3 papers
math.NA2025
StPINNs - Deep learning framework for approximation of stochastic differential equations
Marcin Baranek, Paweł Przybyłowicz
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 o…
math.NA2025
Deep neural network approximation for high-dimensional parabolic partial integro-differential equations
Marcin Baranek
In this article, we investigate the existence of a deep neural network (DNN) capable of approximating solutions to partial integro-differential equations while circumventing the cu…
math.NA2023
On the randomized Euler algorithm under inexact information
Marcin Baranek, Andrzej Kałuża, Paweł M. Morkisz +2
This paper focuses on analyzing the error of the randomized Euler algorithm when only noisy information about the coefficients of the underlying stochastic differential equation (S…