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Lu Zhang

Publications and source records attributed to Lu Zhang.

At least 235 records · Page 13Linked to original sources
arXiv2024

SIMPL: A Simple and Efficient Multi-agent Motion Prediction Baseline for Autonomous Driving

This paper presents a Simple and effIcient Motion Prediction baseLine (SIMPL) for autonomous vehicles. Unlike conventional agent-centric methods with high accuracy but repetitive computations and scene-centric methods with compromised accuracy and generalizability, SIMPL delivers real-time, accurate motion predictions for all relevant traffic participants. To achieve improvements in both accuracy and inference speed, we propose a compact and efficient global feature fusion module that performs directed message passing in a symmetric manner, enabling the network to forecast future motion for all road users in a single feed-forward pass and mitigating accuracy loss caused by viewpoint shifting. Additionally, we investigate the continuous trajectory parameterization using Bernstein basis polynomials in trajectory decoding, allowing evaluations of states and their higher-order derivatives at any desired time point, which is valuable for downstream planning tasks. As a strong baseline, SIMPL exhibits highly competitive performance on Argoverse 1 & 2 motion forecasting benchmarks compared with other state-of-the-art methods. Furthermore, its lightweight design and low inference latency make SIMPL highly extensible and promising for real-world onboard deployment. We open-source the code at https://github.com/HKUST-Aerial-Robotics/SIMPL.

cs.RO↗
arXiv2024

Decomposition-Based Synthesis for Applying Divide-and-Conquer-Like Algorithmic Paradigms

Algorithmic paradigms such as divide-and-conquer (D&C) are proposed to guide developers in designing efficient algorithms, but it can still be difficult to apply algorithmic paradigms to practical tasks. To ease the usage of paradigms, many research efforts have been devoted to the automatic application of algorithmic paradigms. However, most existing approaches to this problem rely on syntax-based program transformations and thus put significant restrictions on the original program. In this paper, we study the automatic application of D&C and several similar paradigms, denoted as D&C-like algorithmic paradigms, and aim to remove the restrictions from syntax-based transformations. To achieve this goal, we propose an efficient synthesizer, named AutoLifter, which does not depend on syntax-based transformations. Specifically, the main challenge of applying algorithmic paradigms is from the large scale of the synthesized programs, and AutoLifter addresses this challenge by applying two novel decomposition methods that do not depend on the syntax of the input program, component elimination and variable elimination, to soundly divide the whole problem into simpler subtasks, each synthesizing a sub-program of the final program and being tractable with existing synthesizers. We evaluate AutoLifter on 96 programming tasks related to 6 different algorithmic paradigms. AutoLifter solves 82/96 tasks with an average time cost of 20.17 seconds, significantly outperforming existing approaches.

cs.PL↗
arXiv2024

PML-based boundary integral equation method for electromagnetic scattering problems in a layered-medium

This paper proposes a new boundary integral equation (BIE) methodology based on the perfectly matched layer (PML) truncation technique for solving the electromagnetic scattering problems in a multi-layered medium. Instead of using the original PML stretched fields, artificial fields which are also equivalent to the solutions in the physical region are introduced. This significantly simplifies the study of the proposed methodology to derive the PML problem. Then some PML transformed layer potentials and the associated boundary integral operators (BIOs) are defined and the corresponding jump relations are shown. Under the assumption that the fields vanish on the PML boundary, the solution representations, as well as the related BIEs and regularization of the hyper-singular operators, in terms of the current density functions on the truncated interface, are derived. Numerical experiments are presented to demonstrate the efficiency and accuracy of the method.

math.NA↗
arXiv2024

Long-Term Fair Decision Making through Deep Generative Models

This paper studies long-term fair machine learning which aims to mitigate group disparity over the long term in sequential decision-making systems. To define long-term fairness, we leverage the temporal causal graph and use the 1-Wasserstein distance between the interventional distributions of different demographic groups at a sufficiently large time step as the quantitative metric. Then, we propose a three-phase learning framework where the decision model is trained on high-fidelity data generated by a deep generative model. We formulate the optimization problem as a performative risk minimization and adopt the repeated gradient descent algorithm for learning. The empirical evaluation shows the efficacy of the proposed method using both synthetic and semi-synthetic datasets.

