arXiv subjects

Lu Lu

Publications and source records attributed to Lu Lu.

At least 163 records · Page 9Linked to original sources

arXiv2023

PPDONet: Deep Operator Networks for Fast Prediction of Steady-State Solutions in Disk-Planet Systems

We develop a tool, which we name Protoplanetary Disk Operator Network (PPDONet), that can predict the solution of disk-planet interactions in protoplanetary disks in real-time. We base our tool on Deep Operator Networks (DeepONets), a class of neural networks capable of learning non-linear operators to represent deterministic and stochastic differential equations. With PPDONet we map three scalar parameters in a disk-planet system -- the Shakura \& Sunyaev viscosity $α$, the disk aspect ratio $h_\mathrm{0}$, and the planet-star mass ratio $q$ -- to steady-state solutions of the disk surface density, radial velocity, and azimuthal velocity. We demonstrate the accuracy of the PPDONet solutions using a comprehensive set of tests. Our tool is able to predict the outcome of disk-planet interaction for one system in less than a second on a laptop. A public implementation of PPDONet is available at \url{https://github.com/smao-astro/PPDONet}.

astro-ph.EP↗

arXiv2023

MedGPTEval: A Dataset and Benchmark to Evaluate Responses of Large Language Models in Medicine

METHODS: First, a set of evaluation criteria is designed based on a comprehensive literature review. Second, existing candidate criteria are optimized for using a Delphi method by five experts in medicine and engineering. Third, three clinical experts design a set of medical datasets to interact with LLMs. Finally, benchmarking experiments are conducted on the datasets. The responses generated by chatbots based on LLMs are recorded for blind evaluations by five licensed medical experts. RESULTS: The obtained evaluation criteria cover medical professional capabilities, social comprehensive capabilities, contextual capabilities, and computational robustness, with sixteen detailed indicators. The medical datasets include twenty-seven medical dialogues and seven case reports in Chinese. Three chatbots are evaluated, ChatGPT by OpenAI, ERNIE Bot by Baidu Inc., and Doctor PuJiang (Dr. PJ) by Shanghai Artificial Intelligence Laboratory. Experimental results show that Dr. PJ outperforms ChatGPT and ERNIE Bot in both multiple-turn medical dialogue and case report scenarios.

cs.CL↗

arXiv2023

Deep Learning for Solving and Estimating Dynamic Macro-Finance Models

We develop a methodology that utilizes deep learning to simultaneously solve and estimate canonical continuous-time general equilibrium models in financial economics. We illustrate our method in two examples: (1) industrial dynamics of firms and (2) macroeconomic models with financial frictions. Through these applications, we illustrate the advantages of our method: generality, simultaneous solution and estimation, leveraging the state-of-art machine-learning techniques, and handling large state space. The method is versatile and can be applied to a vast variety of problems.

q-fin.CP↗

arXiv2023

Robust Andrew's sine estimate adaptive filtering

The Andrew's sine function is a robust estimator, which has been used in outlier rejection and robust statistics. However, the performance of such estimator does not receive attention in the field of adaptive filtering techniques. Two Andrew's sine estimator (ASE)-based robust adaptive filtering algorithms are proposed in this brief. Specifically, to achieve improved performance and reduced computational complexity, the iterative Wiener filter (IWF) is an attractive choice. A novel IWF based on ASE (IWF-ASE) is proposed for impulsive noises. To further reduce the computational complexity, the leading dichotomous coordinate descent (DCD) algorithm is combined with the ASE, developing DCD-ASE algorithm. Simulations on system identification demonstrate that the proposed algorithms can achieve smaller misalignment as compared to the conventional IWF, recursive maximum correntropy criterion (RMCC), and DCD-RMCC algorithms in impulsive noise. Furthermore, the proposed algorithms exhibit improved performance in partial discharge (PD) denoising.

eess.SY↗

arXiv2022

Reliable extrapolation of deep neural operators informed by physics or sparse observations

Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks. As promising surrogate solvers of partial differential equations (PDEs) for real-time prediction, deep neural operators such as deep operator networks (DeepONets) provide a new simulation paradigm in science and engineering. Pure data-driven neural operators and deep learning models, in general, are usually limited to interpolation scenarios, where new predictions utilize inputs within the support of the training set. However, in the inference stage of real-world applications, the input may lie outside the support, i.e., extrapolation is required, which may result to large errors and unavoidable failure of deep learning models. Here, we address this challenge of extrapolation for deep neural operators. First, we systematically investigate the extrapolation behavior of DeepONets by quantifying the extrapolation complexity via the 2-Wasserstein distance between two function spaces and propose a new behavior of bias-variance trade-off for extrapolation with respect to model capacity. Subsequently, we develop a complete workflow, including extrapolation determination, and we propose five reliable learning methods that guarantee a safe prediction under extrapolation by requiring additional information -- the governing PDEs of the system or sparse new observations. The proposed methods are based on either fine-tuning a pre-trained DeepONet or multifidelity learning. We demonstrate the effectiveness of the proposed framework for various types of parametric PDEs. Our systematic comparisons provide practical guidelines for selecting a proper extrapolation method depending on the available information, desired accuracy, and required inference speed.

