arXiv subjects

Yifei Li

Publications and source records attributed to Yifei Li.

At least 127 records · Page 7Linked to original sources

arXiv2023

Robust Control of Unknown Switched Linear Systems from Noisy Data

This paper investigates the problem of data-driven stabilization for linear discrete-time switched systems with unknown switching dynamics. In the absence of noise, a data-based state feedback stabilizing controller can be obtained by solving a semi-definite program (SDP) on-the-fly, which automatically adapts to the changes of switching dynamics. However, when noise is present, the persistency of excitation condition based on the closed-loop data may be undermined, rendering the SDP infeasible. To address this issue, an auxiliary function-based switching control law is proposed, which only requires intermittent SDP solutions when its feasibility is guaranteed. By analyzing the relationship between the controller and the system switching times, it is shown that the proposed controller guarantees input-to-state practical stability (ISpS) of the closed-loop switched linear system, provided that the noise is bounded and the dynamics switches slowly enough. Two numerical examples are presented to verify the effectiveness of the proposed controller.

eess.SY↗

arXiv2023

Efficacy Analysis of Power Swing Blocking and Out-of-Step Tripping Functions in Grid-Following VSC Systems

Power flow oscillations can occur in power systems after major disturbances such as system faults, which may result in significant power swings and even lead to system collapse. This paper provides a detailed analysis of the efficacy of the legacy power swing blocking and out-of-step tripping functions in grid-following voltage-source converter (GFL-VSC) systems. First, the power swing dynamics of GFL-VSC are characterized, considering the outer power control loops and phase-locked loop (PLL). It is found that the loss of synchronism (LOS) of the GFL-VSC system is caused by the divergence of the output angle of the PLL, which is fundamentally different from that of synchronous generator (SG)-based systems, whose LOS originates from the divergence of power angle differences between power sources. Therefore, the legacy setting principles for power swing blocking and out-of-step tripping function designed for SG-based systems can not be directly applied to GFL-VSC systems, and may even malfunction. Time-domain simulations are performed in the PSCAD/EMTDC platform to validate the correctness of the theoretical analysis.

eess.SY↗

arXiv2023

Self-triggered Consensus Control of Multi-agent Systems from Data

This paper considers self-triggered consensus control of unknown linear multi-agent systems (MASs). Self-triggering mechanisms (STMs) are widely used in MASs, thanks to their advantages in avoiding continuous monitoring and saving computing and communication resources. However, existing results require the knowledge of system matrices, which are difficult to obtain in real-world settings. To address this challenge, we present a data-driven approach to designing STMs for unknown MASs building upon the model-based solutions. Our approach leverages a system lifting method, which allows us to derive a data-driven representation for the MAS. Subsequently, a data-driven self-triggered consensus control (STC) scheme is designed, which combines a data-driven STM with a state feedback control law. We establish a data-based stability criterion for asymptotic consensus of the closed-loop MAS in terms of linear matrix inequalities, whose solution provides a matrix for the STM as well as a stabilizing controller gain. In the presence of external disturbances, a model-based STC scheme is put forth for $\mathcal{H}_{\infty}$-consensus of MASs, serving as a baseline for the data-driven STC. Numerical tests are conducted to validate the correctness of the data- and model-based STC approaches. Our data-driven approach demonstrates a superior trade-off between control performance and communication efficiency from finite, noisy data relative to the system identification-based one.

eess.SY↗

arXiv2023

Testing Higher-order Clusterability on graphs

Analysis of higher-order organizations, usually small connected subgraphs called motifs, is a fundamental task on complex networks. This paper studies a new problem of testing higher-order clusterability: given query access to an undirected graph, can we judge whether this graph can be partitioned into a few clusters of highly-connected motifs? This problem is an extension of the former work proposed by Czumaj et al. (STOC' 15), who recognized cluster structure on graphs using the framework of property testing. In this paper, a good graph cluster on high dimensions is first defined for higher-order clustering. Then, query lower bound is given for testing whether this kind of good cluster exists. Finally, an optimal sublinear-time algorithm is developed for testing clusterability based on triangles.

cs.DS↗

arXiv2023

How Can Large Language Models Help Humans in Design and Manufacturing?

