Boltzmann Equation

The Boltzmann equation describes the statistical behavior of particles in a system, aiming to predict macroscopic properties from microscopic interactions. Current research focuses on developing efficient numerical methods for solving the equation, particularly employing machine learning techniques like neural networks (including physics-informed and structure-preserving architectures) and Gaussian processes to improve accuracy and reduce computational cost. These advancements are crucial for applications ranging from material science (predicting thermal conductivity) to fluid dynamics (modeling turbulence and plasma physics) and even marketing (analyzing consumer behavior), highlighting the equation's broad relevance across diverse scientific and engineering domains.