arXiv subjects

Yixuan Wang

Publications and source records attributed to Yixuan Wang.

At least 145 records · Page 8Linked to original sources

arXiv2024

Blowup analysis for a quasi-exact 1D model of 3D Euler and Navier-Stokes

We study the singularity formation of a quasi-exact 1D model proposed by Hou-Li in \cite{hou2008dynamic}. This model is based on an approximation of the axisymmetric Navier-Stokes equations in the $r$ direction. The solution of the 1D model can be used to construct an exact solution of the original 3D Euler and Navier-Stokes equations if the initial angular velocity, angular vorticity, and angular stream function are linear in $r$. This model shares many intrinsic properties similar to those of the 3D Euler and Navier-Stokes equations. It captures the competition between advection and vortex stretching as in the 1D De Gregorio \cite{de1990one, de1996partial} model. We show that the inviscid model with weakened advection and smooth initial data or the original 1D model with Hölder continuous data develops a self-similar blowup. We also show that the viscous model with weakened advection and smooth initial data develops a finite time blowup. To obtain sharp estimates for the nonlocal terms, we perform an exact computation for the low-frequency Fourier modes and extract damping in leading order estimates for the high-frequency modes using singularly weighted norms in the energy estimates. The analysis for the viscous case is more subtle since the viscous terms produce some instability if we just use singular weights. We establish the blowup analysis for the viscous model by carefully designing an energy norm that combines a singularly weighted energy norm and a sum of high-order Sobolev norms.

math.AP↗

arXiv2023

Single-Cell RNA-seq Synthesis with Latent Diffusion Model

The single-cell RNA sequencing (scRNA-seq) technology enables researchers to study complex biological systems and diseases with high resolution. The central challenge is synthesizing enough scRNA-seq samples; insufficient samples can impede downstream analysis and reproducibility. While various methods have been attempted in past research, the resulting scRNA-seq samples were often of poor quality or limited in terms of useful specific cell subpopulations. To address these issues, we propose a novel method called Single-Cell Latent Diffusion (SCLD) based on the Diffusion Model. This method is capable of synthesizing large-scale, high-quality scRNA-seq samples, including both 'holistic' or targeted specific cellular subpopulations within a unified framework. A pre-guidance mechanism is designed for synthesizing specific cellular subpopulations, while a post-guidance mechanism aims to enhance the quality of scRNA-seq samples. The SCLD can synthesize large-scale and high-quality scRNA-seq samples for various downstream tasks. Our experimental results demonstrate state-of-the-art performance in cell classification and data distribution distances when evaluated on two scRNA-seq benchmarks. Additionally, visualization experiments show the SCLD's capability in synthesizing specific cellular subpopulations.

q-bio.GN↗

arXiv2023

State-Wise Safe Reinforcement Learning With Pixel Observations

In the context of safe exploration, Reinforcement Learning (RL) has long grappled with the challenges of balancing the tradeoff between maximizing rewards and minimizing safety violations, particularly in complex environments with contact-rich or non-smooth dynamics, and when dealing with high-dimensional pixel observations. Furthermore, incorporating state-wise safety constraints in the exploration and learning process, where the agent must avoid unsafe regions without prior knowledge, adds another layer of complexity. In this paper, we propose a novel pixel-observation safe RL algorithm that efficiently encodes state-wise safety constraints with unknown hazard regions through a newly introduced latent barrier-like function learning mechanism. As a joint learning framework, our approach begins by constructing a latent dynamics model with low-dimensional latent spaces derived from pixel observations. We then build and learn a latent barrier-like function on top of the latent dynamics and conduct policy optimization simultaneously, thereby improving both safety and the total expected return. Experimental evaluations on the safety-gym benchmark suite demonstrate that our proposed method significantly reduces safety violations throughout the training process, and demonstrates faster safety convergence compared to existing methods while achieving competitive results in reward return.

cs.LG↗

arXiv2023

Evaluating Trustworthiness of AI-Enabled Decision Support Systems: Validation of the Multisource AI Scorecard Table (MAST)

