15.5NAMar 30
StPINNs - Deep learning framework for approximation of stochastic differential equationsMarcin Baranek, PaweÅ PrzybyÅowicz
In this paper, we introduce the SPINNs (stochastic physics-informed neural networks) in a systematic manner. This provides a mathematical framework for approximating the solution of stochastic differential equations (SDEs) driven by Levy noise using artificial neural networks.
31.7NAApr 1
On the error of the Euler scheme for approximation of solutions of nonlinear DDEs under inexact informationPaweÅ PrzybyÅowicz, Martyna WiÄ
cek
We analyze the behavior of the Euler method for delay differential equations under nonstandard assumptions on the right-hand-side function f, when evaluations of f are corrupted by informational noise. We provide theoretical upper bounds on the Euler discretization error and present results from the numerical experiments.