Log in Sign up
Your paper timeline
Scroll AI takes the way you would scroll a great paper aggregator: quick signal first, deeper critique when something earns your attention, and challenges when a claim feels off.
Trending Newest Top
3 papers in cond-mat.stat-mech
Trending mixes fresh papers with community signal.
0
Graph-Recurrent Learning of Emergent Collective Dynamics
cond-mat.str-elcond-mat.stat-mechcs.LG Ali Rayat, Acacia Lee, Gia-Wei Chern · Oct 22, 2026

Collective ordering in correlated electron systems produces emergent, non-Markovian dynamics that cannot be closed at the level of coarse-grained observables alone. This paper proposes a graph-recurrent neural network (GRNN) that fuses gated recurrent memory with graph message passing to learn finite-time evolution maps directly from trajectories, bypassing repeated microscopic force evaluations. Site-resolved hidden states encode unresolved history and communicate across neighboring sites via graph-coupled hidden messages, giving a scalable, translationally invariant update rule. The authors demonstrate the approach on charge-density-wave domain coarsening in the semiclassical Holstein model, showing quantitative agreement with kernel-polynomial-method reference dynamics.

Collective ordering in correlated electron systems emerges from microscopic dynamics, yet the evolution of observable textures need not admit a closed, memoryless description. We introduce a graph-recurrent neural network (GRNN) framework that learns such emergent dynamics directly from trajectories without specifying microscopic equations of motion. The framework integrates gated recurrent memory with graph message passing: local hidden states encode information beyond the instantaneous observables, while spatial coupling allows this information to propagate between sites. The observable and hidden fields evolve jointly through a shared local rule, providing a scalable representation of dynamics with spatial interactions and temporal memory. We demonstrate this framework on the emergent dynamics of charge-density-wave order in the semiclassical Holstein model, successfully reproducing temporal and spatial correlations and dynamical scaling during domain coarsening. By learning finite-time evolution directly, the GRNN offers a route to efficient, data-driven descriptions of collective dynamics with unresolved microscopic degrees of freedom.
AI reviewed
arXivPDF
0
Learning ab initio phase-field models
cond-mat.stat-mechcond-mat.mtrl-scics.LG Mengyi Chen, Peichen Zhong, Zihan Zhang et al. · Oct 1, 2026

Bridging quantum-mechanical accuracy with mesoscopic length and time scales remains a grand challenge in materials modeling. This paper develops an ab initio phase-field framework that derives the mesoscopic evolution equation from molecular dynamics via Mori–Zwanzig projection, leaving only the free energy and mobility to be learned by neural networks from short machine-learning-interatomic-potential trajectories. The result is a data-efficient approach that propagates ab initio accuracy to scales far beyond direct atomistic simulation, demonstrated here on iron–boron melts and hydrogen–helium mixtures under planetary conditions.

Simulating microstructure evolution requires quantum-mechanical accuracy and mesoscopic reach in length and time scales, a combination that no current method achieves. Classical phase-field models provide this reach, but their accuracy is limited by phenomenological free energies and mobilities. Here we develop a framework for learning ab initio phase-field models, where the mesoscopic equation is not postulated but derived from a Mori-Zwanzig projection of molecular dynamics onto species-density fields under explicit assumptions. The nonlocal free energy and mobility left unspecified by this equation are parametrized by neural networks and learned from short molecular dynamics trajectories generated with machine-learning interatomic potentials of ab initio accuracy. We demonstrate the framework on an iron-boron melt and on hydrogen-helium mixtures under planetary conditions. For iron-boron, the model shows that the melt at the FeB$_4$ composition is spinodally unstable at ambient pressure but stabilized at 10 GPa, offering a thermodynamic rationale for why FeB$_4$ has been synthesized only under high pressure. For hydrogen-helium, the model predicts the immiscibility boundary and captures droplet nucleation and growth in helium-rain simulations of a column corresponding to 2.2 million atoms, far beyond the scale of atomistic modeling at comparable accuracy. Trained across compositions and conditions, such models could provide a mesoscopic counterpart to ab initio molecular dynamics.
AI reviewed
arXivPDF
0
Interpreting the Synchronization Gap: The Hidden Mechanism Inside Diffusion Transformers
cs.LGcond-mat.dis-nncond-mat.stat-mech Emil Albrychiewicz, Andr\'es Franco Valiente, Li-Ching Chen et al. · Mar 22, 2026

Recent theoretical models of diffusion as coupled Ornstein-Uhlenbeck processes predict a hierarchy of interaction timescales creating a synchronization gap between global and local committing modes. This work investigates how this gap mechanistically emerges within pretrained Diffusion Transformers by introducing a controlled architectural realization of replica coupling via symmetric cross-attention gates with strength $g$. Through linearized analysis and empirical probing of DiT-XL/2 across all 28 layers, the authors demonstrate that the gap is an intrinsic, depth-localized property that collapses under strong coupling as $\mathcal{O}(\frac{1-g}{1+g})$, providing a bridge between continuous statistical physics and discrete transformer dynamics.

Recent theoretical models of diffusion processes, conceptualized as coupled Ornstein-Uhlenbeck systems, predict a hierarchy of interaction timescales, and consequently, the existence of a synchronization gap between modes that commit at different stages of the reverse process. However, because these predictions rely on continuous time and analytically tractable score functions, it remains unclear how this phenomenology manifests in the deep, discrete architectures deployed in practice. In this work, we investigate how the synchronization gap is mechanistically realized within pretrained Diffusion Transformers (DiTs). We construct an explicit architectural realization of replica coupling by embedding two generative trajectories into a joint token sequence, modulated by a symmetric cross attention gate with variable coupling strength g. Through a linearized analysis of the attention difference, we show that the replica interaction decomposes mechanistically. We empirically validate our theoretical framework on a pretrained DiT-XL/2 model by tracking commitment and per layer internal mode energies. Our results reveal that: (1) the synchronization gap is an intrinsic architectural property of DiTs that persists even when external coupling is turned off; (2) as predicted by our spatial routing bounds, the gap completely collapses under strong coupling; (3) the gap is strictly depth localized, emerging sharply only within the final layers of the Transformer; and (4) global, low frequency structures consistently commit before local, high frequency details. Ultimately, our findings provide a mechanistic interpretation of how Diffusion Transformers resolve generative ambiguity, isolating speciation transitions to the terminal layers of the network.
AI reviewed
arXivPDF