The Multisource AI Scorecard Table (MAST) is a checklist tool based on analytic tradecraft standards to inform the design and evaluation of trustworthy AI systems. In this study, we evaluate whether MAST is associated with people's trust perceptions in AI-enabled decision support systems (AI-DSSs). Evaluating trust in AI-DSSs poses challenges to researchers and practitioners. These challenges include identifying the components, capabilities, and potential of these systems, many of which are based on the complex deep learning algorithms that drive DSS performance and preclude complete manual inspection. We developed two interactive, AI-DSS test environments using the MAST criteria. One emulated an identity verification task in security screening, and another emulated a text summarization system to aid in an investigative reporting task. Each test environment had one version designed to match low-MAST ratings, and another designed to match high-MAST ratings, with the hypothesis that MAST ratings would be positively related to the trust ratings of these systems. A total of 177 subject matter experts were recruited to interact with and evaluate these systems. Results generally show higher MAST ratings for the high-MAST conditions compared to the low-MAST groups, and that measures of trust perception are highly correlated with the MAST ratings. We conclude that MAST can be a useful tool for designing and evaluating systems that will engender high trust perceptions, including AI-DSS that may be used to support visual screening and text summarization tasks. However, higher MAST ratings may not translate to higher joint performance.

cs.CY↗

arXiv2023

Multi-view learning for automatic classification of multi-wavelength auroral images

Auroral classification plays a crucial role in polar research. However, current auroral classification studies are predominantly based on images taken at a single wavelength, typically 557.7 nm. Images obtained at other wavelengths have been comparatively overlooked, and the integration of information from multiple wavelengths remains an underexplored area. This limitation results in low classification rates for complex auroral patterns. Furthermore, these studies, whether employing traditional machine learning or deep learning approaches, have not achieved a satisfactory trade-off between accuracy and speed. To address these challenges, this paper proposes a lightweight auroral multi-wavelength fusion classification network, MLCNet, based on a multi-view approach. Firstly, we develop a lightweight feature extraction backbone, called LCTNet, to improve the classification rate and cope with the increasing amount of auroral observation data. Secondly, considering the existence of multi-scale spatial structures in auroras, we design a novel multi-scale reconstructed feature module named MSRM. Finally, to highlight the discriminative information between auroral classes, we propose a lightweight attention feature enhancement module called LAFE. The proposed method is validated using observational data from the Arctic Yellow River Station during 2003-2004. Experimental results demonstrate that the fusion of multi-wavelength information effectively improves the auroral classification performance. In particular, our approach achieves state-of-the-art classification accuracy compared to previous auroral classification studies, and superior results in terms of accuracy and computational efficiency compared to existing multi-view methods.

cs.CV↗

arXiv2023

Predicting Object Interactions with Behavior Primitives: An Application in Stowing Tasks

Stowing, the task of placing objects in cluttered shelves or bins, is a common task in warehouse and manufacturing operations. However, this task is still predominantly carried out by human workers as stowing is challenging to automate due to the complex multi-object interactions and long-horizon nature of the task. Previous works typically involve extensive data collection and costly human labeling of semantic priors across diverse object categories. This paper presents a method to learn a generalizable robot stowing policy from predictive model of object interactions and a single demonstration with behavior primitives. We propose a novel framework that utilizes Graph Neural Networks to predict object interactions within the parameter space of behavioral primitives. We further employ primitive-augmented trajectory optimization to search the parameters of a predefined library of heterogeneous behavioral primitives to instantiate the control action. Our framework enables robots to proficiently execute long-horizon stowing tasks with a few keyframes (3-4) from a single demonstration. Despite being solely trained in a simulation, our framework demonstrates remarkable generalization capabilities. It efficiently adapts to a broad spectrum of real-world conditions, including various shelf widths, fluctuating quantities of objects, and objects with diverse attributes such as sizes and shapes.