The advancement of Large Language Models (LLMs), including GPT-4, provides exciting new opportunities for generative design. We investigate the application of this tool across the entire design and manufacturing workflow. Specifically, we scrutinize the utility of LLMs in tasks such as: converting a text-based prompt into a design specification, transforming a design into manufacturing instructions, producing a design space and design variations, computing the performance of a design, and searching for designs predicated on performance. Through a series of examples, we highlight both the benefits and the limitations of the current LLMs. By exposing these limitations, we aspire to catalyze the continued improvement and progression of these models.

cs.CL↗

arXiv2023

Data-driven Polytopic Output Synchronization of Heterogeneous Multi-agent Systems from Noisy Data

This paper proposes a novel approach to addressing the output synchronization problem in unknown heterogeneous multi-agent systems (MASs) using noisy data. Unlike existing studies that focus on noiseless data, we introduce a distributed data-driven controller that enables all heterogeneous followers to synchronize with a leader's trajectory. To handle the noise in the state-input-output data, we develop a data-based polytopic representation for the MAS. We tackle the issue of infeasibility in the set of output regulator equations caused by the noise by seeking approximate solutions via constrained fitting error minimization. This method utilizes measured data and a noise-matrix polytope to ensure near-optimal output synchronization. Stability conditions in the form of data-dependent semidefinite programs are derived, providing stabilizing controller gains for each follower. The proposed distributed data-driven control protocol achieves near-optimal output synchronization by ensuring the convergence of the tracking error to a bounded polytope, with the polytope size positively correlated with the noise bound. Numerical tests validate the practical merits of the proposed data-driven design and theory.

eess.SY↗

arXiv2023

Making Large Language Models Better Reasoners with Step-Aware Verifier

Few-shot learning is a challenging task that requires language models to generalize from limited examples. Large language models like GPT-3 and PaLM have made impressive progress in this area, but they still face difficulties in reasoning tasks such as GSM8K, a benchmark for arithmetic problems. To improve their reasoning skills, previous work has proposed to guide the language model with prompts that elicit a series of reasoning steps before giving the final answer, achieving a significant improvement on GSM8K from 17.9% to 58.1% in problem-solving rate. In this paper, we present DIVERSE (Diverse Verifier on Reasoning Step), a novel approach that further enhances the reasoning capability of language models. DIVERSE has three main components: first, it generates diverse prompts to explore different reasoning paths for the same question; second, it uses a verifier to filter out incorrect answers based on a weighted voting scheme; and third, it verifies each reasoning step individually instead of the whole chain. We evaluate DIVERSE on the latest language model code-davinci-002 and show that it achieves new state-of-the-art results on six of eight reasoning benchmarks (e.g., GSM8K 74.4% to 83.2%).

cs.CL↗

arXiv2023

A Method for Animating Children's Drawings of the Human Figure

Children's drawings have a wonderful inventiveness, creativity, and variety to them. We present a system that automatically animates children's drawings of the human figure, is robust to the variance inherent in these depictions, and is simple and straightforward enough for anyone to use. We demonstrate the value and broad appeal of our approach by building and releasing the Animated Drawings Demo, a freely available public website that has been used by millions of people around the world. We present a set of experiments exploring the amount of training data needed for fine-tuning, as well as a perceptual study demonstrating the appeal of a novel twisted perspective retargeting technique. Finally, we introduce the Amateur Drawings Dataset, a first-of-its-kind annotated dataset, collected via the public demo, containing over 178,000 amateur drawings and corresponding user-accepted character bounding boxes, segmentation masks, and joint location annotations.

