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Wenlong Zhang

Publications and source records attributed to Wenlong Zhang.

At least 127 records · Page 7Linked to original sources
arXiv2024

A novel model reduction method to solve inverse problems of parabolic type

In this paper, we propose novel proper orthogonal decomposition (POD)--based model reduction methods that effectively address the issue of inverse crime in solving parabolic inverse problems. Both the inverse initial value problems and inverse source problems are studied. By leveraging the inherent low-dimensional structures present in the data, our approach enables a reduction in the forward model complexity without compromising the accuracy of the inverse problem solution. Besides, we prove the convergence analysis of the proposed methods for solving parabolic inverse problems. Through extensive experimentation and comparative analysis, we demonstrate the effectiveness of our method in overcoming inverse crime and achieving improved inverse problem solutions. The proposed POD model reduction method offers a promising direction for improving the reliability and applicability of inverse problem-solving techniques in various domains.

math.NA↗
arXiv2024

Pontryagin Neural Operator for Solving Parametric General-Sum Differential Games

The values of two-player general-sum differential games are viscosity solutions to Hamilton-Jacobi-Isaacs (HJI) equations. Value and policy approximations for such games suffer from the curse of dimensionality (CoD). Alleviating CoD through physics-informed neural networks (PINN) encounters convergence issues when differentiable values with large Lipschitz constants are present due to state constraints. On top of these challenges, it is often necessary to learn generalizable values and policies across a parametric space of games, e.g., for game parameter inference when information is incomplete. To address these challenges, we propose in this paper a Pontryagin-mode neural operator that outperforms the current state-of-the-art hybrid PINN model on safety performance across games with parametric state constraints. Our key contribution is the introduction of a costate loss defined on the discrepancy between forward and backward costate rollouts, which are computationally cheap. We show that the costate dynamics, which can reflect state constraint violation, effectively enables the learning of differentiable values with large Lipschitz constants, without requiring manually supervised data as suggested by the hybrid PINN model. More importantly, we show that the close relationship between costates and policies makes the former critical in learning feedback control policies with generalizable safety performance.

cs.LG↗
arXiv2024

DVMSR: Distillated Vision Mamba for Efficient Super-Resolution

Efficient Image Super-Resolution (SR) aims to accelerate SR network inference by minimizing computational complexity and network parameters while preserving performance. Existing state-of-the-art Efficient Image Super-Resolution methods are based on convolutional neural networks. Few attempts have been made with Mamba to harness its long-range modeling capability and efficient computational complexity, which have shown impressive performance on high-level vision tasks. In this paper, we propose DVMSR, a novel lightweight Image SR network that incorporates Vision Mamba and a distillation strategy. The network of DVMSR consists of three modules: feature extraction convolution, multiple stacked Residual State Space Blocks (RSSBs), and a reconstruction module. Specifically, the deep feature extraction module is composed of several residual state space blocks (RSSB), each of which has several Vision Mamba Moudles(ViMM) together with a residual connection. To achieve efficiency improvement while maintaining comparable performance, we employ a distillation strategy to the vision Mamba network for superior performance. Specifically, we leverage the rich representation knowledge of teacher network as additional supervision for the output of lightweight student networks. Extensive experiments have demonstrated that our proposed DVMSR can outperform state-of-the-art efficient SR methods in terms of model parameters while maintaining the performance of both PSNR and SSIM. The source code is available at https://github.com/nathan66666/DVMSR.git

eess.IV↗
arXiv2024

Value Approximation for Two-Player General-Sum Differential Games with State Constraints

Solving Hamilton-Jacobi-Isaacs (HJI) PDEs numerically enables equilibrial feedback control in two-player differential games, yet faces the curse of dimensionality (CoD). While physics-informed neural networks (PINNs) have shown promise in alleviating CoD in solving PDEs, vanilla PINNs fall short in learning discontinuous solutions due to their sampling nature, leading to poor safety performance of the resulting policies when values are discontinuous due to state or temporal logic constraints. In this study, we explore three potential solutions to this challenge: (1) a hybrid learning method that is guided by both supervisory equilibria and the HJI PDE, (2) a value-hardening method where a sequence of HJIs are solved with increasing Lipschitz constant on the constraint violation penalty, and (3) the epigraphical technique that lifts the value to a higher dimensional state space where it becomes continuous. Evaluations through 5D and 9D vehicle and 13D drone simulations reveal that the hybrid method outperforms others in terms of generalization and safety performance by taking advantage of both the supervisory equilibrium values and costates, and the low cost of PINN loss gradients.

