arXiv subjects

Wei Pan

Publications and source records attributed to Wei Pan.

At least 163 records · Page 9Linked to original sources

arXiv2021

Theoretical and computational analysis of the thermal quasi-geostrophic model

This work involves theoretical and numerical analysis of the Thermal Quasi-Geostrophic (TQG) model of submesoscale geophysical fluid dynamics (GFD). Physically, the TQG model involves thermal geostrophic balance, in which the Rossby number, the Froude number and the stratification parameter are all of the same asymptotic order. The main analytical contribution of this paper is to construct local-in-time unique strong solutions for the TQG model. For this, we show that solutions of its regularized version $α$-TQG converge to solutions of TQG as its smoothing parameter $α\rightarrow 0$ and we obtain blowup criteria for the $α$-TQG model. The main contribution of the computational analysis is to verify the rate of convergence of $α$-TQG solutions to TQG solutions as $α\rightarrow 0$ for example simulations in appropriate GFD regimes.

math.AP↗

arXiv2021

Magneto-transport evidence for strong topological insulator phase in ZrTe5

The identification of a non-trivial band topology usually relies on directly probing the protected surface/edge states. But, it is difficult to achieve electronically in narrow-gap topological materials due to the small (meV) energy scales. Here, we demonstrate that band inversion, a crucial ingredient of the non-trivial band topology, can serve as an alternative, experimentally accessible indicator. We show that an inverted band can lead to a four-fold splitting of the non-zero Landau levels, contrasting the two-fold splitting (spin splitting only) in the normal band. We confirm our predictions in magneto-transport experiments on a narrow-gap strong topological insulator, zirconium pentatelluride (ZrTe$_5$), with the observation of additional splittings in the quantum oscillations and also an anomalous peak in the extreme quantum limit. Our work establishes an effective strategy for identifying the band inversion as well as the associated topological phases for future topological materials research.

cond-mat.mtrl-sci↗

arXiv2021

Two-level monotonic multistage recommender systems

A recommender system learns to predict the user-specific preference or intention over many items simultaneously for all users, making personalized recommendations based on a relatively small number of observations. One central issue is how to leverage three-way interactions, referred to as user-item-stage dependencies on a monotonic chain of events, to enhance the prediction accuracy. A monotonic chain of events occurs, for instance, in an article sharing dataset, where a ``follow'' action implies a ``like'' action, which in turn implies a ``view'' action. In this article, we develop a multistage recommender system utilizing a two-level monotonic property characterizing a monotonic chain of events for personalized prediction. Particularly, we derive a large-margin classifier based on a nonnegative additive latent factor model in the presence of a high percentage of missing observations, particularly between stages, reducing the number of model parameters for personalized prediction while guaranteeing prediction consistency. On this ground, we derive a regularized cost function to learn user-specific behaviors at different stages, linking decision functions to numerical and categorical covariates to model user-item-stage interactions. Computationally, we derive an algorithm based on blockwise coordinate descent. Theoretically, we show that the two-level monotonic property enhances the accuracy of learning as compared to a standard method treating each stage individually and an ordinal method utilizing only one-level monotonicity. Finally, the proposed method compares favorably with existing methods in simulations and an article sharing dataset.

cs.IR↗

arXiv2021

Reinforcement Learning Compensated Extended Kalman Filter for Attitude Estimation

Inertial measurement units are widely used in different fields to estimate the attitude. Many algorithms have been proposed to improve estimation performance. However, most of them still suffer from 1) inaccurate initial estimation, 2) inaccurate initial filter gain, and 3) non-Gaussian process and/or measurement noise. In this paper, we leverage reinforcement learning to compensate for the classical extended Kalman filter estimation, i.e., to learn the filter gain from the sensor measurements. We also analyse the convergence of the estimate error. The effectiveness of the proposed algorithm is validated on both simulated data and real data.

cs.RO↗

arXiv2021

Reinforcement Learning for Orientation Estimation Using Inertial Sensors with Performance Guarantee

This paper presents a deep reinforcement learning (DRL) algorithm for orientation estimation using inertial sensors combined with magnetometer. The Lyapunov method in control theory is employed to prove the convergence of orientation estimation errors. Based on the theoretical results, the estimator gains and a Lyapunov function are parametrized by deep neural networks and learned from samples. The DRL estimator is compared with three well-known orientation estimation methods on both numerical simulations and real datasets collected from commercially available sensors. The results show that the proposed algorithm is superior for arbitrary estimation initialization and can adapt to very large angular velocities for which other algorithms can be hardly applicable. To the best of our knowledge, this is the first DRL-based orientation estimation method with estimation error boundedness guarantee.