cs.RO↗

arXiv2023

Safety-Assured Speculative Planning with Adaptive Prediction

Recently significant progress has been made in vehicle prediction and planning algorithms for autonomous driving. However, it remains quite challenging for an autonomous vehicle to plan its trajectory in complex scenarios when it is difficult to accurately predict its surrounding vehicles' behaviors and trajectories. In this work, to maximize performance while ensuring safety, we propose a novel speculative planning framework based on a prediction-planning interface that quantifies both the behavior-level and trajectory-level uncertainties of surrounding vehicles. Our framework leverages recent prediction algorithms that can provide one or more possible behaviors and trajectories of the surrounding vehicles with probability estimation. It adapts those predictions based on the latest system states and traffic environment, and conducts planning to maximize the expected reward of the ego vehicle by considering the probabilistic predictions of all scenarios and ensure system safety by ruling out actions that may be unsafe in worst case. We demonstrate the effectiveness of our approach in improving system performance and ensuring system safety over other baseline methods, via extensive simulations in SUMO on a challenging multi-lane highway lane-changing case study.

cs.RO↗

arXiv2023

Dynamic-Resolution Model Learning for Object Pile Manipulation

Dynamics models learned from visual observations have shown to be effective in various robotic manipulation tasks. One of the key questions for learning such dynamics models is what scene representation to use. Prior works typically assume representation at a fixed dimension or resolution, which may be inefficient for simple tasks and ineffective for more complicated tasks. In this work, we investigate how to learn dynamic and adaptive representations at different levels of abstraction to achieve the optimal trade-off between efficiency and effectiveness. Specifically, we construct dynamic-resolution particle representations of the environment and learn a unified dynamics model using graph neural networks (GNNs) that allows continuous selection of the abstraction level. During test time, the agent can adaptively determine the optimal resolution at each model-predictive control (MPC) step. We evaluate our method in object pile manipulation, a task we commonly encounter in cooking, agriculture, manufacturing, and pharmaceutical applications. Through comprehensive evaluations both in the simulation and the real world, we show that our method achieves significantly better performance than state-of-the-art fixed-resolution baselines at the gathering, sorting, and redistribution of granular object piles made with various instances like coffee beans, almonds, corn, etc.

cs.RO↗

arXiv2023

Enforcing Hard Constraints with Soft Barriers: Safe Reinforcement Learning in Unknown Stochastic Environments

It is quite challenging to ensure the safety of reinforcement learning (RL) agents in an unknown and stochastic environment under hard constraints that require the system state not to reach certain specified unsafe regions. Many popular safe RL methods such as those based on the Constrained Markov Decision Process (CMDP) paradigm formulate safety violations in a cost function and try to constrain the expectation of cumulative cost under a threshold. However, it is often difficult to effectively capture and enforce hard reachability-based safety constraints indirectly with such constraints on safety violation costs. In this work, we leverage the notion of barrier function to explicitly encode the hard safety constraints, and given that the environment is unknown, relax them to our design of \emph{generative-model-based soft barrier functions}. Based on such soft barriers, we propose a safe RL approach that can jointly learn the environment and optimize the control policy, while effectively avoiding unsafe regions with safety probability optimization. Experiments on a set of examples demonstrate that our approach can effectively enforce hard safety constraints and significantly outperform CMDP-based baseline methods in system safe rate measured via simulations.

eess.SY↗

arXiv2023

CSED: A Chinese Semantic Error Diagnosis Corpus

Recently, much Chinese text error correction work has focused on Chinese Spelling Check (CSC) and Chinese Grammatical Error Diagnosis (CGED). In contrast, little attention has been paid to the complicated problem of Chinese Semantic Error Diagnosis (CSED), which lacks relevant datasets. The study of semantic errors is important because they are very common and may lead to syntactic irregularities or even problems of comprehension. To investigate this, we build the CSED corpus, which includes two datasets. The one is for the CSED-Recognition (CSED-R) task. The other is for the CSED-Correction (CSED-C) task. Our annotation guarantees high-quality data through quality assurance mechanisms. Our experiments show that powerful pre-trained models perform poorly on this corpus. We also find that the CSED task is challenging, as evidenced by the fact that even humans receive a low score. This paper proposes syntax-aware models to specifically adapt to the CSED task. The experimental results show that the introduction of the syntax-aware approach is meaningful.

cs.CL↗

arXiv2023

POLAR-Express: Efficient and Precise Formal Reachability Analysis of Neural-Network Controlled Systems

