arXiv subjects

Yan Jiang

Publications and source records attributed to Yan Jiang.

At least 91 records · Page 5Linked to original sources

arXiv2024

Upwind summation-by-parts finite differences: error estimates and WENO methodology

High order upwind summation-by-parts finite difference operators have recently been developed. When combined with the simultaneous-approximation-term method to impose boundary conditions, the method converges faster than using traditional summation-by-parts operators. We prove the convergence rate by the normal mode analysis for such methods for a class of hyperbolic partial differential equations. Our analysis shows that the penalty parameter for imposing boundary conditions affects the convergence rate for stable methods. In addition, to solve problems with discontinuous data, we extend the method to also have the weighted essentially nonoscillatory property. The overall method is stable, achieves high order accuracy for smooth problems, and is capable of solving problems with discontinuities.

math.NA↗

arXiv2024

eDIG-CHANGES II: Project Design and Initial Results on NGC 3556

The extraplanar diffuse ionized gas (eDIG) represents ionized gases traced by optical/UV lines beyond the stellar extent of galaxies. We herein introduce a novel multi-slit narrow-band spectroscopy method to conduct spatially resolved spectroscopy of the eDIG around a sample of nearby edge-on disk galaxies (eDIG-CHANGES). In this paper, we introduce the project design and major scientific goals, as well as a pilot study of NGC 3556 (M108). The eDIG is detected to a vertical extent of a few kpc above the disk, comparable to the X-ray and radio images. We do not see significant vertical variation of the [N II]/H$α$ line ratio. A rough examination of the pressure balance between different circum-galactic medium (CGM) phases indicates the magnetic field is in a rough pressure balance with the X-ray emitting hot gas, and may play an important role in the global motion of both the eDIG and the hot gas in the lower halo. At the location of an HST/COS observed UV bright background AGN $\sim29\rm~kpc$ from the center of NGC 3556, the magnetic pressure is much lower than that of the hot gas and the ionized gas traced by UV absorption lines, although the extrapolation of the pressure profiles may cause some biases in this comparison. By comparing the position-velocity diagrams of the optical and CO lines, we also find the dynamics of the two gas phases are consistent with each other, with no evidence of a global inflow/outflow and a maximum rotation velocity of $\sim150\rm~km~s^{-1}$.

astro-ph.GA↗

arXiv2024

Oscillations-Aware Frequency Security Assessment via Efficient Worst-Case Frequency Nadir Computation

Frequency security assessment following major disturbances has long been one of the central tasks in power system operations. The standard approach is to study the center of inertia frequency, an aggregate signal for an entire system, to avoid analyzing the frequency signal at individual buses. However, as the amount of low-inertia renewable resources in a grid increases, the center of inertia frequency is becoming too coarse to provide reliable frequency security assessment. In this paper, we propose an efficient algorithm to determine the worst-case frequency nadir across all buses for bounded power disturbances, as well as identify the power disturbances leading to that severest scenario. The proposed algorithm allows oscillations-aware frequency security assessment without conducting exhaustive simulations and intractable analysis.

eess.SY↗

arXiv2024

A new type of simplified inverse Lax-Wendroff boundary treatment I: hyperbolic conservation laws

In this paper, we design a new kind of high order inverse Lax-Wendroff (ILW) boundary treatment for solving hyperbolic conservation laws with finite difference method on a Cartesian mesh. This new ILW method decomposes the construction of ghost point values near inflow boundary into two steps: interpolation and extrapolation. At first, we impose values of some artificial auxiliary points through a polynomial interpolating the interior points near the boundary. Then, we will construct a Hermite extrapolation based on those auxiliary point values and the spatial derivatives at boundary obtained via the ILW procedure. This polynomial will give us the approximation to the ghost point value. By an appropriate selection of those artificial auxiliary points, high-order accuracy and stable results can be achieved. Moreover, theoretical analysis indicates that comparing with the original ILW method, especially for higher order accuracy, the new proposed one would require fewer terms using the relatively complicated ILW procedure and thus improve computational efficiency on the premise of maintaining accuracy and stability. We perform numerical experiments on several benchmarks, including one- and two-dimensional scalar equations and systems. The robustness and efficiency of the proposed scheme is numerically verified.

