavy-ion collisions

Based on the isospin dependent transport model IBUU, the pion production and its absorption are thoroughly studied in the central collision of $Au+Au$ at a beam energy of 400 MeV/nucleon. It is found that the pions are firstly produced by the hard $Δ$ decay at the average density around $1.75ρ_{0}$, whereas about 18\% of them are absorbed absolutely in the subsequent inelastic collisions. For the free pions observed, more than half of them have been scattered for one or more times before they are free from matter. And the more scattering numbers of pions, the higher the momentum they possess. These pions, due to longer time of their existence in high density nuclear matter, carry more information about the symmetry energy of the nuclear matter at high densities.

nucl-th↗

arXiv2020

An Improved Analysis of Stochastic Gradient Descent with Momentum

SGD with momentum (SGDM) has been widely applied in many machine learning tasks, and it is often applied with dynamic stepsizes and momentum weights tuned in a stagewise manner. Despite of its empirical advantage over SGD, the role of momentum is still unclear in general since previous analyses on SGDM either provide worse convergence bounds than those of SGD, or assume Lipschitz or quadratic objectives, which fail to hold in practice. Furthermore, the role of dynamic parameters has not been addressed. In this work, we show that SGDM converges as fast as SGD for smooth objectives under both strongly convex and nonconvex settings. We also establish \textit{the first} convergence guarantee for the multistage setting, and show that the multistage strategy is beneficial for SGDM compared to using fixed parameters. Finally, we verify these theoretical claims by numerical experiments.

math.OC↗

arXiv2020

PP-YOLO: An Effective and Efficient Implementation of Object Detector

Object detection is one of the most important areas in computer vision, which plays a key role in various practical scenarios. Due to limitation of hardware, it is often necessary to sacrifice accuracy to ensure the infer speed of the detector in practice. Therefore, the balance between effectiveness and efficiency of object detector must be considered. The goal of this paper is to implement an object detector with relatively balanced effectiveness and efficiency that can be directly applied in actual application scenarios, rather than propose a novel detection model. Considering that YOLOv3 has been widely used in practice, we develop a new object detector based on YOLOv3. We mainly try to combine various existing tricks that almost not increase the number of model parameters and FLOPs, to achieve the goal of improving the accuracy of detector as much as possible while ensuring that the speed is almost unchanged. Since all experiments in this paper are conducted based on PaddlePaddle, we call it PP-YOLO. By combining multiple tricks, PP-YOLO can achieve a better balance between effectiveness (45.2% mAP) and efficiency (72.9 FPS), surpassing the existing state-of-the-art detectors such as EfficientDet and YOLOv4.Source code is at https://github.com/PaddlePaddle/PaddleDetection.

cs.CV↗

arXiv2020

Has LIGO Detected Primordial Black Hole Dark Matter? -- Tidal Disruption in Binary Black Hole Formation

The frequent detection of binary mergers of $\sim 30 M_{\odot}$ black holes (BHs) by the Laser Interferometer Gravitational-Wave Observatory (LIGO) rekindled researchers' interest in primordial BHs (PBHs) being dark matter (DM). In this work, we looked at PBHs distributed as DM with a monochromatic mass of $30 M_{\odot}$ and examined the encounter-capture scenario of binary formation, where the densest central region of DM halo dominates. Thus, we paid special attention to the tidal effect by the supermassive black hole (SMBH) present. In doing so, we discovered a necessary tool called loss zone that complements the usage of loss cone. We found that the tidal effect is not prominent in affecting binary formation, which also turned out insufficient in explaining the totality of LIGO's event rate estimation, especially due to a microlensing event constraining the DM fraction in PBH at the mass of interest from near unity to an order smaller. Meanwhile, early-universe binary formation scenario proves so prevailing that the LIGO signal in turn constrains the PBH fraction below one percent. Thus, people should put more faith in alternative PBH windows and other DM candidates.

astro-ph.HE↗

arXiv2020

Non-local SPDE limits of spatially-correlated-noise driven spin systems derived to sample a canonical distribution

We study the macroscopic behavior of a stochastic spin ensemble driven by a discrete Markov jump process motivated by the Metropolis-Hastings algorithm where the proposal is made with spatially correlated (colored) noise, and hence fails to be symmetric. However, we demonstrate a scenario where the failure of proposal symmetry is a higher order effect. Hence, from these microscopic dynamics we derive as a limit as the proposal size goes to zero and the number of spins to infinity, a non-local stochastic version of the harmonic map heat flow (or overdamped Landau-Lipshitz equation). The equation is both mathematically well-posed and samples the canonical/Gibbs distribution related to the kinetic energy. The failure of proposal symmetry due to interaction between the confining geometry of the spin system and the colored noise is in contrast to the uncorrelated, white-noise, driven system. Specifically, the choice of projection of the noise to conserve the magnitude of the spins is crucial to maintaining the proper equilibrium distribution. Numerical simulations are included to verify convergence properties and demonstrate the dynamics.

