Joint-embedding predictive architectures (JEPAs) learn latent dynamics for planning and avoid representation collapse by matching features to maximum-entropy distributions such as isotropic Gaussians,...
arXiv:2606. 05131v1 Announce Type: new Abstract: Koopman theory turns nonlinear dynamics into a linear spectral problem.
arXiv:2607. 09801v1 Announce Type: new Abstract: Governing equations provide compact descriptions of physical systems, yet the variables in which they are simple are often hidden in high-dimensional measurements.
arXiv:2606. 23957v1 Announce Type: new Abstract: Learning Koopman operators with autoencoders enables linear prediction in a latent space, but long-horizon rollouts often drift off the learned manifold, leading to phase and amplitude errors on systems with switching, continuous spectra, or strong transients.
arXiv:2602.02832v4 Announce Type: replace Abstract: Forward forecasting and data assimilation are the two important aspects in physical simulation: one propagates the state forward, the other recover...
arXiv:2410. 10137v5 Announce Type: replace Abstract: We develop Riemannian approaches to variational autoencoders (VAEs) for PDE-type ambient data with regularizing geometric latent dynamics, which we refer to as VAE-DLM, or VAEs with dynamical latent manifolds.
arXiv:2608. 14716v1 Announce Type: cross Abstract: Abrupt transitions in complex systems are often preceded by early warning signals.
arXiv:2608. 04471v1 Announce Type: cross Abstract: Time series in real-world applications are often generated by nonlinear dynamical systems, making accurate forecasting challenging.
arXiv:2608. 22277v2 Announce Type: replace Abstract: Deep learning surrogates for forecasting chaotic dynamical systems suffer from catastrophic error accumulation over long-term autoregressive rollouts.
arXiv:2609.37435v1 Announce Type: new Abstract: Neural Koopman autoencoder models have been shown to successfully build a latent embedding with linear dynamics for arbitrary dynamical systems, enabli...
The paper investigates why latent neural surrogate solvers, which compress physical system dynamics into a lower‑dimensional space, often fail during long‑horizon autoregressive rollouts. It demonstrates that training the latent representation only for reconstruction leads to instability, and proposes a set of training interventions—Koopman operator learning, Hamming noise injection, and multi‑step rollout fine‑tuning—that align the latent space with long‑horizon forecasting. These interventions reduce long‑rollout error by about 40 % and achieve accuracy comparable to full‑resolution models while using far fewer floating‑point operations and GPU memory, enabling stable extrapolation in mesoscale crystal‑plasticity simulations of high‑cycle fatigue.
arXiv:2609.10464v1 Announce Type: cross Abstract: Joint-Embedding Predictive Architecture (JEPA) world models learn a compact latent representation of the world that supports prediction and planning,...