Lihong Guo | Searcharxiv

arXiv2026

A PDE approach for the invariant measure of stochastic oscillators with hysteresis

This paper presents a PDE approach as an alternative to Monte Carlo simulations for computing the invariant measure of a white-noise-driven bilinear oscillator with hysteresis. This model is widely used in engineering to represent highly nonlinear dynamics, such as the Bauschinger effect. The study extends the stochastic elasto-plastic framework of Bensoussan et al. [SIAM J. Numer. Anal. 47 (2009), pp. 3374--3396] from the two-dimensional elasto-perfectly-plastic oscillator to the three-dimensional bilinear elasto-plastic oscillator. By constructing an appropriate Lyapunov function, the existence of an invariant measure is established. This extension thus enables the modelling of richer hysteretic behavior and broadens the scope of PDE alternatives to Monte Carlo methods. Two applications demonstrate the method's efficiency: calculating the oscillator's threshold crossing frequency (providing an alternative to Rice's formula) and probability of serviceability.

math-ph↗

arXiv2021

Updatable Siamese Tracker with Two-stage One-shot Learning

Offline Siamese networks have achieved very promising tracking performance, especially in accuracy and efficiency. However, they often fail to track an object in complex scenes due to the incapacity in online update. Traditional updaters are difficult to process the irregular variations and sampling noises of objects, so it is quite risky to adopt them to update Siamese networks. In this paper, we first present a two-stage one-shot learner, which can predict the local parameters of primary classifier with object samples from diverse stages. Then, an updatable Siamese network is proposed based on the learner (SiamTOL), which is able to complement online update by itself. Concretely, we introduce an extra inputting branch to sequentially capture the latest object features, and design a residual module to update the initial exemplar using these features. Besides, an effective multi-aspect training loss is designed for our network to avoid overfit. Extensive experimental results on several popular benchmarks including OTB100, VOT2018, VOT2019, LaSOT, UAV123 and GOT10k manifest that the proposed tracker achieves the leading performance and outperforms other state-of-the-art methods

cs.CV↗