A regularization-free approach to the Cahn-Hilliard equation with logarithmic potentials
We introduce a regularization-free approach for the wellposedness of the classic Cahn-Hilliard equation with logarithmic potentials.
math.AP↗
arXiv subjects
Dong Li
Publications and source records attributed to Dong Li.
An Efficient Transfer Learning Framework for Multiagent Reinforcement Learning
Transfer Learning has shown great potential to enhance single-agent Reinforcement Learning (RL) efficiency. Similarly, Multiagent RL (MARL) can also be accelerated if agents can share knowledge with each other. However, it remains a problem of how an agent should learn from other agents. In this paper, we propose a novel Multiagent Policy Transfer Framework (MAPTF) to improve MARL efficiency. MAPTF learns which agent's policy is the best to reuse for each agent and when to terminate it by modeling multiagent policy transfer as the option learning problem. Furthermore, in practice, the option module can only collect all agent's local experiences for update due to the partial observability of the environment. While in this setting, each agent's experience may be inconsistent with each other, which may cause the inaccuracy and oscillation of the option-value's estimation. Therefore, we propose a novel option learning algorithm, the successor representation option learning to solve it by decoupling the environment dynamics from rewards and learning the option-value under each agent's preference. MAPTF can be easily combined with existing deep RL and MARL approaches, and experimental results show it significantly boosts the performance of existing methods in both discrete and continuous state spaces.
cs.MA↗
Convolutional Autoencoder-Based Phase Shift Feedback Compression for Intelligent Reflecting Surface-Assisted Wireless Systems
In recent years, intelligent reflecting surface (IRS) has emerged as a promising technology for 6G due to its potential/ability to significantly enhance energy- and spectrum-efficiency. To this end, it is crucial to adjust the phases of reflecting elements of the IRS, and most of the research works focus on how to optimize/quantize the phase for different optimization objectives. In particular, the quantized phase shift (QPS) is assumed to be available at the IRS, which, however, does not always hold and should be fed back to the IRS in practice. Unfortunately, the feedback channel is generally bandwidth-limited, which cannot support a huge amount of feedback overhead of the QPS particularly for a large number of reflecting elements and/or the quantization level of each reflecting element. In order to break this bottleneck, in this letter, we propose a convolutional autoencoder-based scheme, in which the QPS is compressed on the receiver side and reconstructed on the IRS side. In order to solve the problems of mismatched distribution and vanishing gradient, we remove the batch normalization (BN) layers and introduce a denosing module. By doing so, it is possible to achieve a high compression ratio with a reliable reconstruction accuracy in the bandwidth-limited feedback channel, and it is also possible to accommodate existing works assuming available QPS at the IRS. Simulation results confirm the high reconstruction accuracy of the feedback/compressed QPS through a feedback channel, and show that the proposed scheme can significantly outperform the existing compression algorithms.
eess.SP↗
The BDF3/EP3 scheme for MBE with no slope selection is stable
We consider the classical molecular beam epitaxy (MBE) model with logarithmic type potential known as no-slope-selection. We employ a third order backward differentiation (BDF3) in time with implicit treatment of the surface diffusion term. The nonlinear term is approximated by a third order explicit extrapolation (EP3) formula. We exhibit mild time step constraints under which the modified energy dissipation law holds. We break the second Dahlquist barrier and develop a new theoretical framework to prove unconditional uniform energy boundedness with no size restrictions on the time step. This is the first unconditional result for third order BDF methods applied to the MBE models without introducing any stabilization terms or fictitious variables. A novel theoretical framework is also established for the error analysis of high order methods.
math.NA↗
Empirical Policy Optimization for $n$-Player Markov Games
In single-agent Markov decision processes, an agent can optimize its policy based on the interaction with environment. In multi-player Markov games (MGs), however, the interaction is non-stationary due to the behaviors of other players, so the agent has no fixed optimization objective. In this paper, we treat the evolution of player policies as a dynamical process and propose a novel learning scheme for Nash equilibrium. The core is to evolve one's policy according to not just its current in-game performance, but an aggregation of its performance over history. We show that for a variety of MGs, players in our learning scheme will provably converge to a point that is an approximation to Nash equilibrium. Combined with neural networks, we develop the \emph{empirical policy optimization} algorithm, that is implemented in a reinforcement-learning framework and runs in a distributed way, with each player optimizing its policy based on own observations. We use two numerical examples to validate the convergence property on small-scale MGs with $n\ge 2$ players, and a pong example to show the potential of our algorithm on large games.
