Zhenhua Chen

Tao Feng, Xianbing Zhao, Zhenhua Chen et al.

Recent advances in diffusion-based and autoregressive video generation models have achieved remarkable visual realism. However, these models typically lack accurate physical alignment, failing to replicate real-world dynamics in object motion. This limitation arises primarily from their reliance on learned statistical correlations rather than capturing mechanisms adhering to physical laws. To address this issue, we introduce a novel framework that integrates symbolic regression (SR) and trajectory-guided image-to-video (I2V) models for physics-grounded video forecasting. Our approach extracts motion trajectories from input videos, uses a retrieval-based pre-training mechanism to enhance symbolic regression, and discovers equations of motion to forecast physically accurate future trajectories. These trajectories then guide video generation without requiring fine-tuning of existing models. Evaluated on scenarios in Classical Mechanics, including spring-mass, pendulums, and projectile motions, our method successfully recovers ground-truth analytical equations and improves the physical alignment of generated videos over baseline methods.

Wenbin Chen, Zhenhua Chen, Jin Cheng et al.

This paper concerns new continuum phenomenological model for epitaxial thin film growth with three different forms of the Ehrlich-Schwoebel current. Two of these forms were first proposed by Politi and Villain [1996] and then studied by Evans, Thiel and Bartelt [2006]. The other one is completely new. Following the techniques used in Li and Liu [2003], we present rigorous analysis of the well-posedness, regularity and time stability for the new model. We also studied both the global and the local behavior of the surface roughness in the growth process. The new model differs from other known models in that it features a linear convex part and a nonlinear concave part, and thus by using a convex-concave time splitting scheme, one can naturally build unconditionally stable semi-implicit numerical discretizations with linear implicit parts, which is much easier to implement than conventional models requiring nonlinear implicit parts. Despite this fundamental difference in the model, numerical experiments show that the nonlinear morphological instability of the new model agrees well with results of other models published in Li and Liu [2003], which indicates that the new model correctly captures the essential morphological states in the thin film growth process.