cs.CV↗

arXiv2022

A Survey on Knowledge-Enhanced Pre-trained Language Models

Natural Language Processing (NLP) has been revolutionized by the use of Pre-trained Language Models (PLMs) such as BERT. Despite setting new records in nearly every NLP task, PLMs still face a number of challenges including poor interpretability, weak reasoning capability, and the need for a lot of expensive annotated data when applied to downstream tasks. By integrating external knowledge into PLMs, \textit{\underline{K}nowledge-\underline{E}nhanced \underline{P}re-trained \underline{L}anguage \underline{M}odels} (KEPLMs) have the potential to overcome the above-mentioned limitations. In this paper, we examine KEPLMs systematically through a series of studies. Specifically, we outline the common types and different formats of knowledge to be integrated into KEPLMs, detail the existing methods for building and evaluating KEPLMS, present the applications of KEPLMs in downstream tasks, and discuss the future research directions. Researchers will benefit from this survey by gaining a quick and comprehensive overview of the latest developments in this field.

cs.CL↗

arXiv2022

Quantum NETwork: from theory to practice

The quantum internet is envisioned as the ultimate stage of the quantum revolution, which surpasses its classical counterpart in various aspects, such as the efficiency of data transmission, the security of network services, and the capability of information processing. Given its disruptive impact on the national security and the digital economy, a global race to build scalable quantum networks has already begun. With the joint effort of national governments, industrial participants and research institutes, the development of quantum networks has advanced rapidly in recent years, bringing the first primitive quantum networks within reach. In this work, we aim to provide an up-to-date review of the field of quantum networks from both theoretical and experimental perspectives, contributing to a better understanding of the building blocks required for the establishment of a global quantum internet. We also introduce a newly developed quantum network toolkit to facilitate the exploration and evaluation of innovative ideas. Particularly, it provides dual quantum computing engines, supporting simulations in both the quantum circuit and measurement-based models. It also includes a compilation scheme for mapping quantum network protocols onto quantum circuits, enabling their emulations on real-world quantum hardware devices. We showcase the power of this toolkit with several featured demonstrations, including a simulation of the Micius quantum satellite experiment, a testing of a four-layer quantum network architecture with resource management, and a quantum emulation of the CHSH game. We hope this work can give a better understanding of the state-of-the-art development of quantum networks and provide the necessary tools to make further contributions along the way.

quant-ph↗

arXiv2022

A structure-preserving parametric finite element method for area-conserved generalized mean curvature flow

We propose and analyze a structure-preserving parametric finite element method (SP-PFEM) to simulate the motion of closed curves governed by area-conserved generalized mean curvature flow in two dimensions (2D). We first present a variational formulation and rigorously prove that it preserves two fundamental geometric structures of the flows, i.e., (a) the conservation of the area enclosed by the closed curve; (b) the decrease of the perimeter of the curve. Then the variational formulation is approximated by using piecewise linear parametric finite elements in space to develop the semi-discrete scheme. With the help of the discrete Cauchy's inequality and discrete power mean inequality, the area conservation and perimeter decrease properties of the semi-discrete scheme are shown. On this basis, by combining the backward Euler method in time and a proper approximation of the unit normal vector, a structure-preserving fully discrete scheme is constructed successfully, which can preserve the two essential geometric structures simultaneously at the discrete level. Finally, numerical experiments test the convergence rate, area conservation, perimeter decrease and mesh quality, and depict the evolution of curves. Numerical results indicate that the proposed SP-PFEM provides a reliable and powerful tool for the simulation of area-conserved generalized mean curvature flow in 2D.

math.NA↗

arXiv2022

A structure-preserving parametric finite element method for geometric flows with anisotropic surface energy