cs.GT↗
Ranking Cost: Building An Efficient and Scalable Circuit Routing Planner with Evolution-Based Optimization
Circuit routing has been a historically challenging problem in designing electronic systems such as very large-scale integration (VLSI) and printed circuit boards (PCBs). The main challenge is that connecting a large number of electronic components under specific design rules involves a very large search space. Early solutions are typically designed with hard-coded heuristics, which suffer from problems of non-optimal solutions and lack of flexibility for new design needs. Although a few learning-based methods have been proposed recently, they are typically cumbersome and hard to extend to large-scale applications. In this work, we propose a new algorithm for circuit routing, named Ranking Cost, which innovatively combines search-based methods (i.e., A* algorithm) and learning-based methods (i.e., Evolution Strategies) to form an efficient and trainable router. In our method, we introduce a new set of variables called cost maps, which can help the A* router to find out proper paths to achieve the global objective. We also train a ranking parameter, which can produce the ranking order and further improve the performance of our method. Our algorithm is trained in an end-to-end manner and does not use any artificial data or human demonstration. In the experiments, we compare with the sequential A* algorithm and a canonical reinforcement learning approach, and results show that our method outperforms these baselines with higher connectivity rates and better scalability.
cs.AI↗
ROBI: A Multi-View Dataset for Reflective Objects in Robotic Bin-Picking
In robotic bin-picking applications, the perception of texture-less, highly reflective parts is a valuable but challenging task. The high glossiness can introduce fake edges in RGB images and inaccurate depth measurements especially in heavily cluttered bin scenario. In this paper, we present the ROBI (Reflective Objects in BIns) dataset, a public dataset for 6D object pose estimation and multi-view depth fusion in robotic bin-picking scenarios. The ROBI dataset includes a total of 63 bin-picking scenes captured with two active stereo camera: a high-cost Ensenso sensor and a low-cost RealSense sensor. For each scene, the monochrome/RGB images and depth maps are captured from sampled view spheres around the scene, and are annotated with accurate 6D poses of visible objects and an associated visibility score. For evaluating the performance of depth fusion, we captured the ground truth depth maps by high-cost Ensenso camera with objects coated in anti-reflective scanning spray. To show the utility of the dataset, we evaluated the representative algorithms of 6D object pose estimation and multi-view depth fusion on the full dataset. Evaluation results demonstrate the difficulty of highly reflective objects, especially in difficult cases due to the degradation of depth data quality, severe occlusions and cluttered scene. The ROBI dataset is available online at https://www.trailab.utias.utoronto.ca/robi.
cs.RO↗
Outbursts and stellar properties of the classical Be star HD 6226
The bright and understudied classical Be star HD 6226 has exhibited multiple outbursts in the last several years during which the star grew a viscous decretion disk. We analyze 659 optical spectra of the system collected from 2017-2020, along with a UV spectrum from the Hubble Space Telescope and high cadence photometry from both TESS and the KELT survey. We find that the star has a spectral type of B2.5IIIe, with a rotation rate of 74% of critical. The star is nearly pole-on with an inclination of $13.4$ degree. We confirm the spectroscopic pulsational properties previously reported, and report on three photometric oscillations from KELT photometry. The outbursting behavior is studied with equivalent width measurements of H$α$ and H$β$, and the variations in both of these can be quantitatively explained with two frequencies through a Fourier analysis. One of the frequencies for the emission outbursts is equal to the difference between two photometric oscillations, linking these pulsation modes to the mass ejection mechanism for some outbursts. During the TESS observation time period of 2019 October 7 to 2019 November 2, the star was building a disk. With a large dataset of H$α$ and H$β$ spectroscopy, we are able to determine the timescales of dissipation in both of these lines, similar to past work on Be stars that has been done with optical photometry. HD 6226 is an ideal target with which to study the Be disk-evolution given its apparent periodic nature, allowing for targeted observations with other facilities in the future.
astro-ph.SR↗
Remarks on the Bernstein inequality for higher order operators and related results
This note is devoted to several results about frequency localized functions and associated Bernstein inequalities for higher order operators. In particular, we construct some counterexamples for the frequency-localized Bernstein inequalities for higher order Laplacians. We show also that the heat semi-group associated to powers larger than one of the laplacian does not satisfy the strict maximum principle in general. Finally, in a suitable range we provide several positive results.
