arXiv Machine Learning By Anastasis Kratsios, Giulia Livieri, Philipp Schmocker

NeuralChaos: Optimal Adapted Approximation of Square Integrable Predictable Processes

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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 $\mathcal{H}^2_T(\mathbb{R}^{d})$.

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arXiv Machine Learning
Jul 22

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise

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 Machine Learning
Jul 30

Learning Controlled Stochastic Differential Equations

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 Machine Learning
Jun 5

Learning Manifold and It\^o Dynamics with Branched Neural Rough Differential Equations

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