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:2609.37392v1 Announce Type: new Abstract: Modeling the temporal evolution of macroscopic properties of complex systems is an important scientific task. To predict this evolution without full mi...
arXiv:2610.01522v1 Announce Type: cross Abstract: Many scientific and machine learning systems, from molecular dynamics to diffusion models and beyond, are governed by stochastic dynamics with low-di...
arXiv:2608. 01833v1 Announce Type: cross Abstract: Grokking is a striking phenomenon in neural network training, where a model can undergo a prolonged period of pure memorization before abrupt generalization.
The article reviews modern machine learning techniques for estimating the committor and related kinetic statistics from molecular dynamics simulations. It emphasizes self‑supervised methods that solve the underlying dynamical equations instead of relying on labeled data, and unifies various approaches—generator‑based PDEs, variational principles, Markov state models, dynamical Galerkin approximation, and neural networks—under a common operator framework. The review also discusses practical guidance for handling non‑Markovian effects, sampling strategies, and outlines future research directions such as connections to reinforcement learning and generative modeling.
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 introduces a physics-constrained neural network surrogate that learns the microstructural evolution of binary mixtures governed by the Cahn‑Hilliard equation. By imposing conservation of the order parameter as a hard constraint on the network output, the model accurately predicts long‑time phase‑separation dynamics for both critical and off‑critical mixtures, maintaining mixture composition and matching the Lifshitz‑Slyozov domain‑growth law. A variant that enforces conservation only through a penalty term drifts from the initial composition and loses predictive accuracy over long rollouts, underscoring the necessity of the hard constraint for stability.
arXiv:2607. 10285v1 Announce Type: new Abstract: We study how unsupervised autoencoders trained on microscopic spin configurations from the Ising model learn macroscopic, theory-relevant variables underlying the data-generating process.
arXiv:2606. 04100v1 Announce Type: new Abstract: Machine learning interatomic potentials (MLIPs) enable efficient and accurate atomistic simulations but depend critically on the quality and diversity of the training data.
arXiv:2608. 07924v1 Announce Type: cross Abstract: Drifting models are a recent class of one-step generative models that evolve the model distribution during training using a predefined sample-based drift field.
arXiv:2605.12597v3 Announce Type: replace-cross Abstract: Computational sampling has been central to the sciences since the mid-20th century. While machine-learning-based approaches have recently ena...
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:2510. 01788v2 Announce Type: replace Abstract: This work focuses on learning non-canonical Hamiltonian dynamics from data, where long-term predictions require the preservation of structure both in the learned model and in numerical schemes.