math.NA↗

arXiv2024

Weak Collocation Regression method: fast reveal hidden stochastic dynamics from high-dimensional aggregate data

Revealing hidden dynamics from the stochastic data is a challenging problem as randomness takes part in the evolution of the data. The problem becomes exceedingly complex when the trajectories of the stochastic data are absent in many scenarios. Here we present an approach to effectively modeling the dynamics of the stochastic data without trajectories based on the weak form of the Fokker-Planck (FP) equation, which governs the evolution of the density function in the Brownian process. Taking the collocations of Gaussian functions as the test functions in the weak form of the FP equation, we transfer the derivatives to the Gaussian functions and thus approximate the weak form by the expectational sum of the data. With a dictionary representation of the unknown terms, a linear system is built and then solved by the regression, revealing the unknown dynamics of the data. Hence, we name the method with the Weak Collocation Regression (WCR) method for its three key components: weak form, collocation of Gaussian kernels, and regression. The numerical experiments show that our method is flexible and fast, which reveals the dynamics within seconds in multi-dimensional problems and can be easily extended to high-dimensional data such as 20 dimensions. WCR can also correctly identify the hidden dynamics of the complex tasks with variable-dependent diffusion and coupled drift, and the performance is robust, achieving high accuracy in the case with noise added.

math.NA↗

arXiv2024

Zero-Shot Video Editing Using Off-The-Shelf Image Diffusion Models

Large-scale text-to-image diffusion models achieve unprecedented success in image generation and editing. However, how to extend such success to video editing is unclear. Recent initial attempts at video editing require significant text-to-video data and computation resources for training, which is often not accessible. In this work, we propose vid2vid-zero, a simple yet effective method for zero-shot video editing. Our vid2vid-zero leverages off-the-shelf image diffusion models, and doesn't require training on any video. At the core of our method is a null-text inversion module for text-to-video alignment, a cross-frame modeling module for temporal consistency, and a spatial regularization module for fidelity to the original video. Without any training, we leverage the dynamic nature of the attention mechanism to enable bi-directional temporal modeling at test time. Experiments and analyses show promising results in editing attributes, subjects, places, etc., in real-world videos. Code is made available at \url{https://github.com/baaivision/vid2vid-zero}.

cs.CV↗

arXiv2023

UQ at #SMM4H 2023: ALEX for Public Health Analysis with Social Media

As social media becomes increasingly popular, more and more activities related to public health emerge. Current techniques for public health analysis involve popular models such as BERT and large language models (LLMs). However, the costs of training in-domain LLMs for public health are especially expensive. Furthermore, such kinds of in-domain datasets from social media are generally imbalanced. To tackle these challenges, the data imbalance issue can be overcome by data augmentation and balanced training. Moreover, the ability of the LLMs can be effectively utilized by prompting the model properly. In this paper, a novel ALEX framework is proposed to improve the performance of public health analysis on social media by adopting an LLMs explanation mechanism. Results show that our ALEX model got the best performance among all submissions in both Task 2 and Task 4 with a high score in Task 1 in Social Media Mining for Health 2023 (SMM4H)[1]. Our code has been released at https:// github.com/YanJiangJerry/ALEX.

cs.CL↗

arXiv2023

Balanced and Explainable Social Media Analysis for Public Health with Large Language Models

