PMosFM introduces a preconditioned manifold matching framework that enables one‑step physics‑constrained generation by encoding constraints in a manifold decoder. The method learns transport in intrinsic coordinates, eliminating the need for residual losses or trajectory unrolling, and employs a geometric preconditioner and covariance transform to improve conditioning. Experiments demonstrate reduced training and sampling time compared to multi‑step baselines while maintaining comparable physical and distributional fidelity.
By Zhangyong Liang, Haibin Ling
arXiv:2607. 00947v1 Announce Type: new Abstract: Generative models learn data distributions that reside on a low-dimensional manifold within a higher-dimensional ambient space.
By Ludwig Winkler, Andrew Leaver-Fay, Joseph Kleinhenz, Pan Kessel
arXiv:2602. 03082v2 Announce Type: replace Abstract: A growing number of neural architectures have been proposed to enforce geometric constraints, including projection-based networks, exponential-map updates, constrained output layers, and manifold neural ODEs.
By Karthik Elamvazhuthi, Shiba Biswal, Kian Rosenblum, Arushi Katyal, Tianli Qu, Grady Ma, Rishi Sonthalia
arXiv:2611.06711v1 Announce Type: new
Abstract: Deep generative models, particularly Flow Matching frameworks, have emerged as powerful tools for synthesizing complex physical systems. However, stand...
By Giuliano Galadini, Aurelio Uncini, Danilo Comminiello
arXiv:2607. 00095v1 Announce Type: cross Abstract: Generative models have emerged as scalable surrogates for physical simulation, yet they offer no guarantee that their outputs respect the conservation laws, boundary conditions, and nonlinear invariants that govern the underlying physics.
By Alaina Kolli, Theodoros Xenakis, Utkarsh Utkarsh, Pengfei Cai, Rafael Gomez-Bombarelli, Alan Edelman, Christopher Vincent Rackauckas
arXiv:2608.29904v1 Announce Type: new
Abstract: Modern video generators routinely fail at physical dynamics: objects float, trajectories violate gravity, contacts vanish. Standard denoising and flow-...
By Hai Nguyen-Truong, Tuan-Anh Vu, Dang Huynh