cs.LG↗
arXiv2024

Striking a Balance in Fairness for Dynamic Systems Through Reinforcement Learning

While significant advancements have been made in the field of fair machine learning, the majority of studies focus on scenarios where the decision model operates on a static population. In this paper, we study fairness in dynamic systems where sequential decisions are made. Each decision may shift the underlying distribution of features or user behavior. We model the dynamic system through a Markov Decision Process (MDP). By acknowledging that traditional fairness notions and long-term fairness are distinct requirements that may not necessarily align with one another, we propose an algorithmic framework to integrate various fairness considerations with reinforcement learning using both pre-processing and in-processing approaches. Three case studies show that our method can strike a balance between traditional fairness notions, long-term fairness, and utility.

cs.LG↗
arXiv2024

Nonlinear preconditioned primal-dual method for a class of structured minimax problems

We propose and analyze a general framework called nonlinear preconditioned primal-dual with projection for solving nonconvex-nonconcave and non-smooth saddle-point problems. The framework consists of two steps. The first is a nonlinear preconditioned map followed by a relaxed projection onto the separating hyperspace we construct. One key to the method is the selection of preconditioned operators, which tailors to the structure of the saddle-point problem and is allowed to be nonlinear and asymmetric. The other is the construction of separating hyperspace, which guarantees fast convergence. This framework paves the way for constructing nonlinear preconditioned primal-dual algorithms. We show that weak convergence, and so is sublinear convergence under the assumption of the convexity of saddle-point problems and linear convergence under a metric subregularity. We also show that many existing primal-daul methods, such as the generalized primal-dual algorithm method, are special cases of relaxed preconditioned primal-dual with projection.

math.OC↗
arXiv2023

Helmholtz decomposition based windowed Green function methods for elastic scattering problems on a half-space

This paper proposes a new Helmholtz decomposition based windowed Green function (HD-WGF) method for solving the time-harmonic elastic scattering problems on a half-space with Dirichlet boundary conditions in both 2D and 3D. The Helmholtz decomposition is applied to separate the pressure and shear waves, which satisfy the Helmholtz and Helmholtz/Maxwell equations, respectively, and the corresponding boundary integral equations of type $(\mathbb{I}+\mathbb{T})\bsϕ=\bs f$, that couple these two waves on the unbounded surface, are derived based on the free-space fundamental solution of Helmholtz equation. This approach avoids the treatment of the complex elastic displacement tensor and traction operator that involved in the classical integral equation method for elastic problems. Then a smooth ``slow-rise'' windowing function is introduced to truncate the boundary integral equations and a ``correction'' strategy is proposed to ensure the uniformly fast convergence for all incident angles of plane incidence. Numerical experiments for both two and three dimensional problems are presented to demonstrate the accuracy and efficiency of the proposed method.

physics.comp-ph↗
arXiv2023

Scene 3-D Reconstruction System in Scattering Medium

The research on neural radiance fields for new view synthesis has experienced explosive growth with the development of new models and extensions. The NERF algorithm, suitable for underwater scenes or scattering media, is also evolving. Existing underwater 3D reconstruction systems still face challenges such as extensive training time and low rendering efficiency. This paper proposes an improved underwater 3D reconstruction system to address these issues and achieve rapid, high-quality 3D reconstruction.To begin with, we enhance underwater videos captured by a monocular camera to correct the poor image quality caused by the physical properties of the water medium while ensuring consistency in enhancement across adjacent frames. Subsequently, we perform keyframe selection on the video frames to optimize resource utilization and eliminate the impact of dynamic objects on the reconstruction results. The selected keyframes, after pose estimation using COLMAP, undergo a three-dimensional reconstruction improvement process using neural radiance fields based on multi-resolution hash coding for model construction and rendering.

