The paper presents a method for training Lagrangian Neural Networks (LNNs) to learn Schwarzschild geodesic motion. By introducing a decoupled position–velocity normalization and an energy-constrained log-uniform sampling strategy, the authors achieve accurate reproduction of perihelion precession, relativistic time dilation, and conservation of energy and angular momentum across diverse orbital regimes. This work marks the first successful training of LNNs on Schwarzschild geodesics and demonstrates their potential for data-driven modeling of complex relativistic systems.
arXiv:2607. 27320v1 Announce Type: cross Abstract: Field-level inference of cosmological initial conditions from galaxy surveys requires a forward model that is simultaneously accurate in the non-linear regime, computationally efficient, and fully differentiable.
arXiv:2608. 13215v1 Announce Type: new Abstract: Forecasting the long-horizon evolution of mechanical systems from position-only observations is a pivotal yet difficult task, as hidden velocities and trajectory-specific physical properties must be inferred simultaneously.
arXiv:2608.23728v1 Announce Type: new Abstract: Satellite orbit prediction, which aims to forecast future orbital trajectories from historical observations, is important for collision warning and saf...
arXiv:2605. 26790v3 Announce Type: replace Abstract: Low-thrust trajectory design relies heavily on repeated evaluations of fuel consumption and transfer feasibility, which require expensive optimal control solutions.
arXiv:2608.27521v1 Announce Type: new Abstract: Many dynamical processes unfold on the sphere but the default scientific machine learning architectures are Euclidean. Applying these architectures on...
arXiv:2505. 16035v3 Announce Type: replace Abstract: We introduce Equivariant Neural Eikonal Solvers, a novel framework that integrates Equivariant Neural Fields (ENFs) with Neural Eikonal Solvers.
arXiv:2607. 03904v1 Announce Type: new Abstract: Pulsar timing arrays (PTAs) provide a unique window into nanohertz gravitational waves (GWs), but extracting astrophysical parameters from noisy, long-baseline timing residuals remains computationally challenging with traditional Bayesian techniques due to the high dimensionality of the parameter space, complex and correlated noise models, and the cost of repeated likelihood evaluations.
The paper introduces SINFONIA, a family of neural-flow architectures designed to learn finite-time evolution maps for orbital dynamics while preserving key physical structures. Three variants—symplectic/slimplectic, Taylor-anchored, and Magnusian—are applied to a 2.5PN neutron-star inspiral, demonstrating that long-term accuracy depends on a single secular channel tied to energy–angular-momentum balance rather than pointwise errors. These learned maps achieve accurate phase evolution over up to $10^{5}$ orbital periods at lower computational cost than traditional integrators, and can also be used to infer unmodeled forces from accumulated phase data.
Graph Neural Networks (GNNs) are presented as a natural framework for modeling the relational structure inherent in astrophysical and cosmological data, such as galaxies in their environments or photons in detectors. The review argues that GNNs align with the native geometry of these domains, incorporate existing symmetries and prior knowledge, and remain flexible enough to capture unknown phenomena, offering greater interpretability than other deep‑learning models. It surveys applications across cosmology, galaxy formation, dynamics, and instrumentation, noting that only about one in six non‑instrumentation papers apply GNNs to real data rather than simulations, and provides best‑practice guidelines for when to use or avoid graph approaches.
WALT introduces a method to align latent trajectories with pretrained driving world models, creating a compact generative trajectory space that preserves action-relevant semantics without altering the original model. The approach uses a dual-branch autoencoder to map raw waypoints into this latent space and transfers visual world knowledge into trajectory representations. Experiments on NAVSIM benchmarks show modest performance gains and a 30.5% reduction in planner FLOPs, indicating that maintaining world representations while extracting action-relevant information can improve trajectory planning efficiency.
The paper introduces Riemannian Neural Hamiltonian Flows, a generative model that extends Hamiltonian normalizing flows to Riemannian manifolds by combining a fixed kinetic energy, a learned scalar potential, and a geodesic leapfrog integrator. It provides an analysis showing how the learned Hamiltonian can be interpreted through an implicit profile and a matched potential, with special cases such as isotropic Gaussian and local harmonic analysis around modes. Experiments on Euclidean, hyperbolic, and spherical spaces demonstrate competitive sample quality and computational efficiency compared to a Riemannian continuous normalizing flow, while confirming the interpretability of the learned potential.
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,...