We propose and analyze structure-preserving parametric finite element methods (SP-PFEM) for evolution of a closed curve under different geometric flows with arbitrary anisotropic surface energy $γ(\boldsymbol{n})$ for $\boldsymbol{n}\in \mathbb{S}^1$ representing the outward unit normal vector. By introducing a novel surface energy matrix $\boldsymbol{G}_k(\boldsymbol{n})$ depending on $γ(\boldsymbol{n})$ and the Cahn-Hoffman $\boldsymbolξ$-vector as well as a nonnegative stabilizing function $k(\boldsymbol{n}):\ \mathbb{S}^1\to \mathbb{R}$, which is a sum of a symmetric positive definite matrix and an anti-symmetric matrix, we obtain a new geometric partial differential equation and its corresponding variational formulation for the evolution of a closed curve under anisotropic surface diffusion. Based on the new weak formulation, we propose a parametric finite element method for the anisotropic surface diffusion and show that it is area conservation and energy dissipation under a very mild condition on $γ(\boldsymbol{n})$. The SP-PFEM is then extended to simulate evolution of a close curve under other anisotropic geometric flows including anisotropic curvature flow and area-conserved anisotropic curvature flow. Extensive numerical results are reported to demonstrate the efficiency and unconditional energy stability as well as good mesh quality property of the proposed SP-PFEM for simulating anisotropic geometric flows.

math.NA↗

arXiv2022

A symmetrized parametric finite element method for anisotropic surface diffusion in 3D

For the evolution of a closed surface under anisotropic surface diffusion with a general anisotropic surface energy $γ(\boldsymbol{n})$ in three dimensions (3D), where $\boldsymbol{n}$ is the unit outward normal vector, by introducing a novel symmetric positive definite surface energy matrix $\boldsymbol{Z}_k(\boldsymbol{n})$ depending on a stabilizing function $k(\boldsymbol{n})$ and the Cahn-Hoffman $\boldsymbolξ$-vector, we present a new symmetrized variational formulation for anisotropic surface diffusion with weakly or strongly anisotropic surface energy, which preserves two important structures including volume conservation and energy dissipation. Then we propose a structural-preserving parametric finite element method (SP-PFEM) to discretize the symmetrized variational problem, which preserves the volume in the discretized level. Under a relatively mild and simple condition on $γ(\boldsymbol{n})$, we show that SP-PFEM is unconditionally energy-stable for almost all anisotropic surface energies $γ(\boldsymbol{n})$ arising in practical applications. Extensive numerical results are reported to demonstrate the efficiency and accuracy as well as energy dissipation of the proposed SP-PFEM for solving anisotropic surface diffusion in 3D.

math.NA↗

arXiv2022

A symmetrized parametric finite element method for anisotropic surface diffusion of closed curves

We deal with a long-standing problem about how to design an energy-stable numerical scheme for solving the motion of a closed curve under {\sl anisotropic surface diffusion} with a general anisotropic surface energy $γ(\boldsymbol{n})$ in two dimensions, where $\boldsymbol{n}$ is the outward unit normal vector. By introducing a novel symmetric positive definite surface energy matrix $Z_k(\boldsymbol{n})$ depending on the Cahn-Hoffman $\boldsymbolξ$-vector and a stabilizing function $k(\boldsymbol{n})$, we first reformulate the anisotropic surface diffusion into a conservative form and then derive a new symmetrized variational formulation for the anisotropic surface diffusion with weakly or strongly anisotropic surface energies. A semi-discretization in space for the symmetrized variational formulation is proposed and its area (or mass) conservation and energy dissipation are proved. The semi-discretization is then discretized in time by either an implicit structural-preserving scheme (SP-PFEM) which preserves the area in the discretized level or a semi-implicit energy-stable method (ES-PFEM) which needs only solve a linear system at each time step. Under a relatively simple and mild condition on $γ(\boldsymbol{n})$, we show that both SP-PFEM and ES-PFEM are unconditionally energy-stable for almost all anisotropic surface energies $γ(\boldsymbol{n})$ arising in practical applications. Specifically, for several commonly-used anisotropic surface energies, we construct $Z_k(\boldsymbol{n})$ explicitly. Finally, extensive numerical results are reported to demonstrate the high performance of the proposed numerical schemes.

math.NA↗

arXiv2022

Nonreciprocal Charge Transport in Topological Kagome Superconductor CsV$_{3}$Sb$_{5}$