cs.CV↗
arXiv2023

Watertightization of Trimmed Surfaces at Intersection Boundary

This paper introduces a watertight technique to deal with the boundary representation of surface-surface intersection in CAD. Surfaces play an important role in today's geometric design. The mathematical model of non-uniform rational B-spline surfaces (NURBS) is the mainstream and ISO standard. In the situation of surface-surface intersection, things are a little complicated, for some parts of surfaces may be cut-off, so called trimmed surfaces occur, which is the central topic in the past decades in CAD community of both academia and industry. The main problem is that the parametric domain of the trimmed surface generally is not the standard square or rectangle, and rather, typically, bounded by curves, based on point inverse of the intersection points and interpolated. The existence of gaps or overlaps at the intersection boundary makes hard the preprocessing of CAE and other downstream applications. The NURBS are in this case hard to keep a closed form. In common, a special data structure of intersection curves must be affiliated to support downstream applications, while the data structure of the whole CAD system is not unified, and the calculation is not efficient. In terms of Bezier surface, a special case of NURBS, this paper designs a reparameterization or normalization to transform the trimmed surface into a group of Bezier surface patches in standard parametric domain [0,1]X[0,1]. And then the boundary curve of normalized Bezier surface patch can be replaced by the intersection curve to realize watertight along the boundary. In this way, the trimmed surface is wiped out, the "gap" between CAD and CAE is closed.

cs.GR↗
arXiv2023

Deep Neural Operator Enabled Concurrent Multitask Design for Multifunctional Metamaterials under Heterogeneous Fields

Multifunctional metamaterials (MMM) bear promise as next-generation material platforms supporting miniaturization and customization. Despite many proof-of-concept demonstrations and the proliferation of deep learning assisted design, grand challenges of inverse design for MMM, especially those involving heterogeneous fields possibly subject to either mutual meta-atom coupling or long-range interactions, remain largely under-explored. To this end, we present a data-driven design framework, which streamlines the inverse design of MMMs involving heterogeneous fields. A core enabler is implicit Fourier neural operator (IFNO), which predicts heterogeneous fields distributed across a metamaterial array, thus in general at odds with homogenization assumptions, in a parameter-/sample-efficient fashion. Additionally, we propose a standard formulation of inverse problem covering a broad class of MMMs, and gradient-based multitask concurrent optimization identifying a set of Pareto-optimal architecture-stimulus (A-S) pairs. Fourier multiclass blending is proposed to synthesize inter-class meta-atoms anchored on a set of geometric motifs, while enjoying training-free dimension reduction and built-it reconstruction. Interlocking the three pillars, the framework is validated for light-bylight programmable plasmonic nanoantenna, whose design involves vast space jointly spanned by quasi-freeform supercells, maneuverable incident phase distributions, and conflicting figure-of-merits involving on-demand localization patterns. Accommodating all the challenges without a-priori simplifications, our framework could propel future advancements of MMM.

cs.CE↗
arXiv2023

The Functional Average Treatment Effect

This paper establishes the functional average as an important estimand for causal inference. The significance of the estimand lies in its robustness against traditional issues of confounding. We prove that this robustness holds even when the probability distribution of the outcome, conditional on treatment or some other vector of adjusting variables, differs almost arbitrarily from its counterfactual analogue. This paper also examines possible estimators of the functional average, including the sample mid-range, and proposes a new type of bootstrap for robust statistical inference: the Hoeffding bootstrap. After this, the paper explores a new class of variables, the $\mathcal{U}$ class of variables, that simplifies the estimation of functional averages. This class of variables is also used to establish mean exchangeability in some cases and to provide the results of elementary statistical procedures, such as linear regression and the analysis of variance, with causal interpretations. Simulation evidence is provided. The methods of this paper are also applied to a National Health and Nutrition Survey data set to investigate the causal effect of exercise on the blood pressure of adult smokers.

math.ST↗
arXiv2023

Revisiting Machine Learning based Test Case Prioritization for Continuous Integration