Neural networks (NNs) playing the role of controllers have demonstrated impressive empirical performances on challenging control problems. However, the potential adoption of NN controllers in real-life applications also gives rise to a growing concern over the safety of these neural-network controlled systems (NNCSs), especially when used in safety-critical applications. In this work, we present POLAR-Express, an efficient and precise formal reachability analysis tool for verifying the safety of NNCSs. POLAR-Express uses Taylor model arithmetic to propagate Taylor models (TMs) across a neural network layer-by-layer to compute an overapproximation of the neural-network function. It can be applied to analyze any feed-forward neural network with continuous activation functions. We also present a novel approach to propagate TMs more efficiently and precisely across ReLU activation functions. In addition, POLAR-Express provides parallel computation support for the layer-by-layer propagation of TMs, thus significantly improving the efficiency and scalability over its earlier prototype POLAR. Across the comparison with six other state-of-the-art tools on a diverse set of benchmarks, POLAR-Express achieves the best verification efficiency and tightness in the reachable set analysis.

eess.SY↗

arXiv2023

Joint Differentiable Optimization and Verification for Certified Reinforcement Learning

In model-based reinforcement learning for safety-critical control systems, it is important to formally certify system properties (e.g., safety, stability) under the learned controller. However, as existing methods typically apply formal verification \emph{after} the controller has been learned, it is sometimes difficult to obtain any certificate, even after many iterations between learning and verification. To address this challenge, we propose a framework that jointly conducts reinforcement learning and formal verification by formulating and solving a novel bilevel optimization problem, which is differentiable by the gradients from the value function and certificates. Experiments on a variety of examples demonstrate the significant advantages of our framework over the model-based stochastic value gradient (SVG) method and the model-free proximal policy optimization (PPO) method in finding feasible controllers with barrier functions and Lyapunov functions that ensure system safety and stability.

cs.LG↗

arXiv2023

Cross-hospital Sepsis Early Detection via Semi-supervised Optimal Transport with Self-paced Ensemble

Leveraging machine learning techniques for Sepsis early detection and diagnosis has attracted increasing interest in recent years. However, most existing methods require a large amount of labeled training data, which may not be available for a target hospital that deploys a new Sepsis detection system. More seriously, as treated patients are diversified between hospitals, directly applying a model trained on other hospitals may not achieve good performance for the target hospital. To address this issue, we propose a novel semi-supervised transfer learning framework based on optimal transport theory and self-paced ensemble for Sepsis early detection, called SPSSOT, which can efficiently transfer knowledge from the source hospital (with rich labeled data) to the target hospital (with scarce labeled data). Specifically, SPSSOT incorporates a new optimal transport-based semi-supervised domain adaptation component that can effectively exploit all the unlabeled data in the target hospital. Moreover, self-paced ensemble is adapted in SPSSOT to alleviate the class imbalance issue during transfer learning. In a nutshell, SPSSOT is an end-to-end transfer learning method that automatically selects suitable samples from two domains (hospitals) respectively and aligns their feature spaces. Extensive experiments on two open clinical datasets, MIMIC-III and Challenge, demonstrate that SPSSOT outperforms state-of-the-art transfer learning methods by improving 1-3% of AUC.

cs.LG↗

arXiv2023

Exponentially Convergent Multiscale Finite Element Method

We provide a concise review of the exponentially convergent multiscale finite element method (ExpMsFEM) for efficient model reduction of PDEs in heterogeneous media without scale separation and in high-frequency wave propagation. ExpMsFEM is built on the non-overlapped domain decomposition in the classical MsFEM while enriching the approximation space systematically to achieve a nearly exponential convergence rate regarding the number of basis functions. Unlike most generalizations of MsFEM in the literature, ExpMsFEM does not rely on any partition of unity functions. In general, it is necessary to use function representations dependent on the right-hand side to break the algebraic Kolmogorov $n$-width barrier to achieve exponential convergence. Indeed, there are online and offline parts in the function representation provided by ExpMsFEM. The online part depends on the right-hand side locally and can be computed in parallel efficiently. The offline part contains basis functions that are used in the Galerkin method to assemble the stiffness matrix; they are all independent of the right-hand side, so the stiffness matrix can be used repeatedly in multi-query scenarios.