As social media becomes increasingly popular, more and more public health activities emerge, which is worth noting for pandemic monitoring and government decision-making. Current techniques for public health analysis involve popular models such as BERT and large language models (LLMs). Although recent progress in LLMs has shown a strong ability to comprehend knowledge by being fine-tuned on specific domain datasets, the costs of training an in-domain LLM for every specific public health task are especially expensive. Furthermore, such kinds of in-domain datasets from social media are generally highly imbalanced, which will hinder the efficiency of LLMs tuning. To tackle these challenges, the data imbalance issue can be overcome by sophisticated data augmentation methods for social media datasets. In addition, the ability of the LLMs can be effectively utilised by prompting the model properly. In light of the above discussion, in this paper, a novel ALEX framework is proposed for social media analysis on public health. Specifically, an augmentation pipeline is developed to resolve the data imbalance issue. Furthermore, an LLMs explanation mechanism is proposed by prompting an LLM with the predicted results from BERT models. Extensive experiments conducted on three tasks at the Social Media Mining for Health 2023 (SMM4H) competition with the first ranking in two tasks demonstrate the superior performance of the proposed ALEX method. Our code has been released in https://github.com/YanJiangJerry/ALEX.

cs.CL↗

arXiv2023

Inverse problems for nonlinear progressive waves

We propose and study several inverse problems associated with the nonlinear progressive waves that arise in infrasonic inversions. The nonlinear progressive equation (NPE) is of a quasilinear form $\partial_t^2 u=Δf(x, u)$ with $f(x, u)=c_1(x) u+c_2(x) u^n$, $n\geq 2$, and can be derived from the hyperbolic system of conservation laws associated with the Euler equations. We establish unique identifiability results in determining $f(x, u)$ as well as the associated initial data by the boundary measurement. Our analysis relies on high-order linearisation and construction of proper Gaussian beam solutions for the underlying wave equations. In addition to its theoretical interest, we connect our study to applications of practical importance in infrasound waveform inversion.

math.AP↗

arXiv2023

CO-CHANGES I: IRAM 30m CO Observations of Molecular Gas in the Sombrero Galaxy

Molecular gas plays a critical role in explaining the quiescence of star formation (SF) in massive isolated spiral galaxies, which could be a result of either the low molecular gas content and/or the low SF efficiency. We present IRAM 30m observations of the CO lines in the Sombrero galaxy (NGC~4594), the most massive spiral at $d\lesssim30\rm~Mpc$. We detect at least one of the three CO lines covered by our observations in all 13 observed positions located at the galactic nucleus and along a $\sim25\rm~kpc$-diameter dusty ring. The total extrapolated molecular gas mass of the galaxy is $M_{\rm H_2}\approx4\times10^{8}\rm~M_\odot$. The measured maximum CO gas rotation velocity of $\approx379\rm~km~s^{-1}$ suggests that NGC~4594 locates in a dark matter halo with a mass $M_{\rm200}\gtrsim10^{13}\rm~M_\odot$. Comparing to other galaxy samples, NGC~4594 is extremely gas poor and SF inactive, but the SF efficiency is apparently not inconsistent with that predicted by the Kennicutt-Schmidt law, so there is no evidence of enhanced SF quenching in this extremely massive spiral with a huge bulge. We also calculate the predicted gas supply rate from various sources to replenish the cold gas consumed in SF, and find that the galaxy must experienced a starburst stage at high redshift, then the leftover or recycled gas provides SF fuels to maintain the gradual growth of the galactic disk at a gentle rate.

astro-ph.GA↗

arXiv2023

Entropy Structure Informed Learning for Inverse XDE Problems

Entropy, since its first discovery by Ludwig Boltzmann in 1877, has been widely applied in diverse disciplines, including thermodynamics, continuum mechanics, mathematical analysis, machine learning, etc. In this paper, we propose a new method for solving the inverse XDE (ODE, PDE, SDE) problems by utilizing the entropy balance equation instead of the original differential equations. This distinguishing feature constitutes a major difference between our current method and other previous classical methods (e.g. SINDy). Despite concerns about the potential information loss during the compression procedure from the original XDEs to single entropy balance equation, various examples from MM reactions, Schlogl model and chemical Lorenz equations in the form of ODEs to nonlinear porous medium equation and Fokker-Planck equation with a double-well potential in the PDE form all well confirm the accuracy, robustness and reliability of our method, as well as its comparable performance with respect to SINDy.