cs.RO↗

arXiv2021

Microwave response in a topological superconducting quantum interference device

Photon detection at microwave frequency is of great interest due to its application in quantum computation information science and technology. Herein are results from studying microwave response in a topological superconducting quantum interference device (SQUID) realized in Dirac semimetal Cd3As2. The temperature dependence and microwave power dependence of the SQUID junction resistance are studied, from which we obtain an effective temperature at each microwave power level. It is observed the effective temperature increases with the microwave power. This observation of microwave response may pave the way for single photon detection at the microwave frequency in topological quantum materials.

cond-mat.mtrl-sci↗

arXiv2021

Probabilistic Mixture-of-Experts for Efficient Deep Reinforcement Learning

Deep reinforcement learning (DRL) has successfully solved various problems recently, typically with a unimodal policy representation. However, grasping distinguishable skills for some tasks with non-unique optima can be essential for further improving its learning efficiency and performance, which may lead to a multimodal policy represented as a mixture-of-experts (MOE). To our best knowledge, present DRL algorithms for general utility do not deploy this method as policy function approximators due to the potential challenge in its differentiability for policy learning. In this work, we propose a probabilistic mixture-of-experts (PMOE) implemented with a Gaussian mixture model (GMM) for multimodal policy, together with a novel gradient estimator for the indifferentiability problem, which can be applied in generic off-policy and on-policy DRL algorithms using stochastic policies, e.g., Soft Actor-Critic (SAC) and Proximal Policy Optimisation (PPO). Experimental results testify the advantage of our method over unimodal polices and two different MOE methods, as well as a method of option frameworks, based on the above two types of DRL algorithms, on six MuJoCo tasks. Different gradient estimations for GMM like the reparameterisation trick (Gumbel-Softmax) and the score-ratio trick are also compared with our method. We further empirically demonstrate the distinguishable primitives learned with PMOE and show the benefits of our method in terms of exploration.

cs.LG↗

arXiv2021

Microwave Photon Number Resolving Detector Using the Topological Surface State of Superconducting Cadmium Arsenide

Photon number resolving detectors play a central role in quantum optics. A key challenge in resolving the number of absorbed photons in the microwave frequency range is finding a suitable material that provides not only an appropriate band structure for absorbing low-energy photons but also a means of detecting a discrete photoelectron excitation. To this end, we propose to measure the temperature gain after absorbing a photon using superconducting cadmium arsenide (Cd3As2) with a topological semimetallic surface state as the detector. The surface electrons absorb the incoming photons and then transfer the excess energy via heat to the superconducting bulk's phonon modes. The temperature gain can be determined by measuring the change in the zero-bias bulk resistivity, which does not significantly affect the lattice dynamics. Moreover, the obtained temperature gain scales discretely with the number of absorbed photons, enabling a photon-number resolving function. Here, we will calculate the temperature increase as a function of the number and frequency of photons absorbed. We will also derive the timescale for the heat transfer process from the surface electrons to the bulk phonons. We will specifically show that the transfer processes are fast enough to ignore heat dissipation loss.

cond-mat.mes-hall↗

arXiv2021

Gaussian Curvature Filter on 3D Meshes

Minimizing the Gaussian curvature of meshes can play a fundamental role in 3D mesh processing. However, there is a lack of computationally efficient and robust Gaussian curvature optimization method. In this paper, we present a simple yet effective method that can efficiently reduce Gaussian curvature for 3D meshes. We first present the mathematical foundation of our method. Then, we introduce a simple and robust implicit Gaussian curvature optimization method named Gaussian Curvature Filter (GCF). GCF implicitly minimizes Gaussian curvature without the need to explicitly calculate the Gaussian curvature itself. GCF is highly efficient and this method can be used in a large range of applications that involve Gaussian curvature. We conduct extensive experiments to demonstrate that GCF significantly outperforms state-of-the-art methods in minimizing Gaussian curvature, and geometric feature preserving soothing on 3D meshes. GCF program is available at https://github.com/tangwenming/GCF-filter.

cs.GR↗

arXiv2021

Lyapunov-Based Reinforcement Learning State Estimator

In this paper, we consider the state estimation problem for nonlinear stochastic discrete-time systems. We combine Lyapunov's method in control theory and deep reinforcement learning to design the state estimator. We theoretically prove the convergence of the bounded estimate error solely using the data simulated from the model. An actor-critic reinforcement learning algorithm is proposed to learn the state estimator approximated by a deep neural network. The convergence of the algorithm is analysed. The proposed Lyapunov-based reinforcement learning state estimator is compared with a number of existing nonlinear filtering methods through Monte Carlo simulations, showing its advantage in terms of estimate convergence even under some system uncertainties such as covariance shift in system noise and randomly missing measurements. To the best of our knowledge, this is the first reinforcement learning based nonlinear state estimator with bounded estimate error performance guarantee.

