EVENTS

The presentation series “Train your engineering network” on diverse topics of Machine Learning addresses all interested persons at TUHH, from MLE partners as well as from the Hamburg region in general and aims at promoting the exchange of information and knowledge between these persons as well as their networking in a relaxed atmosphere. Thereby, the machine learning activities within MLE, TUHH and in the wider environment shall be made more visible, cooperations shall be promoted and also interested students shall be given an insight.

Abdul Qadir Ibrahim - Parareal with a physics informed neural network as a coarse propagator

Parallel-in-time algorithms provide an additional layer of concurrency for the numerical integration of models based on time-dependent differential equations. Methods like Parareal, which parallelize across multiple time steps, rely on a computationally cheap and coarse integrator to propagate information forward in time, while a parallelizable expensive fine propagator provides accuracy. Typically, the coarse method is a numerical integrator using lower resolution, reduced order or a simplified model. Our paper proposes to use a physics-informed neural network (PINN) instead. We demonstrate for the Black-Scholes equation, a partial differential equation from computational finance, that Parareal with a PINN coarse propagator provides better speedup than a numerical coarse propagator. Training and evaluating a neural network are both tasks whose computing patterns are well suited for GPUs. By contrast, mesh-based algorithms with their low computational intensity struggle to perform well. We show that moving the coarse propagator PINN to a GPU while running the numerical fine propagator on the CPU further improves Parareal's single-node performance. This suggests that integrating machine learning techniques into parallel-in-time integration methods and exploiting their differences in computing patterns might offer a way to better utilize heterogeneous architectures. 

Lectures will be held online via Zoom on Mondays starting at 16:00 in the winter semester 2023 in English. General zoom link for all lectures: Link