math.DS↗

arXiv2023

Structured Neural-PI Control for Networked Systems: Stability and Steady-State Optimality Guarantees

We study the control of networked systems with the goal of optimizing both transient and steady-state performances while providing stability guarantees. Linear proportional-integral (PI) controllers are almost always used in practice, but the linear parameterization of the controller fundamentally limits its performance. Learning-based approaches are becoming popular in designing nonlinear controllers, but the lack of stability guarantees makes the learned controllers difficult to apply in practical applications. This paper bridges the gap between neural network-based controller design and the need for stability guarantees. Using equilibrium-independent passivity, a property present in a wide range of physical systems, we propose structured neural-PI controllers that have provable guarantees on the convergence of output to a desired agreement value. If communication between neighbours is available, we further extend the controller to distributedly achieve optimal resource allocation at the steady state. We explicitly characterize the stability conditions and engineer neural networks that satisfy them by design. Experiments on traffic and power networks demonstrate that the proposed approach can improve transient and steady-state performances compared to existing state-of-the-art, while unstructured neural networks lead to unstable behaviors.

eess.SY↗

arXiv2023

Structured Neural-PI Control with End-to-End Stability and Output Tracking Guarantees

We study the optimal control of multiple-input and multiple-output dynamical systems via the design of neural network-based controllers with stability and output tracking guarantees. While neural network-based nonlinear controllers have shown superior performance in various applications, their lack of provable guarantees has restricted their adoption in high-stake real-world applications. This paper bridges the gap between neural network-based controllers and the need for stabilization guarantees. Using equilibrium-independent passivity, a property present in a wide range of physical systems, we propose neural Proportional-Integral (PI) controllers that have provable guarantees of stability and zero steady-state output tracking error. The key structure is the strict monotonicity on proportional and integral terms, which is parameterized as gradients of strictly convex neural networks (SCNN). We construct SCNN with tunable softplus-$β$ activations, which yields universal approximation capability and is also useful in incorporating communication constraints. In addition, the SCNNs serve as Lyapunov functions, giving us end-to-end performance guarantees. Experiments on traffic and power networks demonstrate that the proposed approach improves both transient and steady-state performances, while unstructured neural networks lead to unstable behaviors.

eess.SY↗

arXiv2023

Equilibria of Fully Decentralized Learning in Networked Systems

Existing settings of decentralized learning either require players to have full information or the system to have certain special structure that may be hard to check and hinder their applicability to practical systems. To overcome this, we identify a structure that is simple to check for linear dynamical system, where each player learns in a fully decentralized fashion to minimize its cost. We first establish the existence of pure strategy Nash equilibria in the resulting noncooperative game. We then conjecture that the Nash equilibrium is unique provided that the system satisfies an additional requirement on its structure. We also introduce a decentralized mechanism based on projected gradient descent to have agents learn the Nash equilibrium. Simulations on a $5$-player game validate our results.

eess.SY↗

arXiv2022

Spectral patterns of elastic transmission eigenfunctions: boundary localisation, surface resonance and stress concentration

We present a comprehensive study of new discoveries on the spectral patterns of elastic transmission eigenfunctions, including boundary localisation, surface resonance, and stress concentration. In the case where the domain is radial and the underlying parameters are constant, we give rigorous justifications and derive a thorough understanding of those intriguing geometric and physical patterns. We also present numerical examples to verify that the same results hold in general geometric and parameter setups.

