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Zhilin Lin

Publications and source records attributed to Zhilin Lin.

12 recordsLinked to original sources

Revealing the Challenges of Sim-to-Real Transfer in Model-Based Reinforcement Learning via Latent Space Modeling

Reinforcement learning (RL) is playing an increasingly important role in fields such as robotic control and autonomous driving. However, the gap between simulation and the real environment remains a major obstacle to the practical deployment of RL. Agents trained in simulators often struggle to maintain performance when transferred to real-world physical environments. In this paper, we propose a latent space based approach to analyze the impact of simulation on real-world policy improvement in model-based settings. As a natural extension of model-based methods, our approach enables an intuitive observation of the challenges faced by model-based methods in sim-to-real transfer. Experiments conducted in the MuJoCo environment evaluate the performance of our method in both measuring and mitigating the sim-to-real gap. The experiments also highlight the various challenges that remain in overcoming the sim-to-real gap, especially for model-based methods.

cs.LG

Low-Rank Similarity Mining for Multimodal Dataset Distillation

Though dataset distillation has witnessed rapid development in recent years, the distillation of multimodal data, e.g., image-text pairs, poses unique and under-explored challenges. Unlike unimodal data, image-text contrastive learning (ITC) data lack inherent categorization and should instead place greater emphasis on modality correspondence. In this work, we propose Low-Rank Similarity Mining (LoRS) for multimodal dataset distillation, that concurrently distills a ground truth similarity matrix with image-text pairs, and leverages low-rank factorization for efficiency and scalability. The proposed approach brings significant improvement to the existing algorithms, marking a significant contribution to the field of visual-language dataset distillation. We advocate adopting LoRS as a foundational synthetic data setup for image-text dataset distillation. Our code is available at https://github.com/silicx/LoRS_Distill.

cs.LG

Stability for the 2-D plane Poiseuille flow in finite channel

In this paper, we study the stability for 2-D plane Poiseuille flow $(1-y^2,0)$ in a channel $\mathbb{T}\times (-1,1)$ with Navier-slip boundary condition. We prove that if the initial perturbation for velocity field $u_0$ satisfies that $\|u_0\|_{H^{\frac{7}{2}+}} \leq \epsilon_1 \nu^{2/3}$ for some suitable small $0<\epsilon_1 \ll 1$ independent of viscosity coefficient $\nu$, then the solution to the Navier-Stokes equations is global in time and does not transit from the plane Poiseuille flow. This result improves the result of \cite{DL1} from $3/4$ to $2/3$.

math.AP

Well-posedness of Navier-Stokes/Cahn-Hilliard equations modeling the dynamics of contact line in a channel

In this paper, we study the contact line problem in a channel. Precisely, we consider the incompressible Navier-Stokes/Cahn-Hilliard system with eneralized Navier boundary condition and relaxation boundary condition in a channel, which is the phase field model for the moving contact line problem in fluid mechanics. We establish the existence and uniqueness of local-in-time strong solution to this initial boundary value problem in 2D. To our knowledge, this is the first result to give the local-in-time well-posedness of Navier-Stokes/Cahn-Hilliard system with generalized Navier boundary condition and relaxation boundary condition. This result provides a rigorous mathematical analysis to confirm that the physical and numerical results by Qian-Wang-Sheng [Phys. Rev. E 68 (2003), 016306, 1-15; J. Fluid Mech. 564 (2006), 333-360] are well-posed and reasonable.

math.AP

Nonlinear stability for 3-D plane Poiseuille flow in a finite channel

In this paper, we study the nonlinear stability for the 3-D plane Poiseuille flow $(1-y^2,0,0)$ at high Reynolds number $Re$ in a finite channel $\mathbb{T}\times [-1,1 ]\times \mathbb{T}$ with non-slip boundary condition. We prove that if the initial velocity $v_0$ satisfies $\|v_0-(1-y^2,0,0)\|_{H^{4}}\leq c_0 Re^{-\frac{7}{4}}$ for some $c_0>0$ independent of $Re$, then the solution of 3-D Naiver-Stokes equations is global in time and does not transit away from the plane Poiseuille flow. To our knowledge, this is the first nonlinear stability result for the 3-D plane Poiseuille flow and the transition threshold is accordant with the numerical result by Lundbladh et al. \cite{LHR}.

math.AP

Global-in-$x$ stability of Prandtl layer expansions for steady magnetohydrodynamics flows over a moving plate

In this paper, we obtain the global-in-$x$ Sobolev stability of Prandtl layer expansions for 2-D steady incompressible MHD flows with shear outer ideal MHD flows $(1,0,\sigma,0)$ ($\sigma\geq 0$) on a moving plate. It is worth noticing that in the Sobolev sense, the degeneracy of the tangential magnetic field in our result is allowed, which is much different from both the unsteady case in [25,26,27] and the steady case in [3,4].

