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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\u2019s 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.<\/jats:p>","DOI":"10.1007\/978-3-031-39698-4_44","type":"book-chapter","created":{"date-parts":[[2023,8,23]],"date-time":"2023-08-23T06:02:40Z","timestamp":1692770560000},"page":"649-663","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Parareal with\u00a0a\u00a0Physics-Informed Neural Network as\u00a0Coarse Propagator"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3452-8500","authenticated-orcid":false,"given":"Abdul Qadir","family":"Ibrahim","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0287-2120","authenticated-orcid":false,"given":"Sebastian","family":"G\u00f6tschel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1904-2473","authenticated-orcid":false,"given":"Daniel","family":"Ruprecht","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,8,24]]},"reference":[{"issue":"8","key":"44_CR1","first-page":"1","volume":"23","author":"W Agboh","year":"2020","unstructured":"Agboh, W., Grainger, O., Ruprecht, D., Dogar, M.: Parareal with a learned coarse model for robotic manipulation. 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