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arXiv Machine Learning

Robust Discovery of Coarse-Grained Continuum Equations from Microscopic Dynamics

The paper applies PDE‑SINDy to phase‑separating systems to discover governing PDEs from spatiotemporal data. It finds that accuracy improves with more data, while larger function libraries reduce efficiency. For the Glauber spin‑flip Ising model, selection probabilities uncover a hierarchy of equations, and a strict threshold recovers a Model‑A‑like equation that reproduces phase‑separation dynamics.

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arXiv Machine Learning
Sep 4

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

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.

By Partha Sarathi Mondal, Manav Kumar Jalan, Anish Kumar, Shradha Mishra
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arXiv Machine Learning
Sep 15

Physics-Constrained Neural Surrogate for Domain Growth Prediction in Systems with Conserved Kinetics

The paper introduces a physics-constrained neural network surrogate that learns the microstructural evolution of binary mixtures governed by the Cahn‑Hilliard equation. By imposing conservation of the order parameter as a hard constraint on the network output, the model accurately predicts long‑time phase‑separation dynamics for both critical and off‑critical mixtures, maintaining mixture composition and matching the Lifshitz‑Slyozov domain‑growth law. A variant that enforces conservation only through a penalty term drifts from the initial composition and loses predictive accuracy over long rollouts, underscoring the necessity of the hard constraint for stability.

By Vijay Yadav, Pallvi Pandey, Madhu Priya, Manish Dev Shrimali, Prabhat K. Jaiswal
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arXiv Machine Learning
Aug 12

DEFT: Data-Efficient Frequency-domain Top-k Sampling via Inverse Discrete Fourier Transform for Spatiotemporal Dynamical Systems Modeling

arXiv:2608. 11019v1 Announce Type: new Abstract: Modeling spatiotemporal dynamical systems governed by partial differential equations (PDEs) poses two major challenges: it either requires expensive physics-based simulators that entail iterative numerical solving at high computational cost, or it depends on abundant training data, yet purely data-driven models often generalize poorly to downstream dynamic operating conditions.

By Hengbo Xiao, Jiale Liu, Jiahao Song, Guannan He
diffusionfine-tuning
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