The paper applies variational autoregressive networks to study the time‑dependent joint distribution of the simple exclusion process (SEP) across symmetric, asymmetric, and totally asymmetric variants in one, two, and three dimensions. It reproduces known finite‑time results in 1D and 2D, provides new finite‑time dynamics for all three models, and uncovers scaling relations for the active‑inactive phase transition in 3D, showing a dimension‑independent characteristic length scale. The work offers a unified computational framework for probing nonequilibrium transport dynamics in high‑dimensional configuration spaces.
By Zhimao Liu, Jing Liu, Pan Zhang, Ying Tang
The paper demonstrates that long‑time stochastic dynamics can be predicted using generative diffusion models trained only on configuration pairs separated by a short, fixed time lag, without requiring the underlying equations of motion. Applied to two‑dimensional Model B and driven colloids in a periodic optical potential, the learned transition kernels accurately reproduce dynamic critical scaling, self‑similar coarsening, and experimental observables such as particle current and mean passage time, even on larger lattices and unseen initial conditions. This shows that short‑time observations contain sufficient information to forecast emergent non‑equilibrium behavior over extended periods.
By Yang-yang Tan, Jinyang Li, Lingxiao Wang
arXiv:2608. 13506v1 Announce Type: cross Abstract: Liquids exhibit collective behavior that depends sensitively on thermodynamic conditions, interfaces and confinement, yet predicting each new state commonly requires a separate atomistic simulation.
By Bingqing Cheng
arXiv:2607. 16281v1 Announce Type: cross Abstract: The analysis of highly non-linear stochastic data within non-equilibrium dynamical systems requires computational frameworks capable of detecting latent phase transitions before systemic structural breakdowns occur.
By Manoj B. Bhatkar, Prashant M. Yawalkar
arXiv:2511. 02258v3 Announce Type: replace-cross Abstract: This paper studies the high-dimensional scaling limits of online stochastic gradient descent (SGD).
By Parsa Rangriz
arXiv:2606. 24660v1 Announce Type: cross Abstract: Phase-field models play a central role in the continuum description of phase separation, in which the bulk free-energy density and the interfacial thickness parameter determine pattern formation and microstructural evolution.
By Callum Marsh, Radek Erban, Andreas Munch
arXiv:2609.28448v1 Announce Type: cross
Abstract: We study the nonequilibrium dynamics of a minimal recurrent transformer with $N$ normalized tokens, $Q=K=I$, and a negative value map $V=-I$. Similar...
By Qucheng Gao, Zuyi Yang, Xiao Chen
The paper introduces SUDO, a simulation‑free framework for unbalanced dynamic optimal transport (UDOT) that supports general convex growth penalties beyond the quadratic Wasserstein‑Fisher‑Rao case. By showing that concave penalties lead to degenerate solutions, the authors focus on convex penalties, learning conditional paths and transport costs to solve a semi‑coupling problem and then applying unbalanced flow matching. On benchmark datasets, SUDO matches the accuracy of analytical WFR solvers while being faster than simulation‑based methods, and it also handles asymmetric penalties that better reflect proliferation‑dominant biological priors.
By Junda Ying, Yuxuan Wang, Bowen Yang, Peijie Zhou, Lei Zhang
arXiv:2606. 09816v1 Announce Type: cross Abstract: Standard diffusion models typically use a single time-homogeneous Gaussian terminal distribution as the reference law for generation.
By Danqi Zhuang, Jisui Huang, Xiaoyue Xi, Andrew Kiggins, Xiaojie Wang, Ke Chen, Yue Wu
Phase-field models play a central role in the continuum description of phase separation, in which the bulk free-energy density and the interfacial thickness parameter determine pattern formation and microstructural evolution. In practice, these constitutive quantities are rarely known a priori and must be inferred from limited dynamical observations.
Standard diffusion models typically use a single time-homogeneous Gaussian terminal distribution as the reference law for generation. While this choice is analytically convenient and empirically powerful, it provides little explicit structure for data concentrated near low-dimensional manifolds, where different regions of the data distribution may correspond to distinct local geometric or semantic factors.
arXiv:2606. 26128v1 Announce Type: new Abstract: The spatiotemporal evolution of many physical, chemical, and biological systems is described by nonlinear partial differential equations (PDEs).
By Vijay Yadav, Madhu Priya, Manish Dev Shrimali, Prabhat K. Jaiswal