Events for 12/13/2024 from all calendars

Nonlinear Partial Differential Equations

Time: 1:50PM - 2:50PM

Location: B302

Speaker: Abdul-Lateef Haji-Ali, Heriot-Watt University

Title: Multiindex Monte Carlo method for semilinear stochastic partial differential equations

Abstract: In this talk, we present an exponential-integrator based mulitiindex Monte Carlo method (MIMC) for weak approximations of mild solutions of semilinear stochastic partial differential equations (SPDE). We present recent theoretical results on multiindex coupled solutions of the SPDE are presented, namely that such couplings are stable and satisfy multiplicative error estimates, and describe how this theory can be utilized to obtain a tractable MIMC method. Numerical examples show that MIMC outperforms alternative methods, such as multilevel Monte Carlo, in settings with low regularity.

Mathematical Physics and Harmonic Analysis Seminar

Time: 1:50PM - 2:50PM

Location: BLOC 302

Speaker: Abdul-Lateef Haji-Ali, Heriot-Watt University

Title: Multiindex Monte Carlo method for semilinear stochastic partial differential equations

Abstract: In this talk, we present an exponential-integrator based mulitiindex Monte Carlo method (MIMC) for weak approximations of mild solutions of semilinear stochastic partial differential equations (SPDE). We present recent theoretical results on multiindex coupled solutions of the SPDE are presented, namely that such couplings are stable and satisfy multiplicative error estimates, and describe how this theory can be utilized to obtain a tractable MIMC method. Numerical examples show that MIMC outperforms alternative methods, such as multilevel Monte Carlo, in settings with low regularity.