To alleviate the cost of regression testing in continuous integration (CI), a large number of machine learning-based (ML-based) test case prioritization techniques have been proposed. However, it is yet unknown how they perform under the same experimental setup, because they are evaluated on different datasets with different metrics. To bridge this gap, we conduct the first comprehensive study on these ML-based techniques in this paper. We investigate the performance of 11 representative ML-based prioritization techniques for CI on 11 open-source subjects and obtain a series of findings. For example, the performance of the techniques changes across CI cycles, mainly resulting from the changing amount of training data, instead of code evolution and test removal/addition. Based on the findings, we give some actionable suggestions on enhancing the effectiveness of ML-based techniques, e.g., pretraining a prioritization technique with cross-subject data to get it thoroughly trained and then finetuning it with within-subject data dramatically improves its performance. In particular, the pretrained MART achieves state-of-the-art performance, producing the optimal sequence on 80% subjects, while the existing best technique, the original MART, only produces the optimal sequence on 50% subjects.

cs.SE↗
arXiv2023

Franck-Condon Simulation of Vibrationally-Resolved X-ray Spectra for Diatomic Systems: Validation of Harmonic Approximation and Density Functional Theory

Under the Franck-Condon approximation, we systematically validated the performance of density functional theory (DFT) and the effects of anharmonicity in simulating C/N/O K-edge vibrationally-resolved X-ray spectra of common diatomic molecules. To get ``transparent'' validations, vibronic fine structures of only the lowest 1s excited or ionized state in the X-ray absorption (XAS) or photoelectron (XPS) spectra were investigated. All 6 systems (N$_2$, N$_2^+$; NO, NO$^+$; CO, CO$^+$) were studied within the harmonic oscillator (HO) approximation using DFT with four functionals (BLYP, BP86, B3LYP, M06-2X) for 10 XAS and 4 XPS spectra, and excellent agreement between theoretical and experimental spectra was found in most systems, except O1s XAS of NO, CO, and NO$^+$. We analyzed and established a connection between their complex vibronic structures (many weak oscillating features within a broad peak) and the significant geometrical changes induced by the O1s hole. The three spectra were well reproduced with anharmonic (AH) calculations by using quantum wavepacket dynamics based on potential energy curves (PECs) generated by DFT methods or multiconfigurational levels, highlighting sensitivity to the anharmonic effect and the PEC quality. In other examples of XAS (CO$^+$, C1s and O1s; NO, N1s) corresponding to smaller structural changes, HO and AH approaches lead to similar fine structures, which are dominated by 0-0 and 0-1 transitions. This study highlights the use of DFT with selected functionals for such diatomic calculations due to its easy execution and generally reliable accuracy. Functional dependence in diatomic systems is generally more pronounced than in polyatomic ones. We found that BLYP, BP86, and B3LYP functionals consistently exhibited high accuracy in predicting spectral profiles, bond lengths, and vibrational frequencies, which slightly outperformed M06-2X.

physics.chem-ph↗
arXiv2023

An energy-based discontinuous Galerkin method for the nonlinear Schrödinger equation with wave operator

This work develops an energy-based discontinuous Galerkin (EDG) method for the nonlinear Schrödinger equation with the wave operator. The focus of the study is on the energy-conserving or energy-dissipating behavior of the method with some simple mesh-independent numerical fluxes we designed. We establish error estimates in the energy norm that require careful selection of a test function for the auxiliary equation involving the time derivative of the displacement variable. A critical part of the convergence analysis is to establish the L2 error bounds for the time derivative of the approximation error in the displacement variable by using the equation that determines its mean value. Using a specially chosen test function, we show that one can create a linear system for the time evolution of the unknowns even when dealing with nonlinear properties in the original problem. Extensive numerical experiments are provided to demonstrate the optimal convergence of the scheme in the L2 norm with our choices of the numerical flux.

math.NA↗
arXiv2023

Holistic Evaluation of GPT-4V for Biomedical Imaging

In this paper, we present a large-scale evaluation probing GPT-4V's capabilities and limitations for biomedical image analysis. GPT-4V represents a breakthrough in artificial general intelligence (AGI) for computer vision, with applications in the biomedical domain. We assess GPT-4V's performance across 16 medical imaging categories, including radiology, oncology, ophthalmology, pathology, and more. Tasks include modality recognition, anatomy localization, disease diagnosis, report generation, and lesion detection. The extensive experiments provide insights into GPT-4V's strengths and weaknesses. Results show GPT-4V's proficiency in modality and anatomy recognition but difficulty with disease diagnosis and localization. GPT-4V excels at diagnostic report generation, indicating strong image captioning skills. While promising for biomedical imaging AI, GPT-4V requires further enhancement and validation before clinical deployment. We emphasize responsible development and testing for trustworthy integration of biomedical AGI. This rigorous evaluation of GPT-4V on diverse medical images advances understanding of multimodal large language models (LLMs) and guides future work toward impactful healthcare applications.

