arXiv:2608. 04239v1 Announce Type: new Abstract: Spectral submanifold (SSM) reduction has emerged as a mathematically principled route to reliable nonlinear reduced-order models, capturing dynamics beyond the reach of linear techniques such as Dynamic Mode Decomposition (DMD).
arXiv:2605. 01835v2 Announce Type: replace Abstract: Nonlinear coupled systems are ubiquitous in science and engineering.
arXiv:2603.13496v2 Announce Type: replace Abstract: Constructing reduced-order models (ROMs) capable of efficiently predicting the evolution of parameter-dependent high-dimensional dynamical systems...
arXiv:2606. 09065v1 Announce Type: cross Abstract: In science and engineering, Lagrangian simulation methods such as Smooth Particle Hydrodynamics (SPH) or Material Point Method (MPM) are often employed to study the behavior of dynamic systems.
arXiv:2606. 06344v1 Announce Type: new Abstract: Probabilistic inference over spatially embedded variables requires beliefs that respect $SE(3)$ symmetry, yet existing equivariant networks produce only scalars and vectors -- not the rank-2 precision tensors needed for anisotropic uncertainty, and single-component messages collapse multi-modal energy landscapes to physically meaningless averages.
arXiv:2509. 24627v2 Announce Type: replace Abstract: Embedding physical intuition into network architectures allows the learning of dynamics that enforce fundamental properties, such as energy conservation laws, thereby leading to physically-plausible predictions.
arXiv:2605. 27756v2 Announce Type: replace-cross Abstract: Linear dimensionality reduction methods such as proper orthogonal decomposition (POD) make high-dimensional data amenable to analysis by identifying the principal components, or modes, that capture the most variance, or energy, in the data and constructing a low-dimensional representation in the subspace they span.
arXiv:2606. 03260v1 Announce Type: cross Abstract: Deep learning surrogates for 3D Partial Differential Equations (PDEs) often fail to generalize across geometric transformations because they depend heavily on specific coordinate systems.
arXiv:2605. 04130v2 Announce Type: replace Abstract: High-fidelity simulations, such as computational fluid dynamics and finite element analysis, are essential for modeling complex engineering systems but are often prohibitively expensive for tasks including parametric studies, optimization, and real-time control.
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:2606. 04623v1 Announce Type: new Abstract: High-dimensional Hamiltonian systems play a central role in many scientific and engineering disciplines, with dynamics evolving on symplectic manifolds.
arXiv:2506. 09398v4 Announce Type: replace Abstract: We consider the task of predicting Hamiltonian matrices to accelerate electronic structure calculations, which plays an important role in physics, chemistry, and materials science.
EquiReg introduces an equivariance‑regularized diffusion framework that penalises sampling trajectories deviating from the data manifold, thereby improving posterior sampling for inverse problems. By formalising manifold‑preferential equivariant functions—naturally arising from data augmentation or inherent symmetries—EquiReg guides diffusion steps toward symmetry‑preserving regions of the solution space. The method shows consistent gains in both linear and nonlinear image restoration tasks and partial differential equation solving, especially under reduced sampling and measurement consistency steps, and is available as open‑source code.