arXiv subjects

Jie Chen

Publications and source records attributed to Jie Chen.

At least 433 records · Page 24Linked to original sources

arXiv2022

Data-driven Self-triggered Control via Trajectory Prediction

Self-triggered control, a well-documented technique for reducing the communication overhead while ensuring desired system performance, is gaining increasing popularity. However, existing methods for self-triggered control require explicit system models that are assumed perfectly known a priori. An end-to-end control paradigm known as data-driven control learns control laws directly from data, and offers a competing alternative to the routine system identification-then-control method. In this context, the present paper puts forth data-driven self-triggered control schemes for unknown linear systems using data collected offline. Specifically, for output feedback control systems, a data-driven model predictive control (MPC) scheme is proposed, which computes a sequence of control inputs while generating a predicted system trajectory. A data-driven self-triggering law is designed using the predicted trajectory, to determine the next triggering time once a new measurement becomes available. For state feedback control systems, instead of capitalizing on MPC to predict the trajectory, a data-fitting problem using the pre-collected input-state data is solved, whose solution is employed to construct the self-triggering mechanism. Both feasibility and stability are established for the proposed self-triggered controllers, which are validated using numerical examples.

eess.SY↗

arXiv2022

A Survey of Decision Making in Adversarial Games

Game theory has by now found numerous applications in various fields, including economics, industry, jurisprudence, and artificial intelligence, where each player only cares about its own interest in a noncooperative or cooperative manner, but without obvious malice to other players. However, in many practical applications, such as poker, chess, evader pursuing, drug interdiction, coast guard, cyber-security, and national defense, players often have apparently adversarial stances, that is, selfish actions of each player inevitably or intentionally inflict loss or wreak havoc on other players. Along this line, this paper provides a systematic survey on three main game models widely employed in adversarial games, i.e., zero-sum normal-form and extensive-form games, Stackelberg (security) games, zero-sum differential games, from an array of perspectives, including basic knowledge of game models, (approximate) equilibrium concepts, problem classifications, research frontiers, (approximate) optimal strategy seeking techniques, prevailing algorithms, and practical applications. Finally, promising future research directions are also discussed for relevant adversarial games.

cs.GT↗

arXiv2022

Discrete Boltzmann modeling of Rayleigh-Taylor instability: effects of interfacial tension, viscosity and heat conductivity

The Rayleigh-Taylor Instability (RTI) in compressible flow with inter-molecular interactions is probed via the Discrete Boltzmann Method (DBM). The effects of interfacial tension, viscosity and heat conduction are investigated. It is found that the influences of interfacial tension on the perturbation amplitude, bubble velocity, and two kinds of entropy production rates all show differences at different stages of RTI evolution. It inhibits the RTI evolution at the bubble acceleration stage, while at the asymptotic velocity stage, it first promotes and then inhibits the RTI evolution. Viscosity and heat conduction inhibit the RTI evolution. Viscosity shows a suppressive effect on entropy generation rate related to heat flow at the early stage but a first promotive and then suppressive effect on entropy generation rate related to heat flow at a later stage. Heat conduction shows a promotive effect on entropy generation rate related to heat flow at an early stage. Still, it offers a first promotive and then suppressive effect on entropy generation rate related to heat flow at a later stage. By introducing the morphological boundary length, we found that the stage of exponential growth of interface length with time corresponds to the bubble acceleration stage. The first maximum point of interface length change rate and the first maximum point of the change rate of entropy generation rate related to viscous stress can be used as a new criterion for RTI to enter the asymptotic velocity stage.

physics.flu-dyn↗

arXiv2022

A Dual-Masked Auto-Encoder for Robust Motion Capture with Spatial-Temporal Skeletal Token Completion

Multi-person motion capture can be challenging due to ambiguities caused by severe occlusion, fast body movement, and complex interactions. Existing frameworks build on 2D pose estimations and triangulate to 3D coordinates via reasoning the appearance, trajectory, and geometric consistencies among multi-camera observations. However, 2D joint detection is usually incomplete and with wrong identity assignments due to limited observation angle, which leads to noisy 3D triangulation results. To overcome this issue, we propose to explore the short-range autoregressive characteristics of skeletal motion using transformer. First, we propose an adaptive, identity-aware triangulation module to reconstruct 3D joints and identify the missing joints for each identity. To generate complete 3D skeletal motion, we then propose a Dual-Masked Auto-Encoder (D-MAE) which encodes the joint status with both skeletal-structural and temporal position encoding for trajectory completion. D-MAE's flexible masking and encoding mechanism enable arbitrary skeleton definitions to be conveniently deployed under the same framework. In order to demonstrate the proposed model's capability in dealing with severe data loss scenarios, we contribute a high-accuracy and challenging motion capture dataset of multi-person interactions with severe occlusion. Evaluations on both benchmark and our new dataset demonstrate the efficiency of our proposed model, as well as its advantage against the other state-of-the-art methods.