eess.IV↗
arXiv2023

Video Frame Interpolation with Many-to-many Splatting and Spatial Selective Refinement

In this work, we first propose a fully differentiable Many-to-Many (M2M) splatting framework to interpolate frames efficiently. Given a frame pair, we estimate multiple bidirectional flows to directly forward warp the pixels to the desired time step before fusing overlapping pixels. In doing so, each source pixel renders multiple target pixels and each target pixel can be synthesized from a larger area of visual context, establishing a many-to-many splatting scheme with robustness to undesirable artifacts. For each input frame pair, M2M has a minuscule computational overhead when interpolating an arbitrary number of in-between frames, hence achieving fast multi-frame interpolation. However, directly warping and fusing pixels in the intensity domain is sensitive to the quality of motion estimation and may suffer from less effective representation capacity. To improve interpolation accuracy, we further extend an M2M++ framework by introducing a flexible Spatial Selective Refinement (SSR) component, which allows for trading computational efficiency for interpolation quality and vice versa. Instead of refining the entire interpolated frame, SSR only processes difficult regions selected under the guidance of an estimated error map, thereby avoiding redundant computation. Evaluation on multiple benchmark datasets shows that our method is able to improve the efficiency while maintaining competitive video interpolation quality, and it can be adjusted to use more or less compute as needed.

cs.CV↗
arXiv2023

PathRL: An End-to-End Path Generation Method for Collision Avoidance via Deep Reinforcement Learning

Robot navigation using deep reinforcement learning (DRL) has shown great potential in improving the performance of mobile robots. Nevertheless, most existing DRL-based navigation methods primarily focus on training a policy that directly commands the robot with low-level controls, like linear and angular velocities, which leads to unstable speeds and unsmooth trajectories of the robot during the long-term execution. An alternative method is to train a DRL policy that outputs the navigation path directly. However, two roadblocks arise for training a DRL policy that outputs paths: (1) The action space for potential paths often involves higher dimensions comparing to low-level commands, which increases the difficulties of training; (2) It takes multiple time steps to track a path instead of a single time step, which requires the path to predicate the interactions of the robot w.r.t. the dynamic environment in multiple time steps. This, in turn, amplifies the challenges associated with training. In response to these challenges, we propose PathRL, a novel DRL method that trains the policy to generate the navigation path for the robot. Specifically, we employ specific action space discretization techniques and tailored state space representation methods to address the associated challenges. In our experiments, PathRL achieves better success rates and reduces angular rotation variability compared to other DRL navigation methods, facilitating stable and smooth robot movement. We demonstrate the competitive edge of PathRL in both real-world scenarios and multiple challenging simulation environments.

cs.RO↗
arXiv2023

Properties and Deviations of Random Sums of Densely Dependent Random Variables

A classical problem of statistical inference is the valid specification of a model that can account for the statistical dependencies between observations when the true structure is dense, intractable, or unknown. To address this problem, a new variance identity is presented, which is closely related to the Moulton factor. This identity does not require the specification of an entire covariance structure and instead relies on the choice of two summary constants. Using this result, a weak law of large numbers is also established for additive statistics and common variance estimators under very general conditions of statistical dependence. Furthermore, this paper proves a sharper version of Hoeffding's inequality for symmetric and bounded random variables under these same conditions of statistical dependence. Put otherwise, it is shown that, under relatively mild conditions, finite sample inference is possible in common settings such as linear regression, and even when every outcome variable is statistically dependent with all others. All results are extended to estimating equations. Simulation experiments and an application to climate data are also provided.

math.ST↗