cs.RO↗
arXiv2024

TFCounter:Polishing Gems for Training-Free Object Counting

Object counting is a challenging task with broad application prospects in security surveillance, traffic management, and disease diagnosis. Existing object counting methods face a tri-fold challenge: achieving superior performance, maintaining high generalizability, and minimizing annotation costs. We develop a novel training-free class-agnostic object counter, TFCounter, which is prompt-context-aware via the cascade of the essential elements in large-scale foundation models. This approach employs an iterative counting framework with a dual prompt system to recognize a broader spectrum of objects varying in shape, appearance, and size. Besides, it introduces an innovative context-aware similarity module incorporating background context to enhance accuracy within messy scenes. To demonstrate cross-domain generalizability, we collect a novel counting dataset named BIKE-1000, including exclusive 1000 images of shared bicycles from Meituan. Extensive experiments on FSC-147, CARPK, and BIKE-1000 datasets demonstrate that TFCounter outperforms existing leading training-free methods and exhibits competitive results compared to trained counterparts.

cs.CV↗
arXiv2024

SEAL: A Framework for Systematic Evaluation of Real-World Super-Resolution

Real-world Super-Resolution (Real-SR) methods focus on dealing with diverse real-world images and have attracted increasing attention in recent years. The key idea is to use a complex and high-order degradation model to mimic real-world degradations. Although they have achieved impressive results in various scenarios, they are faced with the obstacle of evaluation. Currently, these methods are only assessed by their average performance on a small set of degradation cases randomly selected from a large space, which fails to provide a comprehensive understanding of their overall performance and often yields inconsistent and potentially misleading results. To overcome the limitation in evaluation, we propose SEAL, a framework for systematic evaluation of real-SR. In particular, we cluster the extensive degradation space to create a set of representative degradation cases, which serves as a comprehensive test set. Next, we propose a coarse-to-fine evaluation protocol to measure the distributed and relative performance of real-SR methods on the test set. The protocol incorporates two new metrics: acceptance rate (AR) and relative performance ratio (RPR), derived from acceptance and excellence lines. Under SEAL, we benchmark existing real-SR methods, obtain new observations and insights into their performance, and develop a new strong baseline. We consider SEAL as the first step towards creating a comprehensive real-SR evaluation platform, which can promote the development of real-SR. The source code is available at https://github.com/XPixelGroup/SEAL

cs.CV↗
arXiv2023

Stochastic convergence of regularized solutions for backward heat conduction problems

In this paper, we study the stochastic convergence of regularized solutions for backward heat conduction problems. These problems are recognized as ill-posed due to the exponential decay of eigenvalues associated with the forward problems. We derive an error estimate for the least-squares regularized minimization problem within the framework of stochastic convergence. Our analysis reveals that the optimal error of the Tikhonov-type least-squares optimization problem depends on the noise level, the number of sensors, and the underlying ground truth. Moreover, we propose a self-adaptive algorithm to identify the optimal regularization parameter for the optimization problem without requiring knowledge of the noise level or any other prior information, which will be very practical in applications. We present numerical examples to demonstrate the accuracy and efficiency of our proposed method. These numerical results show that our method is efficient in solving backward heat conduction problems.

math.NA↗
arXiv2023

Solving Two-Player General-Sum Games Between Swarms

Hamilton-Jacobi-Isaacs (HJI) PDEs are the governing equations for the two-player general-sum games. Unlike Reinforcement Learning (RL) methods, which are data-intensive methods for learning value function, learning HJ PDEs provide a guaranteed convergence to the Nash Equilibrium value of the game when it exists. However, a caveat is that solving HJ PDEs becomes intractable when the state dimension increases. To circumvent the curse of dimensionality (CoD), physics-informed machine learning methods with supervision can be used and have been shown to be effective in generating equilibrial policies in two-player general-sum games. In this work, we extend the existing work on agent-level two-player games to a two-player swarm-level game, where two sub-swarms play a general-sum game. We consider the \textit{Kolmogorov forward equation} as the dynamic model for the evolution of the densities of the swarms. Results show that policies generated from the physics-informed neural network (PINN) result in a higher payoff than a Nash Double Deep Q-Network (Nash DDQN) agent and have comparable performance with numerical solvers.

cs.MA↗
arXiv2023

Beam Delivery and Beamstrahlung Considerations for Ultra-High Energy Linear Colliders

As part of the Snowmass'21 community planning excercise, the Advanced Accelerator Concepts (AAC) community proposed future linear colliders with center-of-mass energies up to 15 TeV and luminosities up to 50$\times10^{34}$ cm$^{-2}$s$^{-1}$ in a compact footprint. In addition to being compact, these machines must also be energy efficient. We identify two challenges that must be addressed in the design of these machines. First, the Beam Delivery System (BDS) must not add significant length to the accelerator complex. Second, beam parameters must be chosen to mitigate beamstrahlung effects and maximize the luminosity-per-power of the machine. In this paper, we review advances in plasma lens technology that will help to reduce the length of the BDS system and we detail new Particle-in-Cell simulation studies that will provide insight into beamstrahlung mitigation techniques. We apply our analysis to both $e^+e^-$ and $γγ$ colliders.

