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.
arXiv:2608.25606v2 Announce Type: replace-cross Abstract: The simple exclusion process (SEP) is a paradigmatic model for nonequilibrium transport, yet its rich dynamics over an exponentially large co...
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.
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.
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.
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.
arXiv:2512.12767v2 Announce Type: replace-cross Abstract: Training recurrent neuronal networks consisting of excitatory (E) and inhibitory (I) units with additive noise for working memory computation...
arXiv:2604. 23952v2 Announce Type: replace-cross Abstract: Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging.
arXiv:2511. 02258v3 Announce Type: replace-cross Abstract: This paper studies the high-dimensional scaling limits of online stochastic gradient descent (SGD).
arXiv:2608. 18592v1 Announce Type: new Abstract: Whether distinct neural architectures develop common collective dynamics remains an open question.
arXiv:2606. 29679v1 Announce Type: new Abstract: Observable Matrix Dynamics (OMD) is a diagnostic framework that probes the dynamics of high-dimensional internal representations of inputs by a neural network via a fixed-size $N \times N$ distance matrix $M(t)$ on a held set of $N$ inputs.
arXiv:2602. 14885v2 Announce Type: replace-cross Abstract: Recurrent neural networks (RNNs) provide a theoretical framework for understanding computation in biological neural circuits, yet classical results, such as Hopfield's model of associative memory, rely on symmetric connectivity that restricts network dynamics to gradient-like flows.
arXiv:2610.02081v1 Announce Type: new Abstract: There has been a proliferation of sampling algorithms based on Wasserstein gradient flows (WGF) and forward-only diffusion processes (FODP), often acco...