arXiv subjects

Guozhen Li

Publications and source records attributed to Guozhen Li.

6 recordsLinked to original sources

arXiv2026

Shaping the Evolutionary Dynamics of Robot Morphology via Adaptive Control Learning

Robot co-design via bi-level optimization couples within-lifetime controller learning for fitness evaluation with cross-generational morphological evolution. Prior work has established that well-adapted morphology facilitates faster control learning, a property termed morphological intelligence. Yet how control learning reciprocally shapes morphological evolution remains unexplored. This paper examines both directions for a holistic account of brain-body interplay. We first show that morphological contributions to control learning decouple into two orthogonal dimensions. We formalize the convergence speed as morphological intelligence and identify the performance ceiling as a complementary quantity termed true potential. A concise functional relation is then established to jointly characterize both quantities from individual learning curves, which, when aggregated at the population level, capture evolutionary profiles. Through extensive experiments on simulated voxel-based soft robots, we reveal that premature fitness evaluation systematically underestimates true potential and biases selection towards fast learners. This restricts design space exploration, compromising both optimization efficiency and morphological diversity. Notably, the widely recognized morphological Baldwin effect emerges as an artifact of this bias rather than a general evolutionary tendency. We therefore propose AdaControl, which monitors disproportionate selection for morphological intelligence during evolution and allocates minimally sufficient control learning for unbiased fitness evaluation. With AdaControl, a simple genetic algorithm rivals state-of-the-art generative-model-based co-design methods in discovering diverse high-performing designs while cutting computation by up to 80% versus exhaustive control.

cs.RO↗

arXiv2026

An explicit finite-memory scheme for approximating and sampling invariant measures of stochastic functional differential equations with infinite delay

Efficient sampling and numerical approximation of invariant probability measures (IPMs) on infinite-dimensional function spaces are important problems in scientific computing. In this paper, we study the numerical approximation and sampling of IPMs associated with stochastic functional differential equations with infinite delay (SFDEswID). To this end, we develop a fully explicit ergodicity-preserving truncated Euler--Maruyama scheme for SFDEswID that requires only finite historical storage and accommodates superlinearly growing coefficients. We establish strong convergence of the numerical segment process and show that it admits a unique IPM and is exponentially ergodic in the Wasserstein distance. Building on these results, we prove the convergence of the numerical IPM to the exact one and derive an explicit convergence rate. As a consequence, we obtain a quantitative long-time sampling error estimate of order $O\left(e^{-\lambda_\varepsilon t_n}+\Delta^{\rho_\varepsilon}\right)$. The results provide a rigorous and computationally efficient framework for sampling IPMs and quantifying long-time sampling errors for stochastic systems with infinite delay.

math.NA↗

arXiv2026

An explicit adaptive time-stepping scheme for superlinear stochastic diffusion systems

This paper develops an adaptive time-stepping Euler--Maruyama (EM) scheme for stochastic diffusion systems with superlinearly growing coefficients. The adaptive timestep is chosen according to the superlinear growth of both drift and diffusion coefficients. To prevent excessively small timesteps, a truncated EM scheme is employed as a backstop whenever the adaptive timestep falls below a prescribed threshold. By combining the stochastic analysis with the stopping time technique, we establish the strong convergence of the proposed method and obtain the optimal $1/2$-order strong convergence rate in the $L^q$-sense for $q>2$. {Finally, numerical experiments are carried out for stiff, nonstiff, and stochastic Lorenz systems to validate the theoretical findings. The results indicate that the proposed scheme achieves superior accuracy and performance compared to various fixed-step and adaptive alternatives.

math.NA↗

arXiv2025

Hybrid Stochastic Functional Differential Equations with Infinite Delay: Approximations and Numerics

This paper is to investigate if the solution of a hybrid stochastic functional differential equation (SFDE) with infinite delay can be approximated by the solution of the corresponding hybrid SFDE with finite delay. A positive result is established for a large class of highly nonlinear hybrid SFDEs with infinite delay. Our new theory makes it possible to numerically approximate the solution of the hybrid SFDE with infinite delay, via the numerical solution of the corresponding hybrid SFDE with finite delay.

math.PR↗

arXiv2025

Development of numerical methods for nonlinear hybrid stochastic functional differential equations with infinite delay

This paper addresses the challenging numerical simulation of nonlinear hybrid stochastic functional differential equations with infinite delays. We first propose an explicit scheme using space and time truncation, requiring only finite historical storage. Leveraging approximation theory, we prove the boundedness of the numerical solution's $p$th moment and establish its convergence, achieving a rate of $1/2$ order under polynomially growing coefficients. Furthermore, we refine the scheme to better capture the underlying exponential stability of the exact solution, in both moment and almost sure senses. Finally, numerical experiments are presented to validate our theoretical results.

math.NA↗

arXiv2024

Improving Bird's Eye View Semantic Segmentation by Task Decomposition

Semantic segmentation in bird's eye view (BEV) plays a crucial role in autonomous driving. Previous methods usually follow an end-to-end pipeline, directly predicting the BEV segmentation map from monocular RGB inputs. However, the challenge arises when the RGB inputs and BEV targets from distinct perspectives, making the direct point-to-point predicting hard to optimize. In this paper, we decompose the original BEV segmentation task into two stages, namely BEV map reconstruction and RGB-BEV feature alignment. In the first stage, we train a BEV autoencoder to reconstruct the BEV segmentation maps given corrupted noisy latent representation, which urges the decoder to learn fundamental knowledge of typical BEV patterns. The second stage involves mapping RGB input images into the BEV latent space of the first stage, directly optimizing the correlations between the two views at the feature level. Our approach simplifies the complexity of combining perception and generation into distinct steps, equipping the model to handle intricate and challenging scenes effectively. Besides, we propose to transform the BEV segmentation map from the Cartesian to the polar coordinate system to establish the column-wise correspondence between RGB images and BEV maps. Moreover, our method requires neither multi-scale features nor camera intrinsic parameters for depth estimation and saves computational overhead. Extensive experiments on nuScenes and Argoverse show the effectiveness and efficiency of our method. Code is available at https://github.com/happytianhao/TaDe.

cs.CV↗