Machine learning models struggle with viscous Burgers equation errors

Researchers have analyzed the local errors of classical machine-learning surrogate models used to approximate the viscous Burgers equation. Four models—radial basis function (RBF) kernel ridge regression (KRR), linear Ridge, ExtraTrees, and Random Forests—were compared. The study found that errors in these models, particularly KRR, are strongly related to the spatial curvature of the solution, forming a local two-branch fold near predicted extrema. This suggests that surrogate models may retain more small-scale structure than the true future state, indicating insufficient viscous smoothing. AI

IMPACT Highlights limitations in current ML surrogate models for complex physical systems, suggesting areas for improvement in capturing dynamics like viscous smoothing.

RANK_REASON Academic paper detailing a physics-consistent interpretation of errors in classical machine learning surrogate models for a specific differential equation. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.LG →

• ExtraTrees
• radial basis function (RBF) kernel ridge regression (KRR)
• Random Forests
• viscous Burgers equation

• paper
• other

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →