Governing equation discovery of a complex system from snapshots

Complex systems in physics, chemistry, and biology that evolve over time with inherent randomness are typically described by stochastic differential equations (SDEs). A fundamental challenge in science and engineering is to determine the governing equations of a complex system from snapshot data. Traditional equation discovery methods often rely on stringent assumptions, such as the availability of the trajectory information or time-series data, and the presumption that the underlying system is deterministic. In this work, we introduce a data-driven, simulation-free framework, called Sparse Identification of Differential Equations from Snapshots (SpIDES), that discovers the governing equations of a complex system from snapshots by utilizing the advanced machine learning techniques to perform three essential steps: probability flow reconstruction, probability density estimation, and Bayesian sparse identification. We validate the effectiveness and robustness of SpIDES by successfully identifying the governing equation of an over-damped Langevin system confined within two potential wells. By extracting interpretable drift and diffusion terms from the SDEs, our framework provides deeper insights into system dynamics, enhances predictive accuracy, and facilitates more effective strategies for managing and simulating stochastic systems.

GAD-Generative Learning for HD Map-Free Autonomous Driving

Deep-learning-based techniques have been widely adopted for autonomous driving software stacks for mass production in recent years, focusing primarily on perception modules, with some work extending this method to prediction modules. However, the downstream planning and control modules are still designed with hefty handcrafted rules, dominated by optimization-based methods such as quadratic programming or model predictive control. This results in a performance bottleneck for autonomous driving systems in that corner cases simply cannot be solved by enumerating hand-crafted rules. We present a deep-learning-based approach that brings prediction, decision, and planning modules together with the attempt to overcome the rule-based methods' deficiency in real-world applications of autonomous driving, especially for urban scenes. The DNN model we proposed is solely trained with 10 hours of human driver data, and it supports all mass-production ADAS features available on the market to date. This method is deployed onto a Jiyue test car with no modification to its factory-ready sensor set and compute platform. the feasibility, usability, and commercial potential are demonstrated in this article.

Dynamic Typography: Bringing Text to Life via Video Diffusion Prior

Text animation serves as an expressive medium, transforming static communication into dynamic experiences by infusing words with motion to evoke emotions, emphasize meanings, and construct compelling narratives. Crafting animations that are semantically aware poses significant challenges, demanding expertise in graphic design and animation. We present an automated text animation scheme, termed "Dynamic Typography", which combines two challenging tasks. It deforms letters to convey semantic meaning and infuses them with vibrant movements based on user prompts. Our technique harnesses vector graphics representations and an end-to-end optimization-based framework. This framework employs neural displacement fields to convert letters into base shapes and applies per-frame motion, encouraging coherence with the intended textual concept. Shape preservation techniques and perceptual loss regularization are employed to maintain legibility and structural integrity throughout the animation process. We demonstrate the generalizability of our approach across various text-to-video models and highlight the superiority of our end-to-end methodology over baseline methods, which might comprise separate tasks. Through quantitative and qualitative evaluations, we demonstrate the effectiveness of our framework in generating coherent text animations that faithfully interpret user prompts while maintaining readability. Our code is available at: https://animate-your-word.github.io/demo/.