cs.LG↗

arXiv2022

Effective Data Sampling Strategies and Boundary Condition Constraints of Physics-Informed Neural Networks for Identifying Material Properties in Solid Mechanics

Material identification is critical for understanding the relationship between mechanical properties and the associated mechanical functions. However, material identification is a challenging task, especially when the characteristic of the material is highly nonlinear in nature, as is common in biological tissue. In this work, we identify unknown material properties in continuum solid mechanics via physics-informed neural networks (PINNs). To improve the accuracy and efficiency of PINNs, we developed efficient strategies to nonuniformly sample observational data. We also investigated different approaches to enforce Dirichlet boundary conditions as soft or hard constraints. Finally, we apply the proposed methods to a diverse set of time-dependent and time-independent solid mechanic examples that span linear elastic and hyperelastic material space. The estimated material parameters achieve relative errors of less than 1%. As such, this work is relevant to diverse applications, including optimizing structural integrity and developing novel materials.

cond-mat.mtrl-sci↗

arXiv2022

On directed strongly regular Cayley graphs over non-abelian groups with an abelian subgroup of index $2$

In 1988, Duval introduced the concept of directed strongly regular graphs, which can be viewed as a directed graph version of strongly regular graphs. Such directed graphs have similar structural and algebraic properties to strongly regular graphs. In the past three decades, it was found that Cayley graphs, especially those over dihedral groups, play a key role in the construction of directed strongly regular graphs. In this paper, we focus on the characterization of directed strongly regular Cayley graphs over more general groups. Let $G$ be a non-abelian group with an abelian subgroup of index $2$. We give some necessary conditions for a Cayley graph over $G$ to be directed strongly regular, and characterize the directed strongly regular Cayley graphs over $G$ satisfying specified conditions. This extends some previous results of He and Zhang (2019).

math.CO↗

arXiv2022

Aerial Manipulation Using a Novel Unmanned Aerial Vehicle Cyber-Physical System

Unmanned Aerial Vehicles(UAVs) are attaining more and more maneuverability and sensory ability as a promising teleoperation platform for intelligent interaction with the environments. This work presents a novel 5-degree-of-freedom (DoF) unmanned aerial vehicle (UAV) cyber-physical system for aerial manipulation. This UAV's body is capable of exerting powerful propulsion force in the longitudinal direction, decoupling the translational dynamics and the rotational dynamics on the longitudinal plane. A high-level impedance control law is proposed to drive the vehicle for trajectory tracking and interaction with the environments. In addition, a vision-based real-time target identification and tracking method integrating a YOLO v3 real-time object detector with feature tracking, and morphological operations is proposed to be implemented onboard the vehicle with support of model compression techniques to eliminate latency caused by video wireless transmission and heavy computation burden on traditional teleoperation platforms.

cs.RO↗

arXiv2022

In situ characterization of vacancy ordering in Ge-Sb-Te phase-change memory alloys

Tailoring the degree of structural disorder in Ge-Sb-Te alloys is important for the development of non-volatile phase-change memory and neuro-inspired computing. Upon crystallization from the amorphous phase, these alloys form a cubic rocksalt-like structure with a high content of intrinsic vacancies. Further thermal annealing results in a gradual structural transition towards a layered structure and an insulator-to-metal transition. In this work, we elucidate the atomic-level details of the structural transition in crystalline GeSb2Te4 by in situ high-resolution transmission electron microscopy (HRTEM) experiments and ab initio density functional theory (DFT) calculations, providing a comprehensive real-time and real-space view of the vacancy ordering process. We also discuss the impact of vacancy ordering on altering the electronic and optical properties of GeSb2Te4, which is relevant to multilevel storage applications. The phase evolution paths in Ge-Sb-Te alloys are illustrated using a summary diagram, which serves as a guide for designing phase-change memory devices.