cs.CV↗

arXiv2022

ChoreoGraph: Music-conditioned Automatic Dance Choreography over a Style and Tempo Consistent Dynamic Graph

To generate dance that temporally and aesthetically matches the music is a challenging problem, as the following factors need to be considered. First, the aesthetic styles and messages conveyed by the motion and music should be consistent. Second, the beats of the generated motion should be locally aligned to the musical features. And finally, basic choreomusical rules should be observed, and the motion generated should be diverse. To address these challenges, we propose ChoreoGraph, which choreographs high-quality dance motion for a given piece of music over a Dynamic Graph. A data-driven learning strategy is proposed to evaluate the aesthetic style and rhythmic connections between music and motion in a progressively learned cross-modality embedding space. The motion sequences will be beats-aligned based on the music segments and then incorporated as nodes of a Dynamic Motion Graph. Compatibility factors such as the style and tempo consistency, motion context connection, action completeness, and transition smoothness are comprehensively evaluated to determine the node transition in the graph. We demonstrate that our repertoire-based framework can generate motions with aesthetic consistency and robustly extensible in diversity. Both quantitative and qualitative experiment results show that our proposed model outperforms other baseline models.

cs.MM↗

arXiv2022

Adaptive Random Fourier Features Kernel LMS

We propose the adaptive random Fourier features Gaussian kernel LMS (ARFF-GKLMS). Like most kernel adaptive filters based on stochastic gradient descent, this algorithm uses a preset number of random Fourier features to save computation cost. However, as an extra flexibility, it can adapt the inherent kernel bandwidth in the random Fourier features in an online manner. This adaptation mechanism allows to alleviate the problem of selecting the kernel bandwidth beforehand for the benefit of an improved tracking in non-stationary circumstances. Simulation results confirm that the proposed algorithm achieves a performance improvement in terms of convergence rate, error at steady-state and tracking ability over other kernel adaptive filters with preset kernel bandwidth.

eess.SP↗

arXiv2022

A Model for the Tropical Cyclone Wind Field Response to Idealized Landfall

The impacts of a tropical cyclone after landfall depend not only on storm intensity but also on the size and structure of the wind field. Hence, a simple predictive model for the wind field after landfall has significant potential value. This work tests existing theory for wind structure and size over the ocean against idealized axisymmetric landfall experiments in which the surface beneath a mature storm is instantaneously dried and roughened individually or simultaneously. Structure theory captures the response of the low-level wind field to different types of idealized landfalls given intensity and size response. Storm size, modeled to follow the ratio of simulated time-dependent storm intensity to the Coriolis parameter vm(t)/f, can generally predict the transient response of the storm gale wind radii r34kt to inland surface forcings, particularly for at least moderate surface roughening regardless of the level of drying. Given knowledge of the intensity evolution, the above results combine to yield a theoretical model that can predict the full tangential wind field response to idealized landfalls. An example application to a real world landfall is provided to demonstrate its potential utility for risk applications.

physics.ao-ph↗

arXiv2022

Shapley Computations Using Surrogate Model-Based Trees

Shapley-related techniques have gained attention as both global and local interpretation tools because of their desirable properties. However, their computation using conditional expectations is computationally expensive. Approximation methods suggested in the literature have limitations. This paper proposes the use of a surrogate model-based tree to compute Shapley and SHAP values based on conditional expectation. Simulation studies show that the proposed algorithm provides improvements in accuracy, unifies global Shapley and SHAP interpretation, and the thresholding method provides a way to trade-off running time and accuracy.

stat.ML↗

arXiv2022

Global Cauchy problems for the nonlocal (derivative) NLS in $E^s_σ$

We consider the Cauchy problem for the (derivative) nonlocal NLS in super-critical function spaces $E^s_σ$ for which the norms are defined by $$ \|f\|_{E^s_σ} = \|\langleξ\rangle^σ2^{s|ξ|}\hat{f}(ξ)\|_{L^2}, \ s<0, \ σ\in \mathbb{R}. $$ Any Sobolev space $H^{r}$ is a subspace of $E^s_σ$, i.e., $H^r \subset E^s_σ$ for any $ r,σ\in \mathbb{R}$ and $s<0$. Let $s<0$ and $σ>-1/2$ ($σ>0$) for the nonlocal NLS (for the nonlocal derivative NLS). We show the global existence and uniqueness of the solutions if the initial data belong to $E^s_σ$ and their Fourier transforms are supported in $(0, \infty)$, the smallness conditions on the initial data in $E^s_σ$ are not required for the global solutions.