Nonreciprocal charge transport phenomena are widely studied in two-dimensional superconductors, which demonstrate unidirectional-anisotropy magnetoresistances as a result of symmetry breaking. Here, we report a strong nonreciprocal transport phenomenon in superconducting CsV$_{3}$Sb$_{5}$ thin flakes. The second harmonic voltages, mainly originating from the rectification effect of vortex motion, are unambiguously developed with in-plane and out-of-plane magnetic fields, and their magnitudes are comparable to those in noncentrosymmetric superconductors. The second harmonic magnetoresistances split into several peaks and some of them reverse their signs by ramping the magnetic field or the current within the superconducting transition. The nonreciprocity suggests a strong asymmetry in CsV$_{3}$Sb$_{5}$. The centrosymmetric structure and symmetric electronic phases in CsV$_{3}$Sb$_{5}$ can hardly induce the distinct nonreciprocal transport phenomenon, which could be correlated to a symmetry breaking from an unconventional superconducting order parameter symmetry.

cond-mat.supr-con↗

arXiv2022

Phonon transition across an isotopic interface

Natural materials usually consist of isotopic mixtures, for which different isotopic ratios can lead to distinct material properties such as thermal conductivity and nucleation process. However, the knowledge of isotopic interface remains largely unexplored mainly due to the challenges in isotopic identification and property measurement at an atomic scale. Here, by using monochromated electron energy-loss spectroscopy in a scanning transmission electron microscope, we reveal momentum-transfer-dependent lattice vibration behavior at an artificial h-10BN/h-11BN heterostructure with sub-unit-cell resolution. We find the vibrational energy changes across the isotopic interface gradually, featuring a wide transition regime, which suggests strong delocalization of the out-of-plane optical phonons at the interface. In addition, we identify phonons near the Brillouin zone center have a transition regime ~3.34 nm (10 atomic layers), whereas phonons at the Brillouin zone boundary transition in ~1.66 nm (5 atomic layers). We propose that the isotope-induced charge effect at the interface accounts for the distinct delocalization behavior. Moreover, intra-atomic layer variation of vibration energy is also sensitive to the momentum transfer, thus at the interface it depends on both of momentum transfer and mass change. The revealed lattice vibration behavior at an isotopic interface provides new insights to understand the isotopic effects on properties in natural materials.

cond-mat.mtrl-sci↗

arXiv2022

Fluidic Topology Optimization with an Anisotropic Mixture Model

Fluidic devices are crucial components in many industrial applications involving fluid mechanics. Computational design of a high-performance fluidic system faces multifaceted challenges regarding its geometric representation and physical accuracy. We present a novel topology optimization method to design fluidic devices in a Stokes flow context. Our approach is featured by its capability in accommodating a broad spectrum of boundary conditions at the solid-fluid interface. Our key contribution is an anisotropic and differentiable constitutive model that unifies the representation of different phases and boundary conditions in a Stokes model, enabling a topology optimization method that can synthesize novel structures with accurate boundary conditions from a background grid discretization. We demonstrate the efficacy of our approach by conducting several fluidic system design tasks with over four million design parameters.

cs.GR↗

arXiv2022

DiffCloth: Differentiable Cloth Simulation with Dry Frictional Contact

Cloth simulation has wide applications in computer animation, garment design, and robot-assisted dressing. This work presents a differentiable cloth simulator whose additional gradient information facilitates cloth-related applications. Our differentiable simulator extends a state-of-the-art cloth simulator based on Projective Dynamics (PD) and with dry frictional contact. We draw inspiration from previous work to propose a fast and novel method for deriving gradients in PD-based cloth simulation with dry frictional contact. Furthermore, we conduct a comprehensive analysis and evaluation of the usefulness of gradients in contact-rich cloth simulation. Finally, we demonstrate the efficacy of our simulator in a number of downstream applications, including system identification, trajectory optimization for assisted dressing, closed-loop control, inverse design, and real-to-sim transfer. We observe a substantial speedup obtained from using our gradient information in solving most of these applications.

cs.GR↗