Stabilizing PDE-ML system || How Does Neural Network Training Work || Oct 17, 2025

Value of the Information & Strength of the Argument

The talks provide valuable insights into two critical areas of scientific machine learning. The first talk offers a clear diagnosis of instability in PDE-ML systems and a practical stabilization method, supported by numerical experiments. The argumentation is solid, with a logical progression from problem identification to solution and further refinement. The second talk synthesizes recent research on neural network training, presenting the Edge of Stability phenomenon and a novel ‘river valley’ hypothesis. The argumentation is compelling, though some claims are speculative and based on limited empirical evidence. Overall, the value is high for researchers in the field, offering both practical solutions and theoretical frameworks.

Scientific Rigor, Source Quality, Title Accuracy

The seminar demonstrates strong scientific rigor. The first talk references the Mori-Zwanzig formalism and provides a detailed analysis of the prototype problem. The second talk cites recent papers on Edge of Stability and Schedule-Free AdamW. The sources are appropriate and up-to-date. The title accurately reflects the content, covering both talks. The presentation is well-structured, with clear explanations and mathematical derivations. The discussions and Q&A sessions add depth and clarify potential ambiguities. Overall, the scientific quality is high, though the seminar format limits the depth of peer review.

The title accurately reflects the two main talks: stabilizing PDE-ML coupled systems and understanding neural network training dynamics.

8/10

The seminar presents original research from two speakers, with detailed technical explanations and references to recent papers. The content is rigorous and well-structured, though it is a seminar recording with limited peer review.

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

• 00:00Introduction to the seminar and first speaker.
• 02:00Saad Qadeer introduces PDE-ML coupled systems and the viscous Burgers' equation.
• 10:00Discussion on spectral bias and its role in instability.
• 20:00Proposal of low-pass filtering to stabilize the system.
• 30:00Introduction to Mori-Zwanzig formalism for improving accuracy.
• 40:00Transition to second talk on neural network training.
• 50:00Explanation of Edge of Stability phenomenon.
• 1:00:00Discussion on river valley landscape hypothesis.
• 1:10:00Analysis of Schedule-Free AdamW optimizer.
• 1:20:00Q&A and concluding remarks.

• Mori-Zwanzig formalism — Referenced in the first talk as a method to improve the accuracy of reduced-order models.
• Edge of Stability paper — Referenced in the second talk as a key paper on the Edge of Stability phenomenon.
• Schedule-Free AdamW paper — Referenced in the second talk as the source of the Schedule-Free AdamW optimizer.

• Spectral bias in neural networks — Supports the claim that neural networks struggle with high-frequency components.
• Reduced order models — Relevant to the discussion of reduced-order models in the first talk.

• Low-dimensional subspace hypothesis — The second talk challenges this hypothesis, suggesting that training may not occur in a low-dimensional subspace.