arXiv:2604.00689v1 Announce Type: new
Abstract: We consider the problem of constructing surrogate operators for parameter-to-solution maps arising from parametric partial differential equations, where repeated forward model evaluations are computation…
arXiv:2604.00333v1 Announce Type: cross
Abstract: Collective behaviors that emerge from interactions are fundamental to numerous biological systems. To learn such interacting forces from observations, we introduce a measure-valued neural network that …
arXiv:2409.12296v3 Announce Type: replace-cross
Abstract: Inspired by the gradient flow viewpoint of the Landau equation and the corresponding dynamic formulation of the Landau metric in [arXiv:2007.08591], we develop a novel implicit particle method …
arXiv:2603.28939v1 Announce Type: new
Abstract: This work revisits operator learning from a spectral perspective by introducing Polar Linear Algebra, a structured framework based on polar geometry that combines a linear radial component with a periodi…
arXiv:2601.00728v4 Announce Type: replace
Abstract: We propose a reinforcement learning (RL) framework for adaptive precision tuning for linear solvers, which can be extended to general algorithms. The framework is formulated as a contextual bandit pr…
arXiv:2603.29184v1 Announce Type: new
Abstract: Nonconvex multi-well energies in cell-induced phase transitions give rise to sharp interfaces, fine-scale microstructures, and distance-dependent inter-cell coupling, all of which pose significant challe…
arXiv:2603.29237v1 Announce Type: new
Abstract: Enforcing exact macroscopic conservation laws, such as mass and energy, in neural partial differential equation (PDE) solvers is computationally challenging in high dimensions. Traditional discrete proje…
arXiv:2508.12627v2 Announce Type: replace
Abstract: Higher-order $U$-statistics abound in fields such as statistics, machine learning, and computer science, but are known to be highly time-consuming to compute in practice. Despite their widespread app…
arXiv:2603.23397v2 Announce Type: replace-cross
Abstract: Constrained sampling is an important and challenging task in computational statistics, concerned with generating samples from a distribution under certain constraints. There are numerous types …
arXiv:2603.28288v1 Announce Type: new
Abstract: Kolmogorov-Arnold Networks (KAN) employ B-spline bases on a fixed grid, providing no intrinsic multi-scale decomposition for non-smooth function approximation. We introduce Fractal Interpolation KAN (FI-…