arXiv Machine Learning

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.

arXiv Machine Learning

Aug 24

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.

By Partha Sarathi Mondal, Manav Kumar Jalan, Anish Kumar, Shradha Mishra

arXiv Machine Learning

Jun 9

Data-driven discovery of governing differential equations across physical systems

arXiv:2606. 09638v1 Announce Type: new Abstract: Differential equations play a critical role in scientific discovery because they provide a mathematical framework to describe the behaviour of physical phenomena.

By Siyu Lou, Hao Xu, Wenguan Wang, Lu Lu, Hao Sun, Yang Liu, Linfeng Zhang, Dongxiao Zhang, Yuntian Chen

arXiv Machine Learning

Jun 16

Conditional Score-Based Modeling of Effective Langevin Dynamics

arXiv:2604. 23952v2 Announce Type: replace-cross Abstract: Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging.

By Ludovico T. Giorgini

diffusion

arXiv Machine Learning

Jun 26

Physics-guided Convolutional Neural Network for Domain Growth Prediction in Systems with Conserved Kinetics

arXiv:2606. 26128v1 Announce Type: new Abstract: The spatiotemporal evolution of many physical, chemical, and biological systems is described by nonlinear partial differential equations (PDEs).

By Vijay Yadav, Madhu Priya, Manish Dev Shrimali, Prabhat K. Jaiswal

arXiv Machine Learning

Jul 14

LLM-PDESR: Robust PDE Discovery via Subdomain Weighted Residuals and LLM-Guided Symbolic Hypothesis Generation

arXiv:2607. 10546v1 Announce Type: new Abstract: Discovering governing partial differential equations (PDEs) from noisy observational data is a fundamental challenge in scientific machine learning.

By Jinyang Du, Hao Ma, Xiaohu Shi, Bo Yang, Yanchun Liang, Heow Pueh Lee, Chunguo Wu

llms benchmarks

arXiv Machine Learning

Jun 24

Extended pseudo-spectral physics-informed neural networks for phase-field models

arXiv:2606. 24660v1 Announce Type: cross Abstract: Phase-field models play a central role in the continuum description of phase separation, in which the bulk free-energy density and the interfacial thickness parameter determine pattern formation and microstructural evolution.

By Callum Marsh, Radek Erban, Andreas Munch

arXiv AI

Jun 17

ASTEROID: A Spatiotemporal Information Transformer for Forecasting Multi-Step Time Series of Molecular Dynamics

arXiv:2606. 17668v1 Announce Type: cross Abstract: Molecular dynamics (MD) simulation is computationally demanding, particularly for large-scale systems requiring long-term analysis.

By Kexin Wu, Luonan Chen, Renxiao Wang

llms benchmarks

Hugging Face Trending Papers

Jun 23

Extended pseudo-spectral physics-informed neural networks for phase-field models

Phase-field models play a central role in the continuum description of phase separation, in which the bulk free-energy density and the interfacial thickness parameter determine pattern formation and microstructural evolution. In practice, these constitutive quantities are rarely known a priori and must be inferred from limited dynamical observations.

arXiv Machine Learning

Jul 14

Interpreting learning dynamics of autoencoders: Transient scaling and emerging concepts of the Ising model

arXiv:2607. 10285v1 Announce Type: new Abstract: We study how unsupervised autoencoders trained on microscopic spin configurations from the Ising model learn macroscopic, theory-relevant variables underlying the data-generating process.

By Max Weinmann, Miriam Klopotek

rag

Hugging Face Trending Papers

Jul 16

Ptolemy's Equant Equates to a Universal Dynamical Clock via Machine Learning

Oscillatory dynamics arise ubiquitously in nonlinear systems, yet identifying a physically interpretable phase and phase dynamics in nonlinear, high-dimensional oscillations remains a central unresolved problem. Here we establish the principle of a universal dynamical clock, a physical perspective in which oscillations of arbitrary dimensionality and geometry are equivalently represented as uniform rotation through an equant-induced nonlinear viewing coordinate, inspired by Ptolemy's equant and formalised through an areal-uniformity principle reminiscent of Kepler's second law.

arXiv Machine Learning

Jun 25

LLM-ACES: Closed-Loop Discovery of Dynamical Systems with LLM-Guided Adaptive Search

arXiv:2606. 25039v1 Announce Type: new Abstract: Recovering governing Ordinary Differential Equations (ODEs) from data is a central challenge in modeling dynamical systems across scientific domains.

By Nikhil Abhyankar, Sha Li, Sanchit Kabra, Naren Ramakrishnan, Yulia Gel, Chandan K. Reddy

llms benchmarks

arXiv Machine Learning

4d ago

Efficient and Scalable Physics-Guided Fully Convolutional Spatiotemporal Learning for 3D Microstructure Evolution Prediction

arXiv:2609.36504v1 Announce Type: new Abstract: Accurate prediction of three-dimensional (3D) microstructure evolution remains computationally demanding because high-fidelity phase-field simulations...

By Michael Trimboli, Wenxi Liu, Xianqi Li

efficiency

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