math.AP↗

arXiv2022

Bridging Mean-Field Games and Normalizing Flows with Trajectory Regularization

Mean-field games (MFGs) are a modeling framework for systems with a large number of interacting agents. They have applications in economics, finance, and game theory. Normalizing flows (NFs) are a family of deep generative models that compute data likelihoods by using an invertible mapping, which is typically parameterized by using neural networks. They are useful for density modeling and data generation. While active research has been conducted on both models, few noted the relationship between the two. In this work, we unravel the connections between MFGs and NFs by contextualizing the training of an NF as solving the MFG. This is achieved by reformulating the MFG problem in terms of agent trajectories and parameterizing a discretization of the resulting MFG with flow architectures. With this connection, we explore two research directions. First, we employ expressive NF architectures to accurately solve high-dimensional MFGs, sidestepping the curse of dimensionality in traditional numerical methods. Compared with other deep learning approaches, our trajectory-based formulation encodes the continuity equation in the neural network, resulting in a better approximation of the population dynamics. Second, we regularize the training of NFs with transport costs and show the effectiveness on controlling the model's Lipschitz bound, resulting in better generalization performance. We demonstrate numerical results through comprehensive experiments on a variety of synthetic and real-life datasets.

math.OC↗

arXiv2022

PSP: Million-level Protein Sequence Dataset for Protein Structure Prediction

Proteins are essential component of human life and their structures are important for function and mechanism analysis. Recent work has shown the potential of AI-driven methods for protein structure prediction. However, the development of new models is restricted by the lack of dataset and benchmark training procedure. To the best of our knowledge, the existing open source datasets are far less to satisfy the needs of modern protein sequence-structure related research. To solve this problem, we present the first million-level protein structure prediction dataset with high coverage and diversity, named as PSP. This dataset consists of 570k true structure sequences (10TB) and 745k complementary distillation sequences (15TB). We provide in addition the benchmark training procedure for SOTA protein structure prediction model on this dataset. We validate the utility of this dataset for training by participating CAMEO contest in which our model won the first place. We hope our PSP dataset together with the training benchmark can enable a broader community of AI/biology researchers for AI-driven protein related research.

q-bio.BM↗

arXiv2022

Assessing Phonon Coherence Using Spectroscopy

As a fundamental physical quantity of thermal phonons, temporal coherence participates in a broad range of thermal and phononic processes, while a clear methodology for the measurement of phonon coherence is still lacking. In this Lettter, we derive a theoretical model for the experimental exploration of phonon coherence based on spectroscopy, which is then validated by comparison with Brillouin light scattering data and direct molecular dynamic simulations of confined modes in nanostructures. The proposed model highlights that confined modes exhibit a pronounced wavelike behavior characterized by a higher ratio of coherence time to lifetime. The dependence of phonon coherence on system size is also demonstrated from spectroscopy data. The proposed theory allows for reassessing data of conventional spectroscopy to yield coherence times, which are essential for the understanding and the estimation of phonon characteristics and heat transport in solids in general.

physics.app-ph↗

arXiv2022

Distributed Optimization with Projection-free Dynamics

We consider continuous-time dynamics for distributed optimization with set constraints in the paper. To handle the computational complexity of projection-based dynamics due to solving a general quadratic optimization subproblem with projection, we propose a distributed projection-free dynamics by employing the Frank-Wolfe method, also known as the conditional gradient algorithm. The process searches a feasible descent direction by solving an alternative linear optimization instead of a quadratic one. To make the approach applicable over weight-balanced digraphs, we design a dynamics for the consensus of local decision variables and another dynamics of auxiliary variables to track the global gradient. Then we prove the convergence of the dynamical systems to the optimal solution, and provide detailed numerical comparisons with both projection-based dynamics and other distributed projection-free algorithms. Also, we derive the distributed discrete-time scheme following the instructive ideas of the proposed dynamics and provide its accordingly convergence rate.