cond-mat.stat-mech↗

arXiv2020

Graph-PCNN: Two Stage Human Pose Estimation with Graph Pose Refinement

Recently, most of the state-of-the-art human pose estimation methods are based on heatmap regression. The final coordinates of keypoints are obtained by decoding heatmap directly. In this paper, we aim to find a better approach to get more accurate localization results. We mainly put forward two suggestions for improvement: 1) different features and methods should be applied for rough and accurate localization, 2) relationship between keypoints should be considered. Specifically, we propose a two-stage graph-based and model-agnostic framework, called Graph-PCNN, with a localization subnet and a graph pose refinement module added onto the original heatmap regression network. In the first stage, heatmap regression network is applied to obtain a rough localization result, and a set of proposal keypoints, called guided points, are sampled. In the second stage, for each guided point, different visual feature is extracted by the localization subnet. The relationship between guided points is explored by the graph pose refinement module to get more accurate localization results. Experiments show that Graph-PCNN can be used in various backbones to boost the performance by a large margin. Without bells and whistles, our best model can achieve a new state-of-the-art 76.8% AP on COCO test-dev split.

cs.CV↗

arXiv2020

Automatic Differentiation for Second Renormalization of Tensor Networks

Tensor renormalization group (TRG) constitutes an important methodology for accurate simulations of strongly correlated lattice models. Facilitated by the automatic differentiation technique widely used in deep learning, we propose a uniform framework of differentiable TRG ($\partial$TRG) that can be applied to improve various TRG methods, in an automatic fashion. Essentially, $\partial$TRG systematically extends the concept of second renormalization [PRL 103, 160601 (2009)] where the tensor environment is computed recursively in the backward iteration, in the sense that given the forward process of TRG, $\partial$TRG automatically finds the gradient through backpropagation, with which one can deeply "train" the tensor networks. We benchmark $\partial$TRG in solving the square-lattice Ising model, and demonstrate its power by simulating one- and two-dimensional quantum systems at finite temperature. The deep optimization as well as GPU acceleration renders $\partial$TRG manybody simulations with high efficiency and accuracy.

cond-mat.str-el↗

arXiv2020

Increasing Iterate Averaging for Solving Saddle-Point Problems

Many problems in machine learning and game theory can be formulated as saddle-point problems, for which various first-order methods have been developed and proven efficient in practice. Under the general convex-concave assumption, most first-order methods only guarantee an ergodic convergence rate, that is, the uniform averages of the iterates converge at a $O(1/T)$ rate in terms of the saddle-point residual. However, numerically, the iterates themselves can often converge much faster than the uniform averages. This observation motivates increasing averaging schemes that put more weight on later iterates, in contrast to the usual uniform averaging. We show that such increasing averaging schemes, applied to various first-order methods, are able to preserve the $O(1/T)$ convergence rate with no additional assumptions or computational overhead. Extensive numerical experiments on zero-sum game solving, market equilibrium computation and image denoising demonstrate the effectiveness of the proposed schemes. In particular, the increasing averages consistently outperform the uniform averages in all test problems by orders of magnitude. When solving matrix and extensive-form games, increasing averages consistently outperform the last iterates as well. For matrix games, a first-order method equipped with increasing averaging outperforms the highly competitive CFR$^+$ algorithm.

cs.LG↗

arXiv2020

Inbetweening auto-animation via Fokker-Planck dynamics and thresholding

We propose an equilibrium-driven deformation algorithm (EDDA) to simulate the inbetweening transformations starting from an initial image to an equilibrium image, which covers images varying from a greyscale type to a colorful type on plane or manifold. The algorithm is based on Fokker-Planck dynamics on manifold, which automatically cooperates positivity, unconditional stability, mass conservation law, exponentially convergence and also the manifold structure suggested by dataset. The thresholding scheme is adapted for the sharp interface dynamics and is used to achieve the finite time convergence. Using EDDA, three challenging examples, (I) facial aging process, (II) coronavirus disease 2019 (COVID-19) invading/treatment process, and (III) continental evolution process are conducted efficiently.

math.NA↗