math.AP↗
Bionic Optical Physical Unclonable Functions for Authentication and Encryption
Information security is of great importance for modern society with all things connected. Physical unclonable function (PUF) as a promising hardware primitive has been intensively studied for information security. However, the widely investigated silicon PUF with low entropy is vulnerable to various attacks. Herein, we introduce a concept of bionic optical PUFs inspired from unique biological architectures, and fabricate four types of bionic PUFs by molding the surface micro-nano structures of natural plant tissues with a simple, low-cost, green and environmentally friendly manufacturing process. The laser speckle responses of all bionic PUFs are statistically demonstrated to be random, unique, unpredictable and robust enough for cryptographic applications, indicating the broad applicability of bionic PUFs. On this ground, the feasibility of implementing bionic PUFs as cryptographic primitives in entity authentication and encrypted communication is experimentally validated, which shows its promising potential in the application of future information security.
cs.CR↗
Fast random number generator based on optical physical unclonable functions
We propose an approach for fast random number generation based on homemade optical physical unclonable functions (PUFs). The optical PUF is illuminated with input laser wavefront of continuous modulation to obtain different speckle patterns. Random numbers are fully extracted from speckle patterns through a simple post-processing algorithm. Our proof-of-principle experiment achieves total random number generation rate of 0.96 Gbit/s with verified randomness, which is far faster than previous optical-PUF-based schemes. Our results demonstrate that the presented random number generator (RNG) proposal has great potential to achieve ultrafast random number generation rate up to several hundreds of Gbit/s.
cs.CR↗
Towards Discriminative Representation Learning for Unsupervised Person Re-identification
In this work, we address the problem of unsupervised domain adaptation for person re-ID where annotations are available for the source domain but not for target. Previous methods typically follow a two-stage optimization pipeline, where the network is first pre-trained on source and then fine-tuned on target with pseudo labels created by feature clustering. Such methods sustain two main limitations. (1) The label noise may hinder the learning of discriminative features for recognizing target classes. (2) The domain gap may hinder knowledge transferring from source to target. We propose three types of technical schemes to alleviate these issues. First, we propose a cluster-wise contrastive learning algorithm (CCL) by iterative optimization of feature learning and cluster refinery to learn noise-tolerant representations in the unsupervised manner. Second, we adopt a progressive domain adaptation (PDA) strategy to gradually mitigate the domain gap between source and target data. Third, we propose Fourier augmentation (FA) for further maximizing the class separability of re-ID models by imposing extra constraints in the Fourier space. We observe that these proposed schemes are capable of facilitating the learning of discriminative feature representations. Experiments demonstrate that our method consistently achieves notable improvements over the state-of-the-art unsupervised re-ID methods on multiple benchmarks, e.g., surpassing MMT largely by 8.1\%, 9.9\%, 11.4\% and 11.1\% mAP on the Market-to-Duke, Duke-to-Market, Market-to-MSMT and Duke-to-MSMT tasks, respectively.
cs.CV↗
Quasi-Periodic Pulsations Detected in Ly$α$ and Nonthermal Emissions During Solar Flares
We report quasi-periodic pulsations (QPPs) with double periods during three solar flares (viz. SOL2011-Feb-15T01:44, SOL2011-Sep-25T04:31, SOL2012-May-17T01:25). The flare QPPs were observed from light curves in Ly$α$, hard X-ray (HXR) and microwave emissions, with the Ly$α$ emission recorded by the Geostationary Operational Environmental Satellite, the HXR emission recorded by the Reuven Ramaty High-Energy Solar Spectroscopic Imager and the Fermi Gamma-ray Burst Monitor, and the microwave emission recorded by the Nobeyama Radio Polarimeters and Radioheliograph. By using the Markov chain Monte Carlo (MCMC) method, QPPs with double periods of about two minutes and one minute were first found in the Ly$α$ emission. Then using the same method, a QPP with nearly the same period of about two minutes was also found in HXR and microwave emissions. Considering the possible common origin (nonthermal electrons) between Ly$α$ and HXR/microwave emission, we suggest that the two-minute QPP results from the periodic acceleration of nonthermal electrons during magnetic reconnections. The ratio between the double periods in the Ly$α$ emission was found to be close to two, which is consistent with the theoretical expectation between the fundamental and harmonic modes. However, we cannot rule out other possible driving mechanisms for the one-minute QPPs in HXR/microwave emissions due to their relatively large deviations.
