Stochastic PINNs solvers|| Multi-Resolution Independent Simulations for Turbulence || March 27, 2026

Value of the Information & Strength of the Argument

The first talk provides a rigorous theoretical framework for stochastic PINNs, addressing a gap in the literature by proposing a direct loss function for SDEs via the Doss–Sussmann transformation. The argumentation is solid, with clear assumptions and proofs of consistency, coercivity, and uniqueness of the minimizer. The second talk presents a practical and innovative computational strategy for turbulence simulations, backed by impressive results on exascale hardware. The argumentation is compelling, emphasizing the efficiency of the MRIS approach in capturing small-scale dynamics. Both talks are well-structured and supported by concrete examples and references.

Scientific Rigor, Source Quality, Title Accuracy

The seminar demonstrates high scientific rigor. The first talk is based on a preprint (arXiv:2512.14258) and includes references to related work, though some claims are not fully detailed in the presentation. The second talk references the use of the Frontier supercomputer and the MRIS paradigm, but specific publications are not mentioned. The title accurately reflects the content, covering both stochastic PINNs and turbulence simulations. The sources cited are credible, and the presentations are consistent with current research trends.

The title accurately reflects the two main topics: stochastic PINNs solvers and multi-resolution independent simulations for turbulence.

8/10

The seminar features two expert speakers presenting rigorous mathematical and computational methods. The first talk introduces a novel stochastic PINNs approach for SDEs, grounded in a Doss–Sussmann transformation and backed by a preprint on arXiv. The second talk discusses a multi-resolution independent simulations paradigm for turbulence, leveraging exascale computing. Both presentations are technical, with clear theoretical foundations and references to recent work. The content is reliable and well-sourced, though the seminar format limits depth in some areas.

Markers derived by PSI from the transcript: the creator did not define chapters.

• 00:00Introduction to the seminar and speaker bios.
• 03:00First talk begins: Stochastic PINNs for SDEs, problem statement and motivation.
• 10:00Discussion of the Doss–Sussmann transformation and its role in defining the loss function.
• 20:00Presentation of theoretical properties: consistency, coercivity, and uniqueness of minimizer.
• 30:00Numerical experiments and implementation details by Marcin Baranek.
• 1:00:00Second talk begins: Multi-Resolution Independent Simulations for Turbulence.
• 1:10:00Explanation of the MRIS approach and its advantages over long simulations.
• 1:30:00Results on Frontier exascale computer and GPU acceleration techniques.
• 1:50:00Q&A and discussion on the presented methods.

• Stochastic PINNs-deep learning solvers for SDEs (preprint) — The first talk is based on this preprint, which details the StPINNs methodology.

• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations — The StPINNs approach builds upon the original PINNs framework, which is a well-established method for solving PDEs.
• Doss–Sussmann transformation — The transformation is a classical result connecting SDEs and RODEs, used in the first talk.