cond-mat.mtrl-sci↗

arXiv2022

Spectral radius of graphs with given size and odd girth

Let $\mathcal{G}(m,k)$ be the set of graphs with size $m$ and odd girth (the length of shortest odd cycle) $k$. In this paper, we determine the graph maximizing the spectral radius among $\mathcal{G}(m,k)$ when $m$ is odd. As byproducts, we show that, there is a number $η(m)>\sqrt{m-k+3}$ such that every non-bipartite graph $G$ with size $m$ and spectral radius $ρ\ge η(m)$ must contains an odd cycle of length less than $k$ unless $m$ is odd and $G\cong SK_{k,m}$, which is the graph obtained by subdividing an edge $k-2$ times of complete bipartite $K_{2,\frac{m-k+2}{2}}$. This result implies the main results of [Discrete Math. 345 (2022)] and \cite{li-peng}, and settles the conjecture in \cite{li-peng} as well.

math.CO↗

arXiv2022

Phase Code Discovery for Pulse Compression Radar: A Genetic Algorithm Approach

Discovering sequences with desired properties has long been an interesting intellectual pursuit. In pulse compression radar (PCR), discovering phase codes with low aperiodic autocorrelations is essential for a good estimation performance. The design of phase code, however, is mathematically non-trivial as the aperiodic autocorrelation properties of a sequence are intractable to characterize. In this paper, we put forth a genetic algorithm (GA) approach to discover new phase codes for PCR with the mismatched filter (MMF) receiver. The developed GA, dubbed GASeq, discovers better phase codes than the state of the art. At a code length of 59, the sequence discovered by GASeq achieves a signal-to-clutter ratio (SCR) of 50.84, while the best-known sequence has an SCR of 45.16. In addition, the efficiency and scalability of GASeq enable us to search phase codes with a longer code length, which thwarts existing deep learning-based approaches. At a code length of 100, the best phase code discovered by GASeq exhibit an SCR of 63.23.

cs.IT↗

arXiv2022

A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks

Physics-informed neural networks (PINNs) have shown to be an effective tool for solving forward and inverse problems of partial differential equations (PDEs). PINNs embed the PDEs into the loss of the neural network, and this PDE loss is evaluated at a set of scattered residual points. The distribution of these points are highly important to the performance of PINNs. However, in the existing studies on PINNs, only a few simple residual point sampling methods have mainly been used. Here, we present a comprehensive study of two categories of sampling: non-adaptive uniform sampling and adaptive nonuniform sampling. We consider six uniform sampling, including (1) equispaced uniform grid, (2) uniformly random sampling, (3) Latin hypercube sampling, (4) Halton sequence, (5) Hammersley sequence, and (6) Sobol sequence. We also consider a resampling strategy for uniform sampling. To improve the sampling efficiency and the accuracy of PINNs, we propose two new residual-based adaptive sampling methods: residual-based adaptive distribution (RAD) and residual-based adaptive refinement with distribution (RAR-D), which dynamically improve the distribution of residual points based on the PDE residuals during training. Hence, we have considered a total of 10 different sampling methods, including six non-adaptive uniform sampling, uniform sampling with resampling, two proposed adaptive sampling, and an existing adaptive sampling. We extensively tested the performance of these sampling methods for four forward problems and two inverse problems in many setups. Our numerical results presented in this study are summarized from more than 6000 simulations of PINNs. We show that the proposed adaptive sampling methods of RAD and RAR-D significantly improve the accuracy of PINNs with fewer residual points. The results obtained in this study can also be used as a practical guideline in choosing sampling methods.

physics.comp-ph↗

arXiv2022

High-Energy and Ultra-High-Energy Neutrinos

Astrophysical neutrinos are excellent probes of astroparticle physics and high-energy physics. With energies far beyond solar, supernovae, atmospheric, and accelerator neutrinos, high-energy and ultra-high-energy neutrinos probe fundamental physics from the TeV scale to the EeV scale and beyond. They are sensitive to physics both within and beyond the Standard Model through their production mechanisms and in their propagation over cosmological distances. They carry unique information about their extreme non-thermal sources by giving insight into regions that are opaque to electromagnetic radiation. This white paper describes the opportunities astrophysical neutrino observations offer for astrophysics and high-energy physics, today and in coming years.

