arXiv:2608. 08040v1 Announce Type: cross Abstract: We introduce conditional cylindrical neural networks for approximating functionals of conditional laws in McKean-Vlasov equations with common noise.
arXiv:2606. 03820v1 Announce Type: cross Abstract: We develop a quantitative approximation framework for diffusion distillation, viewing few-step sampling as error propagation under compositions of learned flow maps.
arXiv:2607. 02003v1 Announce Type: cross Abstract: Although neural networks are remarkably effective, their underlying optimization principles remain theoretically elusive, often characterized by non-convex landscapes and stochastic heuristics.
arXiv:2607. 15291v1 Announce Type: cross Abstract: We develop a physics-informed neural network (PINN) framework for nonlocal partial differential equations arising in dynamic density functional theory (DDFT).
Stochastic-process models are, as a rule, far easier to simulate than to condition. Non-linear observations, non-Gaussian likelihoods, black-box information, and global constraints all induce intractable conditional laws, requiring bespoke, model-specific constructions.
arXiv:2606. 04000v1 Announce Type: cross Abstract: We present a probabilistic modeling framework for incorporating small-scale spatial heterogeneity into macroscopic descriptions of material behavior for polycrystalline metallic materials.
arXiv:2607. 12922v1 Announce Type: cross Abstract: Stochastic-process models are, as a rule, far easier to simulate than to condition.
arXiv:2510. 14656v3 Announce Type: replace-cross Abstract: This work proposes a two-stage physics-informed deep learning framework that combines neural-network-based sampling with statistical inference and constrained parameter refinement.
arXiv:2607. 14361v1 Announce Type: cross Abstract: We address fundamental challenges in representing and computing $\mathbb{R}^{d}$-valued predictable square-integrable processes over $[0,T]$, collected in the space $\mathcal{H}^2_T(\mathbb{R}^{d})$.
arXiv:2608. 15198v1 Announce Type: cross Abstract: Parameter identification of stochastic dynamical systems driven by mixed noises is challenging due to intractable likelihood functions.
arXiv:2606. 09434v1 Announce Type: new Abstract: The Fokker-Planck equation (FPE) plays a pivotal role in describing the time evolution of probability density functions (PDFs) for systems governed by stochastic dynamics.
arXiv:2606. 11650v1 Announce Type: new Abstract: Recent advances in scientific machine learning provide a means of near-real-time solution to partial differential equations (PDEs), but lack the theoretical underpinnings of conventional simulators that support contemporary verification and validation.
arXiv:2607. 04360v1 Announce Type: cross Abstract: Conditional generative models have emerged as powerful tools for sampling from target conditional distributions, driving substantial advances across a wide range of scientific and applied domains.