Generative models for function-valued data, such as time series and solutions of partial differential equations, must learn distributions over infinite-dimensional spaces. Functional Flow Matching (FFM) extends Flow Matching to this setting, learning a velocity field whose flow transports a Gaussian prior to the data d...
Fred Xu, Thomas Markovich, Barbora Barancikova et al.· 0 citations
A capacity theorem shows that, under a full-rank feature assumption, a restricted subfamily matches the chaos coefficients of any Gaussian-latent random graph signal, with exponentially decaying truncation error under a growth condition; the task-level claims are established empirically.
Fred Xu, Thomas Markovich, Florence Regol et al.· 0 citations
Photoplethysmography (PPG) is widely recorded by clinical monitors and consumer wearables, providing a scalable source of continuous physiological information. These recordings offer an opportunity for physiological assessment at scale, but realizing this potential requires models to learn from both signal-derived phys...
Xiao-Da Wang, Min-Xiao Wang, Maxwell A. Xu et al.· 0 citations
By formalizing the classical conditions for well-posedness within neural operators, this framework demonstrates the theoretical benefits of explicitly conditioning on PDE parameters and boundary conditions and achieves superior generalization across heterogeneous physical regimes while maintaining strict inference effi...