cs.LG↗

arXiv2020

Stochastic mesoscale circulation dynamics in the thermal ocean

In analogy with similar effects in adiabatic compressible fluid dynamics, the effects of buoyancy gradients on incompressible stratified flows are said to be `thermal'. The thermal rotating shallow water (TRSW) model equations contain three small nondimensional parameters. These are the Rossby number, the Froude number and the buoyancy parameter. Asymptotic expansion of the TRSW model equations in these three small parameters leads to the deterministic thermal versions of the Salmon's L1 (TL1) model and the thermal quasi-geostrophic (TQG) model, upon expanding in the neighbourhood of thermal quasi-geostrophic balance among the flow velocity and the gradients of free surface elevation and buoyancy. The linear instability of TQG at high wave number tends to create circulation at small scales. Such a high wave number instability could be unresolvable in many computational simulations, but its presence at small scales may contribute significantly to fluid transport at resolvable scales. Sometimes such effects are modelled via `stochastic backscatter of kinetic energy'. Here we try another approach. Namely, we model `stochastic transport' in the hierarchy of models TRSW/TL1/TQG. The models are derived via the approach of stochastic advection by Lie transport (SALT) as obtained from a recently introduced stochastic version of the Euler--Poincaré variational principle. We also indicate the potential next steps for applying these models in uncertainty quantification and data assimilation of the rapid, high wavenumber effects of buoyancy fronts at these three levels of description by using the data-driven stochastic parametrisation algorithms derived previously using the SALT approach.

physics.flu-dyn↗

arXiv2020

Social-VRNN: One-Shot Multi-modal Trajectory Prediction for Interacting Pedestrians

Prediction of human motions is key for safe navigation of autonomous robots among humans. In cluttered environments, several motion hypotheses may exist for a pedestrian, due to its interactions with the environment and other pedestrians. Previous works for estimating multiple motion hypotheses require a large number of samples which limits their applicability in real-time motion planning. In this paper, we present a variational learning approach for interaction-aware and multi-modal trajectory prediction based on deep generative neural networks. Our approach can achieve faster convergence and requires significantly fewer samples comparing to state-of-the-art methods. Experimental results on real and simulation data show that our model can effectively learn to infer different trajectories. We compare our method with three baseline approaches and present performance results demonstrating that our generative model can achieve higher accuracy for trajectory prediction by producing diverse trajectories.

cs.RO↗

arXiv2020

Reinforcement Learning Control of Constrained Dynamic Systems with Uniformly Ultimate Boundedness Stability Guarantee

Reinforcement learning (RL) is promising for complicated stochastic nonlinear control problems. Without using a mathematical model, an optimal controller can be learned from data evaluated by certain performance criteria through trial-and-error. However, the data-based learning approach is notorious for not guaranteeing stability, which is the most fundamental property for any control system. In this paper, the classic Lyapunov's method is explored to analyze the uniformly ultimate boundedness stability (UUB) solely based on data without using a mathematical model. It is further shown how RL with UUB guarantee can be applied to control dynamic systems with safety constraints. Based on the theoretical results, both off-policy and on-policy learning algorithms are proposed respectively. As a result, optimal controllers can be learned to guarantee UUB of the closed-loop system both at convergence and during learning. The proposed algorithms are evaluated on a series of robotic continuous control tasks with safety constraints. In comparison with the existing RL algorithms, the proposed method can achieve superior performance in terms of maintaining safety. As a qualitative evaluation of stability, our method shows impressive resilience even in the presence of external disturbances.

eess.SY↗

arXiv2020

X-ray tomography investigation of cyclically sheared granular materials

We perform combined X-ray tomography and shear force measurements on a cyclically sheared granular system with highly transient behaviors, and obtain the evolution of microscopic structures and the macroscopic shear force during the shear cycle. We explain the macroscopic behaviors of the system based on microscopic processes, including the particle level structural rearrangement and frictional contact variation. Specifically, we show how contact friction can induce large structural fluctuations and cause significant shear dilatancy effect for granular materials, and we also construct an empirical constitutive relationship for the macroscopic shear force.