math.AP↗

arXiv2022

On the Performance of Data Compression in Clustered Fog Radio Access Networks

The fog-radio-access-network (F-RAN) has been proposed to address the strict latency requirements, which offloads computation tasks generated in user equipments (UEs) to the edge to reduce the processing latency. However, it incorporates the task transmission latency, which may become the bottleneck of latency requirements. Data compression (DC) has been considered as one of the promising techniques to reduce the transmission latency. By compressing the computation tasks before transmitting, the transmission delay is reduced due to the shrink transmitted data size, and the original computing task can be retrieved by employing data decompressing (DD) at the edge nodes or the centre cloud. Nevertheless, the DC and DD incorporate extra processing latency, and the latency performance has not been investigated in the large-scale DC-enabled F-RAN. Therefore, in this work, the successful data compression probability (SDCP) is defined to analyse the latency performance of the F-RAN. Moreover, to analyse the effect of compression offloading ratio (COR), a novel hybrid compression mode is proposed based on the queueing theory. Based on this, the closed-form result of SDCP in the large-scale DC-enabled F-RAN is derived by combining the Matern cluster process and M/G/1 queueing model, and validated by Monte Carlo simulations. Based on the derived SDCP results, the effects of COR on the SDCP is analysed numerically. The results show that the SDCP with the optimal COR can be enhanced with a maximum value of 0.3 and 0.55 as compared with the cases of compressing all computing tasks at the edge and at the UE, respectively. Moreover, for the system requiring the minimal latency, the proposed hybrid compression mode can alleviate the requirement on the backhaul capacity.

eess.SP↗

arXiv2022

Few-Shot Stance Detection via Target-Aware Prompt Distillation

Stance detection aims to identify whether the author of a text is in favor of, against, or neutral to a given target. The main challenge of this task comes two-fold: few-shot learning resulting from the varying targets and the lack of contextual information of the targets. Existing works mainly focus on solving the second issue by designing attention-based models or introducing noisy external knowledge, while the first issue remains under-explored. In this paper, inspired by the potential capability of pre-trained language models (PLMs) serving as knowledge bases and few-shot learners, we propose to introduce prompt-based fine-tuning for stance detection. PLMs can provide essential contextual information for the targets and enable few-shot learning via prompts. Considering the crucial role of the target in stance detection task, we design target-aware prompts and propose a novel verbalizer. Instead of mapping each label to a concrete word, our verbalizer maps each label to a vector and picks the label that best captures the correlation between the stance and the target. Moreover, to alleviate the possible defect of dealing with varying targets with a single hand-crafted prompt, we propose to distill the information learned from multiple prompts. Experimental results show the superior performance of our proposed model in both full-data and few-shot scenarios.

cs.CL↗

arXiv2022

Stable Reinforcement Learning for Optimal Frequency Control: A Distributed Averaging-Based Integral Approach

Frequency control plays a pivotal role in reliable power system operations. It is conventionally performed in a hierarchical way that first rapidly stabilizes the frequency deviations and then slowly recovers the nominal frequency. However, as the generation mix shifts from synchronous generators to renewable resources, power systems experience larger and faster frequency fluctuations due to the loss of inertia, which adversely impacts the frequency stability. This has motivated active research in algorithms that jointly address frequency degradation and economic efficiency in a fast timescale, among which the distributed averaging-based integral (DAI) control is a notable one that sets controllable power injections directly proportional to the integrals of frequency deviation and economic inefficiency signals. Nevertheless, DAI do not typically consider the transient performance of the system following power disturbances and has been restricted to quadratic operational cost functions. This manuscript aims to leverage nonlinear optimal controllers to simultaneously achieve optimal transient frequency control and find the most economic power dispatch for frequency restoration. To this end, we integrate reinforcement learning (RL) to the classic DAI, which results in RL-DAI. Specifically, we use RL to learn a neural network-based control policy mapping from the integral variables of DAI to the controllable power injections which provides optimal transient frequency control, while DAI inherently ensures the frequency restoration and optimal economic dispatch. Compared to existing methods, we provide provable guarantees on the stability of the learned controllers and extend allowable cost functions to a much larger class. Simulations on the 39-bus New England system illustrate our results.

eess.SY↗