Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2601.20462

CM-GAI: Continuum Mechanistic Generative Artificial Intelligence Theory for Data Dynamics

Shan Tang·Ziwei Cao·Zhenling Yang·Jiachen Guo·Yicheng Lu·Wing Kam Liu·Xu Guo
View original source ↗Read source document ↗Export metadata ↓

Abstract

Generative artificial intelligence (GAI) plays a fundamental role in high-impact AI-based systems such as SORA and AlphaFold. Currently, GAI shows limited capability in the specialized domains due to data scarcity. In this paper, we develop a continuum mechanics-based theoretical framework to generalize the optimal transport theory from pure mathematics, which can be used to describe the dynamics of data, realizing the generative tasks with a small amount of data. The developed theory is used to solve three typical problem involved in many mechanical designs and engineering applications: at material level, how to generate the stress-strain response outside the range of experimental conditions based on experimentally measured stress-strain data; at structure level, how to generate the temperature-dependent stress fields under the thermal loading; at system level, how to generate the plastic strain fields under transient dynamic loading. Our results show the proposed theory can complete the generation successfully, showing its potential to solve many difficult problems involved in engineering applications, not limited to mechanics problems, such as image generation. The present work shows that mechanics can provide new tools for computer science. The limitation of the proposed theory is also discussed.

Explore related subjects

cs.CEphysics.comp-ph

Keep this discovery

BibTeXRIS

Shan Tang, Ziwei Cao, Zhenling Yang, Jiachen Guo, Yicheng Lu, Wing Kam Liu, Xu Guo. 2026-01-28. CM-GAI: Continuum Mechanistic Generative Artificial Intelligence Theory for Data Dynamics. https://arxiv.org/abs/2601.20462

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A Framework for Discharge Time Prediction of Energy Storage Units Based on Coupled Dynamics and Multi-Factor Aging Models

This paper presents a physically interpretable framework for predicting time to empty (TTE) in portable embedded systems. The framework couples usage-driven load-power decomposition, electrical power-voltage-current closure, a semi-empirical aging model, and SOC-temperature dynamics. Smartphone telemetry is mapped to battery current through an interpretable load model and conversion-efficiency correction. Battery capacity loss is modeled by combining Arrhenius temperature dependence, SEI diffusion behavior, and cycle-related power-law degradation. The coupled dynamic model then predicts TTE under different initial SOC values, ambient temperatures, and usage profiles. Chronological hold-out evaluation on a 6.9-h smartphone discharge session yielded a current RMSE of 0.0095 $\pm$ 0.0006 A, a temperature RMSE of 2.93 $\pm$ 0.24$^\circ$C, and a TTE MAPE of 4.81 $\pm$ 0.61%. Evaluation on NASA cell B0005 produced a capacity-loss RMSE of 0.031 Ah. Baseline, ablation, and counterfactual analyses further illustrate the contributions of thermal and aging corrections and the relative influence of load features. The results demonstrate the feasibility and interpretability of the proposed framework, while broader validation across devices and batteries remains necessary.

cs.CE↗
arXiv2026

Node-Shift-Encoding Genetic Algorithm with fuzzy-enhanced reference tour to solve the bi-objective service-oriented TSP

The Travelling Salesman Problem (TSP) remains a key area of research in combinatorial optimization, with applications in logistics, manufacturing, and service delivery. This paper addresses a bi-objective service-oriented TSP in which the clients' ranks in the delivery path matter. Unlike conventional depot-based TSP formulations, the considered problem does not assume a distinguished depot or a fixed tour origin. To address this setting, we adapt the Miller--Tucker--Zemlin (MTZ)-based formulation and derive an original linearization of the resulting model, enabling its solution with off-the-shelf integer linear programming solvers. This adaptation avoids the rigid tour origin imposed by the conventional MTZ formulation, for which fixing the starting node does not affect the tour cost but can affect the objective in a customer-rank-sensitive TSP. To solve this problem, we present a Node-Shift-Encoding (NSE)-based Genetic Algorithm augmented with fuzzy reasoning to update the reference tour throughout the evolutionary process. Experimental evaluation on TSPLIB benchmarks demonstrates that the proposed method achieves improved performance compared with the classical NSE approach.

cs.CE↗
arXiv2026

Geometric organization of olfactory descriptor data in the Poincar\'e disk

Odor quality is commonly represented using high dimensional descriptor profiles, yet their low dimensional organization remains unclear. We investigated whether a two-dimensional hyperbolic embedding can provide an interpretable representation of this structure. We applied hyperbolic metric multidimensional scaling to two complementary datasets: 480 Sagar rating profiles from three participants rating 160 odorants on 15 continuous descriptors, and 4983 GoodScents--Leffingwell molecules annotated with 138 binary descriptors. The embeddings substantially preserved pairwise descriptor distances, supporting subsequent analyses of radial and angular organization. In Sagar, rating profile entropy was strongly and negatively associated with hyperbolic radius, with diffuse profiles closer to the center and concentrated profiles closer to the boundary. This radial organization emerged primarily at the level of the full descriptor profile, rather than any individual descriptor, and remained robust across alternative descriptor representations, participant specific analyses, and averaged ratings. Sweet, musky, fruity, pleasantness showed the strongest directional trends. In GoodScents--Leffingwell, active label entropy, reflecting descriptor multiplicity, increased with radius, whereas orthogonalized descriptor entropy, reflecting spread across orthogonal modes, decreased with radius. Related binary descriptors occupied coherent localized high-density regions. These findings reveal complementary radial and angular organization in the hyperbolic representation of olfactory descriptor data. They support hyperbolic mapping as an interpretable descriptive framework in which radius summarizes global profile properties, while the angular component captures continuous descriptor gradients and categorical organization.

cs.CE↗