math.AP

Stability of the boundary layer expansion for the 3D plane parallel MHD flow

In this paper, we establish the mathematical validity of the Prandtl boundary layer theory for a class of nonlinear plane parallel flows of viscous incompressible magnetohydrodynamic (MHD) flow with no-slip boundary condition of velocity and perfectly conducting wall for magnetic fields. The convergence is shown under various Sobolev norms, including the physically important space-time uniform norm $L^\infty(H^1)$. In addition, the similar convergence results are also obtained under the case with uniform magnetic fields. This implies the stabilizing effects of magnetic fields. Besides, the higher-order expansion is also considered.

math.AP

Validity of Prandtl layer theory for steady magnetohydrodynamics over a moving plate with nonshear outer ideal MHD flows

In this paper, we validate the boundary layer theory for 2D steady viscous incompressible magnetohydrodynamics (MHD) equations in a domain $\{(X, Y)\in[0, L]\times\mathbb{R}_+\}$ under the assumption of a moving boundary at $\{Y=0\}$. The validity of the boundary layer expansion and the convergence rates are established in Sobolev sense. We extend the results for the case with the shear outer ideal MHD flows [3] to the case of the nonshear flows.

math.AP

Enhanced dissipation and transition threshold for the 2-D plane Poiseuille flow via resolvent estimate

In this paper, we study the transition threshold problem for the 2-D Navier-Stokes equations around the Poiseuille flow $(1-y^2,0)$ in a finite channel with Navier-slip boundary condition. Based on the resolvent estimates for the linearized operator around the Poiseuille flow, we first establish the enhanced dissipation estimates for the linearized Navier-Stokes equations with a sharp decay rate $e^{-c\sqrtνt}$. As an application, we prove that if the initial perturbation of vortiticy satisfies $$\|ω_0\|_{L^2}\leq c_0ν^{\frac{3}{4}},$$ for some small constant $c_0>0$ independent of the viscosity $ν$, then the solution dose not transition away from the Poiseuille flow for any time.

math.AP

Stability for two-dimensional plane Couette flow to the incompressible Navier-Stokes equations with Navier boundary conditions

This paper concerns with the stability of the plane Couette flow resulted from the motions of boundaries that the top boundary $Σ_1$ and the bottom one $Σ_0$ move with constant velocities $(a,0)$ and $(b,0)$, respectively. If one imposes Dirichlet boundary condition on the top boundary and Navier boundary condition on the bottom boundary with Navier coefficient $α$, there always exists a plane Couette flow which is exponentially stable for nonnegative $α$ and any positive viscosity $μ$ and any $a, b \in \mathbb{R}$, or, for $α<0$ but viscosity $μ$ and the moving velocities of boundaries $(a,0), (b,0)$ satisfy some conditions stated in Theorem 1.1. However, if we impose Navier boundary conditions on both boundaries with Navier coefficients $α_0$ and $α_1$, then it is proved that there also exists a plane Couette flow (including constant flow or trivial steady states) which is exponentially stable provided that any one of two conditions on $α_0,α_1$, $a, b$ and $μ$ in Theorem 1.2 holds. Therefore, the known results for the stability of incompressible Couette flow to no-slip (Dirichlet) boundary value problems are extended to the Navier boundary value problems.

math.AP

Verification of Prandtl boundary layer ansatz for the steady electrically conducting fluids with a moving physical boundary

In this paper, we are concerned with the validity of Prandtl boundary layer expansion for the solutions to two dimensional (2D) steady viscous incompressible magnetohydrodynamics (MHD) equations in a domain $\{(X, Y)\in[0, L]\times\mathbb{R}_+\}$ with a moving flat boundary $\{Y=0\}$. As a direct consequence, even though there exist strong boundary layers, the inviscid type limit is still established for the solutions of 2D steady viscous incompressible MHD equations in Sobolev spaces provided that the following three assumptions hold: the hydrodynamics and magnetic Reynolds numbers take the same order in term of the reciprocal of a small parameter $ε$, the tangential component of the magnetic field does not degenerate near the boundary and the ratio of the strength of tangential component of magnetic field and tangential component of velocity is suitably small. And the error terms are estimated in $L^\infty$ sense.

math.AP

Boundary layer for 3D plane parallel channel flows of nonhomogeneous incompressible Navier-Stokes equations

In this paper, we establish the mathematical validity of the Prandtl boundary layer theory for a class of nonlinear plane parallel flow of nonhomogeneous incompressible Navier-Stokes equations. The convergence for the density and velocity are shown under various Sobolev norms, including the physically important space-time uniform norm, as well as the $L^\infty(H^1)$ norm. It is mentioned that the mathematical validity of the Prandtl boundary layer theory for nonlinear plane parallel flow is generalized to the nonhomogeneous case.

math.AP