math.OC↗

arXiv2022

Complex valued semi-linear heat equations in super-critical spaces $E^s_σ$

We consider the Cauchy problem for the complex valued semi-linear heat equation $$ \partial_t u - Δu - u^m =0, \ \ u (0,x) = u_0(x), $$ where $m\geq 2$ is an integer and the initial data belong to super-critical spaces $E^s_σ$ for which the norms are defined by $$ \|f\|_{E^s_σ} = \|\langle ξ\rangle^σ2^{s|ξ|}\hat{f}(ξ)\|_{L^2}, \ \ σ\in \mathbb{R}, \ s<0. $$ If $s<0$, then any Sobolev space $H^{r}$ is a subspace of $E^s_σ$, i.e., $\cup_{r \in \mathbb{R}} H^r \subset E^s_σ$. We obtain the global existence and uniqueness of the solutions if the initial data belong to $E^s_σ$ ($s<0, \ σ\geq d/2-2/(m-1)$) and their Fourier transforms are supported in the first octant, the smallness conditions on the initial data in $E^s_σ$ are not required for the global solutions. Moreover, we show that the error between the solution $u$ and the iteration solution $u^{(j)}$ is $C^j/(j\,!)^2$. Similar results also hold if the nonlinearity $u^m$ is replaced by an exponential function $e^u-1$.

math.AP↗

arXiv2022

Universal Deep GNNs: Rethinking Residual Connection in GNNs from a Path Decomposition Perspective for Preventing the Over-smoothing

The performance of GNNs degrades as they become deeper due to the over-smoothing. Among all the attempts to prevent over-smoothing, residual connection is one of the promising methods due to its simplicity. However, recent studies have shown that GNNs with residual connections only slightly slow down the degeneration. The reason why residual connections fail in GNNs is still unknown. In this paper, we investigate the forward and backward behavior of GNNs with residual connections from a novel path decomposition perspective. We find that the recursive aggregation of the median length paths from the binomial distribution of residual connection paths dominates output representation, resulting in over-smoothing as GNNs go deeper. Entangled propagation and weight matrices cause gradient smoothing and prevent GNNs with residual connections from optimizing to the identity mapping. Based on these findings, we present a Universal Deep GNNs (UDGNN) framework with cold-start adaptive residual connections (DRIVE) and feedforward modules. Extensive experiments demonstrate the effectiveness of our method, which achieves state-of-the-art results over non-smooth heterophily datasets by simply stacking standard GNNs.

cs.LG↗

arXiv2022

Interpretable Feature Engineering for Time Series Predictors using Attention Networks

Regression problems with time-series predictors are common in banking and many other areas of application. In this paper, we use multi-head attention networks to develop interpretable features and use them to achieve good predictive performance. The customized attention layer explicitly uses multiplicative interactions and builds feature-engineering heads that capture temporal dynamics in a parsimonious manner. Convolutional layers are used to combine multivariate time series. We also discuss methods for handling static covariates in the modeling process. Visualization and explanation tools are used to interpret the results and explain the relationship between the inputs and the extracted features. Both simulation and real dataset are used to illustrate the usefulness of the methodology. Keyword: Attention heads, Deep neural networks, Interpretable feature engineering

cs.LG↗

arXiv2022

Distributed coordination for seeking the optimal Nash equilibrium of aggregative games

This paper aims to design a distributed coordination algorithm for solving a multi-agent decision problem with a hierarchical structure. The primary goal is to search the Nash equilibrium of a noncooperative game such that each player has no incentive to deviate from the equilibrium under its private objective. Meanwhile, the agents can coordinate to optimize the social cost within the set of Nash equilibria of the underlying game. Such an optimal Nash equilibrium problem can be modeled as a distributed optimization problem with variational inequality constraints. We consider the scenario where the objective functions of both the underlying game and social cost optimization problem have a special aggregation structure. Since each player only has access to its local objectives while cannot know all players' decisions, a distributed algorithm is highly desirable. By utilizing the Tikhonov regularization and dynamical averaging tracking technique, we propose a distributed coordination algorithm by introducing an incentive term in addition to the gradient-based Nash equilibrium seeking, so as to intervene players' decisions to improve the system efficiency. We prove its convergence to the optimal Nash equilibrium of a monotone aggregative game with simulation studies.

math.OC↗

arXiv2022

An Optimal Distributed Algorithm with Operator Extrapolation for Stochastic Aggregative Games

This work studies Nash equilibrium seeking for a class of stochastic aggregative games, where each player has an expectation-valued objective function depending on its local strategy and the aggregate of all players' strategies. We propose a distributed algorithm with operator extrapolation, in which each player maintains an estimate of this aggregate by exchanging this information with its neighbors over a time-varying network, and updates its decision through the mirror descent method. An operator extrapolation at the search direction is applied such that the two step historical gradient samples are utilized to accelerate the convergence. Under the strongly monotone assumption on the pseudo-gradient mapping, we prove that the proposed algorithm can achieve the optimal convergence rate of $\mathcal{O}(1/k)$ for Nash equilibrium seeking of stochastic games. Finally, the algorithm performance is demonstrated via numerical simulations.

math.OC↗