AI-Driven Simulation of Complex Physical Systems: Insights from Statistical Mechanics

Abstract

This research paper presents an in-depth study of AI-driven simulations for complex physical systems, with a focus on the Ising model and Lennard-Jones fluids. The integration of artificial intelligence (AI) with statistical mechanics allows for accurate predictions of key system properties such as magnetization, susceptibility, energy per spin, and radial distribution functions. AI simulations for the Ising model closely align with analytical solutions, demonstrating a relative error of less than 1% in magnetization predictions and below 4% for susceptibility near critical temperatures. Energy per spin results show a slight deviation with errors ranging from 0.5% to 9%, particularly at higher temperatures.

The radial distribution function g(r) for Lennard-Jones fluids, simulated using AI, successfully captures the oscillatory behavior and decay with increasing distance, highlighting AI's ability to model inter-particle interactions. Moreover, AI-driven simulations show significant computational advantages, with execution times and scalability factors surpassing traditional analytical methods, especially for large system sizes. The scalability factor increases from 1.33 for small systems (1,000 particles/spins) to 1.54 for large-scale simulations (500,000 particles/spins), demonstrating superior efficiency for handling complex, large-scale systems.

This study confirms the potential of AI as a powerful tool for simulating complex physical phenomena, offering high accuracy and computational efficiency. The results underscore the applicability of AI in diverse fields such as condensed matter physics, fluid dynamics, and large-scale system modeling, where traditional methods are often limited by computational costs. This work lays the groundwork for future AI-driven research in solving complex real-world problems in physics, chemistry, and engineering.