SearcharxivSearch

arXiv subjects

Huajun Gong

Publications and source records attributed to Huajun Gong.

13 recordsLinked to original sources

AADS: Augmented Autonomous Driving Simulation using Data-driven Algorithms

Simulation systems have become an essential component in the development and validation of autonomous driving technologies. The prevailing state-of-the-art approach for simulation is to use game engines or high-fidelity computer graphics (CG) models to create driving scenarios. However, creating CG models and vehicle movements (e.g., the assets for simulation) remains a manual task that can be costly and time-consuming. In addition, the fidelity of CG images still lacks the richness and authenticity of real-world images and using these images for training leads to degraded performance. In this paper we present a novel approach to address these issues: Augmented Autonomous Driving Simulation (AADS). Our formulation augments real-world pictures with a simulated traffic flow to create photo-realistic simulation images and renderings. More specifically, we use LiDAR and cameras to scan street scenes. From the acquired trajectory data, we generate highly plausible traffic flows for cars and pedestrians and compose them into the background. The composite images can be re-synthesized with different viewpoints and sensor models. The resulting images are photo-realistic, fully annotated, and ready for end-to-end training and testing of autonomous driving systems from perception to planning. We explain our system design and validate our algorithms with a number of autonomous driving tasks from detection to segmentation and predictions. Compared to traditional approaches, our method offers unmatched scalability and realism. Scalability is particularly important for AD simulation and we believe the complexity and diversity of the real world cannot be realistically captured in a virtual environment. Our augmented approach combines the flexibility in a virtual environment (e.g., vehicle movements) with the richness of the real world to allow effective simulation of anywhere on earth.

cs.CV

Local well-posedness of isentropic compressible Navier-Stokes equations with vacuum

In this paper, the local well-posedness of strong solutions to the Cauchy problem of the isentropic compressible Navier-Stokes equations is proved with the initial date being allowed to have vacuum. The main contribution of this paper is that the well-posedness is established without assuming any compatibility condition on the initial data, which was widely used before in many literatures concerning the well-posedness of compressible Navier-Stokes equations in the presence of vacuum.

math.AP

A priori estimates and Blow-up behavior for solutions of $-Q_{N}u=Ve^{u}$ in bounded domain in $\mathbb{R}^{N}$

Let $Q_{N}$ be $N$-anisotropic Laplacian operator, which contains the ordinary Laplacian operator, $N$-Laplacian operator and anisotropic Laplacian operator. In this paper, we firstly obtain the properties for $Q_{N}$, which contain the weak maximal principle, the comparison principle and the mean value property. Then a priori estimates and blow-up analysis for solutions of $-Q_{N}u=Ve^{u}$ in bounded domain in $\mathbb{R}^{N}$, $N\geq 2$ are established. Finally, the behavior of sole blow-up point is further considered.

math.AP

Multilinear fractional integral operators on non-homogeneous metric measure spaces

Let $(X,d,μ)$ be a non-homogeneous metric measure space satisfying both the geometrically doubling and the upper doubling measure conditions. In this paper, the boundedness of multilinear fractional integral operator in this setting is proved. Via a sharp maximal operator, the boundedness of commutators generated by multilinear fractional integral operator with $RBMO(μ)$ function on non-homogeneous metric measure spaces in Lebesgue spaces is obtained.

math.CA

Local well-posedness of strong solutions to density-dependent liquid crystal system

In this paper, we study the Cauchy problem to the density-dependent liquid crystal system in $\mathbb R^3$. We establish the local existence and uniqueness of strong solutions to this system. In order to overcome the difficulties caused by the high order coupling terms, a biharmonic regularization of the system, as an auxiliary system, is introduced, and we make full use of the intrinsic cancellation properties between the high order coupling terms.

math.AP

Topological pressure dimension for almost additive potentials

This paper is devoted to the study of the topological pressure dimension for almost additive sequences, which is an extension of topological entropy dimension. We investigate fundamental properties of the topological pressure dimension for almost additive sequences. In particular, we study the relationships among different types of topological pressure dimension and identifies an inequality relating them. Also, we show that the topological pressure dimension is always equal to or greater than 1 for certain special almost additive sequence.

math.DS

Commutators of multilinear singular integral operators on non-homogeneous metric measure spaces

Let $(X,d,μ)$ be a metric measure space satisfying both the geometrically doubling and the upper doubling measure conditions, which is called non-homogeneous metric measure space. In this paper, via a sharp maximal operator, the boundedness of commutators generated by multilinear singular integral with $RBMO(μ)$ function on non-homogeneous metric measure spaces in $m$-multiple Lebesgue spaces is obtained.

math.FA

Global Strong Solutions to Incompressible Ericksen-Leslie System in $\mathbb R^3$

In this paper, we consider the Cauchy problem to the Ericksen-Leslie system of liquid crystals in $\mathbb R^3$. Global well-posedness of strong solutions are obtained under the condition that the product of $\|u_0\|_2+\|\nabla d_0\|_2$ and $\|\nabla u_0\|_2+\|\nabla^2d_0\|_2$ is suitably small. This result can be viewed as a supplement to the local existence and blow up criteria discussed in \cite{Hong1}.

math.AP

Global Existence of Strong Solutions to Incompressible MHD

We establish the global existence and uniqueness of strong solutions to the initial boundary value problem for incompressible MHD equations in a bounded smooth domain of three spatial dimensions with initial density being allowed to have vacuum, in particular, the initial density can vanish in a set of positive Lebessgue measure. More precisely, under the assumption that the production of the quantities $|\sqrtρ_0u_0|_{L^2(Ω)}^2+|H_0|_{L^2(Ω)}^2$ and $|\nabla u_0|_{L^2(Ω)}^2+|\nabla H_0|_{L^2(Ω)}^2$ is suitably small, with the smallness depending only on the bound of the initial density and the domain, we prove that there is a unique strong solution to the Dirichlet problem of the incompressible MHD system.

math.AP

Boundary regularity of stationary biharmonic maps

We consider the Dirichlet problem for stationary biharmonic maps $u$ from a bounded, smooth domain $Ω\subset\mathbb R^n$ ($n\ge 5$) to a compact, smooth Riemannian manifold $N\subset\mathbb R^l$ without boundary. For any smooth boundary data, we show that if, in addition, $u$ satisfies a certain boundary monotonicity inequality, then there exists a closed subset $Σ\subset\barΩ$, with $H^{n-4}(Σ)=0$, such that $u\in C^\infty(\barΩ\setminusΣ, N)$.

math.AP