astro-ph.SR↗
Detection of flare multi-periodic pulsations in mid-ultraviolet Balmer continuum, Ly-alpha, hard X-ray, and radio emissions simultaneously
Quasi-periodic pulsations (QPPs), which usually appear as temporal pulsations of the total flux, are frequently detected in the light curves of solar/stellar flares. In this study, we present the investigation of non-stationary QPPs with multiple periods during the impulsive phase of a powerful flare on 2017 September 06, which were simultane- ously measured by the Large-Yield RAdiometer (LYRA) and the Hard X-ray Modula- tion Telescope (Insight-HXMT), as well as the ground-based BLENSW. The multiple periods, detected by applying a wavelet transform and Lomb-Scargle periodogram to the detrended light curves, are found to be about 20-55 s in the Ly-alpha and mid-ultraviolet Balmer continuum emissions during the flare impulsive phase. Similar QPPs with multi- ple periods are also found in the hard X-ray emission and low-frequency radio emission. Our observations suggest that the flare QPPs could be related to nonthermal electrons accelerated by the repeated energy release process, i.e., triggering of repetitive magnetic reconnection, while the multiple periods might be modulated by the sausage oscillation of hot plasma loops. For the multi-periodic pulsations, other generation mechanisms could not be completely ruled out.
astro-ph.SR↗
Effective maximum principles for spectral methods
Many physical problems such as Allen-Cahn flows have natural maximum principles which yield strong point-wise control of the physical solutions in terms of the boundary data, the initial conditions and the operator coefficients. Sharp/strict maximum principles insomuch of fundamental importance for the continuous problem often do not persist under numerical discretization. A lot of past research concentrates on designing fine numerical schemes which preserves the sharp maximum principles especially for nonlinear problems. However these sharp principles not only sometimes introduce unwanted stringent conditions on the numerical schemes but also completely leaves many powerful frequency-based methods unattended and rarely analyzed directly in the sharp maximum norm topology. A prominent example is the spectral methods in the family of weighted residual methods. In this work we introduce and develop a new framework of almost sharp maximum principles which allow the numerical solutions to deviate from the sharp bound by a controllable discretization error: we call them effective maximum principles. We showcase the analysis for the classical Fourier spectral methods including Fourier Galerkin and Fourier collocation in space with forward Euler in time or second order Strang splitting. The model equations include the Allen-Cahn equations with double well potential, the Burgers equation and the Navier-Stokes equations. We give a comprehensive proof of the effective maximum principles under very general parametric conditions.
math.NA↗
Negative time splitting is stable
For high order (than two) in time operator-splitting methods applied to dissipative systems, a folklore issue is the appearance of negative-time/backward-in-time linear evolution operators such as backward heat operators interwoven with nonlinear evolutions. The stability of such methods has remained an ensuing difficult open problem. In this work we consider a fourth order operator splitting discretization for the Allen-Cahn equation which is a prototypical high order splitting method with negative time-stepping, i.e. backward in time integration for the linear parabolic part. We introduce a new theoretical framework and prove uniform energy stability and higher Sobolev stability. This is the first strong stability result for negative time stepping operator-splitting methods.
math.NA↗
On the energy stability of Strang-splitting for Cahn-Hilliard
We consider a Strang-type second order operator-splitting discretization for the Cahn-Hilliard equation. We introduce a new theoretical framework and prove uniform energy stability of the numerical solution and persistence of all higher Sobolev norms. This is the first strong stability result for second order operator-splitting methods for the Cahn-Hilliard equation. In particular we settle several long-standing open issues in the work of Cheng, Kurganov, Qu and Tang \cite{Tang15}.
math.NA↗
The operator-splitting method for Cahn-Hilliard is stable
We prove energy stability of a standard operator-splitting method for the Cahn-Hilliard equation. We establish uniform bound of Sobolev norms of the numerical solution and convergence of the splitting approximation. This is the first unconditional energy stability result for the operator-splitting method for the Cahn-Hilliard equation. Our analysis can be extended to many other models.
math.NA↗