math.NA↗

arXiv2022

POLAR: A Polynomial Arithmetic Framework for Verifying Neural-Network Controlled Systems

We present POLAR, a polynomial arithmetic-based framework for efficient bounded-time reachability analysis of neural-network controlled systems (NNCSs). Existing approaches that leverage the standard Taylor Model (TM) arithmetic for approximating the neural-network controller cannot deal with non-differentiable activation functions and suffer from rapid explosion of the remainder when propagating the TMs. POLAR overcomes these shortcomings by integrating TM arithmetic with \textbf{Bernstein B{é}zier Form} and \textbf{symbolic remainder}. The former enables TM propagation across non-differentiable activation functions and local refinement of TMs, and the latter reduces error accumulation in the TM remainder for linear mappings in the network. Experimental results show that POLAR significantly outperforms the current state-of-the-art tools in terms of both efficiency and tightness of the reachable set overapproximation. The source code can be found in https://github.com/ChaoHuang2018/POLAR_Tool

eess.SY↗

arXiv2022

CLIP2GAN: Towards Bridging Text with the Latent Space of GANs

In this work, we are dedicated to text-guided image generation and propose a novel framework, i.e., CLIP2GAN, by leveraging CLIP model and StyleGAN. The key idea of our CLIP2GAN is to bridge the output feature embedding space of CLIP and the input latent space of StyleGAN, which is realized by introducing a mapping network. In the training stage, we encode an image with CLIP and map the output feature to a latent code, which is further used to reconstruct the image. In this way, the mapping network is optimized in a self-supervised learning way. In the inference stage, since CLIP can embed both image and text into a shared feature embedding space, we replace CLIP image encoder in the training architecture with CLIP text encoder, while keeping the following mapping network as well as StyleGAN model. As a result, we can flexibly input a text description to generate an image. Moreover, by simply adding mapped text features of an attribute to a mapped CLIP image feature, we can effectively edit the attribute to the image. Extensive experiments demonstrate the superior performance of our proposed CLIP2GAN compared to previous methods.

cs.CV↗

arXiv2022

Exponentially convergent multiscale methods for high frequency heterogeneous Helmholtz equations

In this paper, we present a multiscale framework for solving the Helmholtz equation in heterogeneous media without scale separation and in the high frequency regime where the wavenumber $k$ can be large. The main innovation is that our methods achieve a nearly exponential rate of convergence with respect to the computational degrees of freedom, using a coarse grid of mesh size $O(1/k)$ without suffering from the well-known pollution effect. The key idea is a non-overlapped domain decomposition and its associated coarse-fine scale decomposition of the solution space that adapts to the media property and wavenumber; this decomposition is inspired by the multiscale finite element method (MsFEM). We show that the coarse part is of \textit{low complexity} in the sense that it can be approximated with a nearly exponential rate of convergence via local basis functions, due to the compactness of a restriction operator that maps Helmholtz-harmonic functions to their interpolation residues on edges, while the fine part is \textit{local} such that it can be computed efficiently using the local information of the right hand side. The combination of the two parts yields the overall nearly exponential rate of convergence of our multiscale method. Our method draws many connections to multiscale methods in the literature, which we will comment in detail. We demonstrate the effectiveness of our methods theoretically and numerically; an exponential rate of convergence is consistently observed and confirmed. In addition, we observe the robustness of our methods regarding the high contrast in the media numerically. We specifically focus on 2D problems in our exposition since the geometry of non-overlapped domain decomposition is simplest to explain in such cases; generalizations to 3D will be outlined at the end.

math.NA↗

arXiv2022

A Tool for Neural Network Global Robustness Certification and Training

With the increment of interest in leveraging machine learning technology in safety-critical systems, the robustness of neural networks under external disturbance receives more and more concerns. Global robustness is a robustness property defined on the entire input domain. And a certified globally robust network can ensure its robustness on any possible network input. However, the state-of-the-art global robustness certification algorithm can only certify networks with at most several thousand neurons. In this paper, we propose the GPU-supported global robustness certification framework GROCET, which is more efficient than the previous optimization-based certification approach. Moreover, GROCET provides differentiable global robustness, which is leveraged in the training of globally robust neural networks.

cs.LG↗