arXiv:2605. 15806v2 Announce Type: replace Abstract: Neural operators excel as deterministic surrogates, but inevitably collapse to the conditional mean when applied to stochastic PDEs, discarding the variance and tail structure upon which uncertainty quantification depends.
By Kai Hidajat
arXiv:2607. 23110v1 Announce Type: cross Abstract: In this paper, we study the extension of Neural Jump ODEs to infinite-dimensional function spaces.
By Florian Krach, Oliver L\"othgren, Josef Teichmann
arXiv:2607. 19173v1 Announce Type: new Abstract: Neural stochastic differential equations (SDEs) have emerged as powerful tools for learning noisy or stochastic dynamics directly from data; however, existing approaches largely assume uncoupled and continuous noise, limiting their applicability to realistic stochastic drivers, and often scale poorly in time, requiring expensive autoregressive training.
By Arthur Bizzi, Olga Fink
arXiv:2411. 01982v2 Announce Type: replace-cross Abstract: We study the problem of learning controlled stochastic differential equations (SDEs) \[ dX_t = b(t,X_t,u_t)\,dt + \sigma(t,X_t,u_t)\,dW_t, \] whose drift and diffusion depend nonlinearly on time, state, and control values.
By Luc Brogat-Motte, Riccardo Bonalli, Alessandro Rudi
arXiv:2603. 20467v2 Announce Type: replace-cross Abstract: Stochastic differential equations (SDEs), which serve as the governing equations for dynamical systems in a broad range of applications, can become cost-prohibitive for numerical simulation at scales necessary for quantifying key properties.
By Joanna Zou, Han Cheng Lie, Youssef Marzouk
arXiv:2606. 05272v1 Announce Type: new Abstract: Neural rough differential equations (NRDEs) stay accurate under irregular sampling while taking far fewer integration steps than standard neural differential equations, summarising a finely sampled driver by its log-signature and advancing the hidden state over coarse intervals using the log-ODE method.
By Luke Thompson, Dai Shi, Lequan Lin, Junbin Gao, Andi Han