arXiv Machine Learning September 4, 2026 By Partha Sarathi Mondal, Manav Kumar Jalan, Anish Kumar, Shradha Mishra

Data Driven Equation Discovery for Phase-Ordering Dynamics : From Allen Cahn to the Ising Model

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The paper investigates the use of PDE‑SINDy to discover governing equations for phase‑ordering dynamics, benchmarking against the Allen–Cahn equation and applying it to the Ising model with Glauber spin‑flip dynamics. It systematically studies how data availability, library size, and noise affect term identification and coefficient recovery, finding that stability‑selection with library bagging improves robustness. The recovered coarse‑grained equations successfully reproduce the characteristic phase‑separation and coarsening behavior of the microscopic Ising system.

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