physics.acc-ph↗
arXiv2023

Approximating Discontinuous Nash Equilibrial Values of Two-Player General-Sum Differential Games

Finding Nash equilibrial policies for two-player differential games requires solving Hamilton-Jacobi-Isaacs (HJI) PDEs. Self-supervised learning has been used to approximate solutions of such PDEs while circumventing the curse of dimensionality. However, this method fails to learn discontinuous PDE solutions due to its sampling nature, leading to poor safety performance of the resulting controllers in robotics applications when player rewards are discontinuous. This paper investigates two potential solutions to this problem: a hybrid method that leverages both supervised Nash equilibria and the HJI PDE, and a value-hardening method where a sequence of HJIs are solved with a gradually hardening reward. We compare these solutions using the resulting generalization and safety performance in two vehicle interaction simulation studies with 5D and 9D state spaces, respectively. Results show that with informative supervision (e.g., collision and near-collision demonstrations) and the low cost of self-supervised learning, the hybrid method achieves better safety performance than the supervised, self-supervised, and value hardening approaches on equal computational budget. Value hardening fails to generalize in the higher-dimensional case without informative supervision. Lastly, we show that the neural activation function needs to be continuously differentiable for learning PDEs and its choice can be case dependent.

cs.LG↗
arXiv2023

Recon: Reducing Conflicting Gradients from the Root for Multi-Task Learning

A fundamental challenge for multi-task learning is that different tasks may conflict with each other when they are solved jointly, and a cause of this phenomenon is conflicting gradients during optimization. Recent works attempt to mitigate the influence of conflicting gradients by directly altering the gradients based on some criteria. However, our empirical study shows that ``gradient surgery'' cannot effectively reduce the occurrence of conflicting gradients. In this paper, we take a different approach to reduce conflicting gradients from the root. In essence, we investigate the task gradients w.r.t. each shared network layer, select the layers with high conflict scores, and turn them to task-specific layers. Our experiments show that such a simple approach can greatly reduce the occurrence of conflicting gradients in the remaining shared layers and achieve better performance, with only a slight increase in model parameters in many cases. Our approach can be easily applied to improve various state-of-the-art methods including gradient manipulation methods and branched architecture search methods. Given a network architecture (e.g., ResNet18), it only needs to search for the conflict layers once, and the network can be modified to be used with different methods on the same or even different datasets to gain performance improvement. The source code is available at https://github.com/moukamisama/Recon.

cs.LG↗
arXiv2023

Improving Responsiveness to Robots for Tacit Human-Robot Interaction via Implicit and Naturalistic Team Status Projection

Fluent human-human teaming is often characterized by tacit interaction without explicit communication. This is because explicit communication, such as language utterances and gestures, are inherently interruptive. On the other hand, tacit interaction requires team situation awareness (TSA) to facilitate, which often relies on explicit communication to maintain, creating a paradox. In this paper, we consider implicit and naturalistic team status projection for tacit human-robot interaction. Implicitness minimizes interruption while naturalness reduces cognitive demand, and they together improve responsiveness to robots. We introduce a novel process for such Team status Projection via virtual Shadows, or TPS. We compare our method with two baselines that use explicit projection for maintaining TSA. Results via human factors studies demonstrate that TPS provides a more fluent human-robot interaction experience by significantly improving human responsiveness to robots in tacit teaming scenarios, which suggests better TSA. Participants acknowledged robots implementing TPS as more acceptable as a teammate and favorable. Simultaneously, we demonstrate that TPS is comparable to, and sometimes better than, the best-performing baseline in maintaining accurate TSA

cs.RO↗
arXiv2023

A Soft-Bodied Aerial Robot for Collision Resilience and Contact-Reactive Perching

Current aerial robots demonstrate limited interaction capabilities in unstructured environments when compared with their biological counterparts. Some examples include their inability to tolerate collisions and to successfully land or perch on objects of unknown shapes, sizes, and texture. Efforts to include compliance have introduced designs that incorporate external mechanical impact protection at the cost of reduced agility and flight time due to the added weight. In this work, we propose and develop a light-weight, inflatable, soft-bodied aerial robot (SoBAR) that can pneumatically vary its body stiffness to achieve intrinsic collision resilience. Unlike the conventional rigid aerial robots, SoBAR successfully demonstrates its ability to repeatedly endure and recover from collisions in various directions, not only limited to in-plane ones. Furthermore, we exploit its capabilities to demonstrate perching where the 3D collision resilience helps in improving the perching success rates. We also augment SoBAR with a novel hybrid fabric-based, bistable (HFB) grasper that can utilize impact energies to perform contact-reactive grasping through rapid shape conforming abilities. We exhaustively study and offer insights into the collision resilience, impact absorption, and manipulation capabilities of SoBAR with the HFB grasper. Finally, we compare the performance of conventional aerial robots with the SoBAR through collision characterizations, grasping identifications, and experimental validations of collision resilience and perching in various scenarios and on differently shaped objects.

cs.RO↗
arXiv2022

Adaptive Attitude Control for Foldable Quadrotors

Recent quadrotors have transcended conventional designs, emphasizing more on foldable and reconfigurable bodies. The state of the art still focuses on the mechanical feasibility of such designs with limited discussions on the tracking performance of the vehicle during configuration switching. In this article, we first present a common framework to analyse the attitude errors of a folding quadrotor via the theory of switched systems. We then employ this framework to investigate the attitude tracking performance for two case scenarios - one with a conventional geometric controller for precisely known system dynamics; and second, with our proposed morphology-aware adaptive controller that accounts for any modeling uncertainties and disturbances. Finally, we cater to the desired switching requirements from our stability analysis by exploiting the trajectory planner to obtain superior tracking performance while switching. Simulation results are presented that validate the proposed control and planning framework for a foldable quadrotor's flight through a passageway.

eess.SY↗
arXiv2022

Configuration Tracking Control of a Multi-Segment Soft Robotic Arm Using a Cosserat Rod Model

Controlling soft continuum robotic arms is challenging due to their hyper-redundancy and dexterity. In this paper we demonstrate, for the first time, closed-loop control of the configuration space variables of a soft robotic arm, composed of independently controllable segments, using a Cosserat rod model of the robot and the distributed sensing and actuation capabilities of the segments. Our controller solves the inverse dynamic problem by simulating the Cosserat rod model in MATLAB using a computationally efficient numerical solution scheme, and it applies the computed control output to the actual robot in real time. The position and orientation of the tip of each segment are measured in real time, while the remaining unknown variables that are needed to solve the inverse dynamics are estimated simultaneously in the simulation. We implement the controller on a multi-segment silicone robotic arm with pneumatic actuation, using a motion capture system to measure the segments' positions and orientations. The controller is used to reshape the arm into configurations that are achieved through different combinations of bending and extension deformations in 3D space. The resulting tracking performance indicates the effectiveness of the controller and the accuracy of the simulated Cosserat rod model that is used to estimate the unmeasured variables.

cs.RO↗
arXiv2022

Invariant Extended Kalman Filtering for Human Motion Estimation with Imperfect Sensor Placement

This paper introduces a new invariant extended Kalman filter design that produces real-time state estimates and rapid error convergence for the estimation of the human body movement even in the presence of sensor misalignment and initial state estimation errors. The filter fuses the data returned by an inertial measurement unit (IMU) attached to the body (e.g., pelvis or chest) and a virtual measurement of zero stance-foot velocity (i.e., leg odometry). The key novelty of the proposed filter lies in that its process model meets the group affine property while the filter explicitly addresses the IMU placement error by formulating its stochastic process model as Brownian motions and incorporating the error in the leg odometry. Although the measurement model is imperfect (i.e., it does not possess an invariant observation form) and thus its linearization relies on the state estimate, experimental results demonstrate fast convergence of the proposed filter (within 0.2 seconds) during squatting motions even under significant IMU placement inaccuracy and initial estimation errors.

cs.RO↗
arXiv2022

Design and Evaluation of an Invariant Extended Kalman Filter for Trunk Motion Estimation with Sensor Misalignment

Understanding human motion is of critical importance for health monitoring and control of assistive robots, yet many human kinematic variables cannot be directly or accurately measured by wearable sensors. In recent years, invariant extended Kalman filtering (InEKF) has shown a great potential in nonlinear state estimation, but its applications to human poses new challenges, including imperfect placement of wearable sensors and inaccurate measurement models. To address these challenges, this paper proposes an augmented InEKF design which considers the misalignment of the inertial sensor at the trunk as part of the states and preserves the group affine property for the process model. Personalized lower-extremity forward kinematic models are built and employed as the measurement model for the augmented InEKF. Observability analysis for the new InEKF design is presented. The filter is evaluated with three subjects in squatting, rolling-foot walking, and ladder-climbing motions. Experimental results validate the superior performance of the proposed InEKF over the state-of-the-art InEKF. Improved accuracy and faster convergence in estimating the velocity and orientation of human, in all three motions, are achieved despite the significant initial estimation errors and the uncertainties associated with the forward kinematic measurement model.

cs.RO↗