The paper introduces CIPHER, a two‑stage identify‑then‑realize framework that learns latent port‑Hamiltonian models from partial, high‑dimensional observations. In the first stage, a contrastive teacher jointly trains an encoder and a neural ODE to produce predictive state representations. The second stage trains a student to learn an invertible coordinate transformation and port‑Hamiltonian dynamics that match encoded future observations, with theoretical guarantees for recovering the physical state up to a diffeomorphism. Experiments on ten datasets show that CIPHER matches or surpasses state‑of‑the‑art baselines, especially in long‑horizon forecasting, and remains robust to over‑specified latent dimensions while benefiting from port‑Hamiltonian parameterization.
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:2610.15267v1 Announce Type: cross Abstract: Joint-embedding predictive architectures (JEPAs) learn world models directly in latent space, but unconstrained autoregressive predictors may contrac...
The paper introduces kernel-based methods for learning Hamiltonian systems directly from trajectory data, offering both a 2‑step approach (reconstruct trajectories first, then learn the Hamiltonian) and a 1‑step approach (joint inference). Experiments on mass‑spring dynamics, a nonlinear pendulum, and the Henon‑Heiles system show that the methods achieve accurate, data‑efficient predictions, outperforming 2‑step baselines especially when data are scarce, while preserving the Hamiltonian structure. The authors also provide a priori error estimates and a general numerical framework applicable to arbitrary dynamical systems.
arXiv:2608. 11435v1 Announce Type: new Abstract: Forward and inverse modeling of parametric dynamical systems requires surrogate models that are not only accurate for state prediction, but also informative for parameter calibration.
arXiv:2604. 19465v3 Announce Type: replace-cross Abstract: Understanding how complex systems respond to perturbations, such as whether they will remain stable or what their most sensitive patterns are, is a fundamental challenge across science and engineering.
arXiv:2606. 15053v1 Announce Type: new Abstract: Surrogate models are central to scientific machine learning, where they enable fast prediction, simulation, inference, and control for complex physical systems.
arXiv:2505.09063v2 Announce Type: replace Abstract: Solving time-dependent parametric partial differential equations (PDEs) with high-fidelity solvers is expensive in multi-query settings. This motiv...
arXiv:2610.08475v1 Announce Type: new Abstract: In many-query scenarios, data-driven surrogate models provide an efficient alternative to high-fidelity solvers for simulating physical systems governe...
arXiv:2607. 23337v1 Announce Type: new Abstract: Neural operators provide data-driven mappings for modeling dynamical systems.
arXiv:2505. 23863v3 Announce Type: replace-cross Abstract: Understanding chaotic dynamics is a fundamental problem across scientific disciplines, including climate science, neuroscience, and fluid dynamics, yet direct experimentation and intervention in such systems are often infeasible.
arXiv:2605. 00412v3 Announce Type: replace Abstract: World models have recently re-emerged as a central paradigm for embodied intelligence, robotics, autonomous driving, and model-based reinforcement learning.
arXiv:2604. 24662v2 Announce Type: replace-cross Abstract: Identifying the dynamical state variables of a system from high-dimensional observations is a central problem across physical sciences.