arXiv subjects

Jianing Guo

Publications and source records attributed to Jianing Guo.

4 recordsLinked to original sources

arXiv2026

An a Posteriori Error Estimator for $C^0$ IPG Approximation of Multiple and Clustered Eigenvalues of the Biharmonic Operator

In this paper, based on the $C^0$ interior penalty Galerkin ($C^0$IPG) discretization, we propose and analyze an a posteriori error estimator for eigenfunctions associated with multiple and clustered eigenvalues of the biharmonic operator. The proposed estimator may capture the local singularities of the target eigenfunctions efficiently and play an important role in adaptive procedures. We develop a rigorous cluster-projection-based analysis and introduce an auxiliary theoretical error estimator to connect the invariant subspace error with a computable residual estimator. Most importantly, the resulting reliability and efficiency bounds are robust with respect to the mesh size, the mesh level and the internal spectral gaps within the target cluster. Numerical experiments support the theoretical results and demonstrate the robustness of the proposed estimator.

math.NA↗

arXiv2026

Frequency-Aware Flow Matching for Continuous and Consistent Robotic Action Generation

Flow matching has emerged as a standard paradigm for robotic manipulation owing to its strong expressive power for modelling complex, multimodal action distributions, alongside similar approaches like diffusion policy. However, existing methods rely on discretized action chunks, making them brittle to demonstrations collected at heterogeneous control frequencies and prone to temporally inconsistent actions that degrade control stability. In this paper, we propose Frequency-Aware Flow Matching (FAFM), which outputs continuous, temporally consistent actions. To handle heterogeneous frequency input, we transform discrete action sequences into the frequency domain with the discrete cosine transform (DCT), perform flow matching over the resulting coefficients, and reconstruct continuous actions via cosine basis expansion. To generate temporally consistent actions, we regularize the first-order temporal derivative to promote smooth actions. This corresponds to a Sobolev-type constraint that suppresses high-frequency errors and discourages abrupt action changes. Our FAFM is simple, introduces no additional network parameters and applies to standalone flow-matching policies and vision-language action models. Across synthetic toy benchmark, obstacle avoidance, LapGym, and LIBERO, FAFM improves success rates, multimodal expressivity, motion smoothness, convergence speed, robustness to mechanical bias and mixed-frequency input. These gains are consistent when deployed on a real-world Franka robot. Code available at https://anonymous.4open.science/r/FAFM.

cs.RO↗

arXiv2025

Local Multilevel Preconditioned Jacobi-Davidson Method for Elliptic Eigenvalue Problems on Adaptive Meshes

In this work, we propose an efficient adaptive multilevel preconditioned Jacobi-Davidson (PJD) method for eigenvalue problems with singularity. Our multilevel method utilizes a local smoothing strategy to solve the preconditioned Jacobi-Davidson algebraic systems arising from adaptive finite element methods (AFEM). As a result, the algorithm holds optimal computational complexity $O(N)$. The theoretical analysis reveals that our method has a uniform convergence rate with respect to mesh levels and degrees of freedom. Further, the convergence rate is not affected by highly discontinuous coefficients within the domain. Numerical results verify our theoretical findings.

math.NA↗

arXiv2025

RobustVLA: On Robustness of Vision-Language-Action Model against Multi-Modal Perturbations

In Vision-Language-Actionf(VLA) models, robustness to real-world perturbations is critical for deployment. Existing methods target simple visual disturbances, overlooking the broader multi-modal perturbations that arise in actions, instructions, environments, and observations. Here, we first evaluate the robustness of mainstream VLAs under 17 perturbations across four modalities. We find (1) actions as the most fragile modality, (2) Existing visual-robust VLA do not gain robustness in other modality, and (3) pi0 demonstrates superior robustness. To build multi-modal robust VLAs, we propose RobustVLA against perturbations in VLA inputs and outputs. For output robustness, we perform offline robust optimization against worst-case action noise that maximizes mismatch in flow matching objective. This can be seen as adversarial training, label smoothing, and outlier penalization. For input robustness, we enforce consistent actions across input variations that preserve task semantics. To account for multiple perturbations, we formulate robustness as a multi-armed bandit problem and apply an upper confidence bound algorithm to automatically identify the most harmful noise. Experiments on LIBERO demonstrate our RobustVLA delivers absolute gains over baselines of 12.6% on the pi0 backbone and 10.4% on the OpenVLA backbone across all 17 perturbations, achieving 50.6x faster inference than existing visual-robust BYOVLA that requires external LLMs, and a 10.4% gain under mixed perturbations. On the real-world FR5 robot, under four types of multimodal perturbations, RobustVLA shows strong low-data performance, outperforming pi0 by 65.6% success rate with 25 demonstrations. Even with abundant demos, our method still outperform pi0 by 30% success rate. Code and demo videos available at https://github.com/gakakulicc/RobustVLA.

cs.CV↗