cond-mat.soft↗

arXiv2020

Penalized model-based clustering of fMRI data

Functional magnetic resonance imaging (fMRI) data have become increasingly available and are useful for describing functional connectivity (FC), the relatedness of neuronal activity in regions of the brain. This FC of the brain provides insight into certain neurodegenerative diseases and psychiatric disorders, and thus is of clinical importance. To help inform physicians regarding patient diagnoses, unsupervised clustering of subjects based on FC is desired, allowing the data to inform us of groupings of patients based on shared features of connectivity. Since heterogeneity in FC is present even between patients within the same group, it is important to allow subject-level differences in connectivity, while still pooling information across patients within each group to describe group-level FC. To this end, we propose a random covariance clustering model (RCCM) to concurrently cluster subjects based on their FC networks, estimate the unique FC networks of each subject, and to infer shared network features. Although current methods exist for estimating FC or clustering subjects using fMRI data, our novel contribution is to cluster or group subjects based on similar FC of the brain while simultaneously providing group- and subject-level FC network estimates. The competitive performance of RCCM relative to other methods is demonstrated through simulations in various settings, achieving both improved clustering of subjects and estimation of FC networks. Utility of the proposed method is demonstrated with application to a resting-state fMRI data set collected on 43 healthy controls and 61 participants diagnosed with schizophrenia.

stat.ML↗

arXiv2020

Lyapunov-Based Reinforcement Learning for Decentralized Multi-Agent Control

Decentralized multi-agent control has broad applications, ranging from multi-robot cooperation to distributed sensor networks. In decentralized multi-agent control, systems are complex with unknown or highly uncertain dynamics, where traditional model-based control methods can hardly be applied. Compared with model-based control in control theory, deep reinforcement learning (DRL) is promising to learn the controller/policy from data without the knowing system dynamics. However, to directly apply DRL to decentralized multi-agent control is challenging, as interactions among agents make the learning environment non-stationary. More importantly, the existing multi-agent reinforcement learning (MARL) algorithms cannot ensure the closed-loop stability of a multi-agent system from a control-theoretic perspective, so the learned control polices are highly possible to generate abnormal or dangerous behaviors in real applications. Hence, without stability guarantee, the application of the existing MARL algorithms to real multi-agent systems is of great concern, e.g., UAVs, robots, and power systems, etc. In this paper, we aim to propose a new MARL algorithm for decentralized multi-agent control with a stability guarantee. The new MARL algorithm, termed as a multi-agent soft-actor critic (MASAC), is proposed under the well-known framework of "centralized-training-with-decentralized-execution". The closed-loop stability is guaranteed by the introduction of a stability constraint during the policy improvement in our MASAC algorithm. The stability constraint is designed based on Lyapunov's method in control theory. To demonstrate the effectiveness, we present a multi-agent navigation example to show the efficiency of the proposed MASAC algorithm.

eess.SY↗

arXiv2020

Towards Lossless Binary Convolutional Neural Networks Using Piecewise Approximation

Binary Convolutional Neural Networks (CNNs) can significantly reduce the number of arithmetic operations and the size of memory storage, which makes the deployment of CNNs on mobile or embedded systems more promising. However, the accuracy degradation of single and multiple binary CNNs is unacceptable for modern architectures and large scale datasets like ImageNet. In this paper, we proposed a Piecewise Approximation (PA) scheme for multiple binary CNNs which lessens accuracy loss by approximating full precision weights and activations efficiently and maintains parallelism of bitwise operations to guarantee efficiency. Unlike previous approaches, the proposed PA scheme segments piece-wisely the full precision weights and activations, and approximates each piece with a scaling coefficient. Our implementation on ResNet with different depths on ImageNet can reduce both Top-1 and Top-5 classification accuracy gap compared with full precision to approximately 1.0%. Benefited from the binarization of the downsampling layer, our proposed PA-ResNet50 requires less memory usage and two times Flops than single binary CNNs with 4 weights and 5 activations bases. The PA scheme can also generalize to other architectures like DenseNet and MobileNet with similar approximation power as ResNet which is promising for other tasks using binary convolutions. The code and pretrained models will be publicly available.

cs.CV↗

arXiv2020

Assessing Impact of Unobserved Confounders with Sensitivity Index Probabilities through Pseudo-Experiments

Unobserved confounders are a long-standing issue in causal inference using propensity score methods. This study proposed nonparametric indices to quantify the impact of unobserved confounders through pseudo-experiments with an application to real-world data. The study finding suggests that the proposed indices can reflect the true impact of confounders. It is hoped that this study will lead to further discussion on this important issue and help move the science of causal inference forward.

stat.ME↗