hep-ph↗

arXiv2022

Dynamic gNodeB Sleep Control for Energy-Conserving 5G Radio Access Network

5G radio access network (RAN) is consuming much more energy than legacy RAN due to the denser deployments of gNodeBs (gNBs) and higher single-gNB power consumption. In an effort to achieve an energy-conserving RAN, this paper develops a dynamic on-off switching paradigm, where the ON/OFF states of gNBs can be dynamically configured according to the evolvements of the associated users. We formulate the dynamic sleep control for a cluster of gNBs as a Markov decision process (MDP) and analyze various switching policies to reduce the energy expenditure. The optimal policy of the MDP that minimizes the energy expenditure can be derived from dynamic programming, but the computation is expensive. To circumvent this issue, this paper puts forth a greedy policy and an index policy for gNB sleep control. When there is no constraint on the number of gNBs that can be turned off, we prove the dual-threshold structure of the greedy policy and analyze its connections with the optimal policy. Inspired by the dual-threshold structure and Whittle index, we develop an index policy by decoupling the original MDP into multiple one-dimensional MDPs -- the indexability of the decoupled MDP is proven and an algorithm to compute the index is proposed. Extensive simulation results verify that the index policy exhibits close-to-optimal performance in terms of the energy expenditure of the gNB cluster. As far as the computational complexity is concerned, on the other hand, the index policy is much more efficient than the optimal policy, which is computationally prohibitive when the number of gNBs is large.

cs.IT↗

arXiv2022

Sampling-based Estimation of the Number of Distinct Values in Distributed Environment

In data mining, estimating the number of distinct values (NDV) is a fundamental problem with various applications. Existing methods for estimating NDV can be broadly classified into two categories: i) scanning-based methods, which scan the entire data and maintain a sketch to approximate NDV; and ii) sampling-based methods, which estimate NDV using sampling data rather than accessing the entire data warehouse. Scanning-based methods achieve a lower approximation error at the cost of higher I/O and more time. Sampling-based estimation is preferable in applications with a large data volume and a permissible error restriction due to its higher scalability. However, while the sampling-based method is more effective on a single machine, it is less practical in a distributed environment with massive data volumes. For obtaining the final NDV estimators, the entire sample must be transferred throughout the distributed system, incurring a prohibitive communication cost when the sample rate is significant. This paper proposes a novel sketch-based distributed method that achieves sub-linear communication costs for distributed sampling-based NDV estimation under mild assumptions. Our method leverages a sketch-based algorithm to estimate the sample's {\em frequency of frequency} in the {\em distributed streaming model}, which is compatible with most classical sampling-based NDV estimators. Additionally, we provide theoretical evidence for our method's ability to minimize communication costs in the worst-case scenario. Extensive experiments show that our method saves orders of magnitude in communication costs compared to existing sampling- and sketch-based methods.

cs.DB↗

arXiv2022

Digital Twin for Networking: A Data-driven Performance Modeling Perspective

Emerging technologies and applications make the network unprecedentedly complex and heterogeneous, leading physical network practices to be costly and risky. The digital twin network (DTN) can ease these burdens by virtually enabling users to understand how performance changes accordingly with modifications. For this "What-if" performance evaluation, conventional simulation and analytical approaches are inefficient, inaccurate, and inflexible, and we argue that data-driven methods are most promising. In this article, we identify three requirements (fidelity, efficiency, and flexibility) for performance evaluation. Then we present a comparison of selected data-driven methods and investigate their potential trends in data, models, and applications. Although extensive applications have been enabled, there are still significant conflicts between models' capacities to handle diversified inputs and limited data collected from the production network. We further illustrate the opportunities for data collection, model construction, and application prospects. This survey aims to provide a reference for performance evaluation while also facilitating future DTN research.

cs.NI↗

arXiv2022

Importance is in your attention: agent importance prediction for autonomous driving

Trajectory prediction is an important task in autonomous driving. State-of-the-art trajectory prediction models often use attention mechanisms to model the interaction between agents. In this paper, we show that the attention information from such models can also be used to measure the importance of each agent with respect to the ego vehicle's future planned trajectory. Our experiment results on the nuPlans dataset show that our method can effectively find and rank surrounding agents by their impact on the ego's plan.

cs.RO↗

arXiv2022

Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport

Deep neural operators can learn operators mapping between infinite-dimensional function spaces via deep neural networks and have become an emerging paradigm of scientific machine learning. However, training neural operators usually requires a large amount of high-fidelity data, which is often difficult to obtain in real engineering problems. Here, we address this challenge by using multifidelity learning, i.e., learning from multifidelity datasets. We develop a multifidelity neural operator based on a deep operator network (DeepONet). A multifidelity DeepONet includes two standard DeepONets coupled by residual learning and input augmentation. Multifidelity DeepONet significantly reduces the required amount of high-fidelity data and achieves one order of magnitude smaller error when using the same amount of high-fidelity data. We apply a multifidelity DeepONet to learn the phonon Boltzmann transport equation (BTE), a framework to compute nanoscale heat transport. By combining a trained multifidelity DeepONet with genetic algorithm or topology optimization, we demonstrate a fast solver for the inverse design of BTE problems.

physics.comp-ph↗