Physics Informed Neural Networks to solve the Boltzmann Transport Equation (Ref: 4741)

物理信息神经网络求解玻尔兹曼传输方程（参考：4741）

• 批准号: 2879436
• 金额: --
• 依托单位: UNIVERSITY OF EXETER
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2023
• 资助国家: 英国
• 起止时间: 2023 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2879436
• 关键词: Physics; Informed; Neural; Networks; solve

Plasma physics presents a number of physical challenges. In some regimes the physics is best described by the Boltzmann equation. This models the gas in a 6 dimensional space of spatial coordinates and velocity components; the evolution of the state of the plasma corresponds to the transport of the particles in this 6-d space. The plasma can be collisionless, or collisions can be represented by an additional term in the equation. The solution of this is challenging due to the high dimensionality of the phase space, and standard techniques such as finite difference methods quickly explode in memory and computational cost.Machine Learning techniques are making significant impacts in all areas of physical modelling. In applying a Neural Network to a physics problem, the objective is for the NN to "learn" the behaviour of the system. In "physics informed Neural Networks" (PINNs), the structure of the ODE or PDE to be solved is built into the NN. This can be highly advantageous for high dimensional systems. The objective of the project is to apply PINN to solve the Boltzmann equation and extend this to complex domains; after training the NN could provide almost instantaneous solution to this very challenging equation.

等离子体物理提出了许多物理挑战。在某些情况下，玻尔兹曼方程是最好的物理描述。这在空间坐标和速度分量的6维空间中模拟气体;等离子体状态的演变对应于粒子在该6维空间中的传输。等离子体可以是无碰撞的，或者碰撞可以用方程中的附加项来表示。由于相空间的高维性，解决这一问题具有挑战性，而有限差分方法等标准技术在内存和计算成本方面迅速爆炸。机器学习技术正在物理建模的各个领域产生重大影响。在将神经网络应用于物理问题时，目标是NN“学习”系统的行为。在“物理学神经网络”（PINNs）中，要求解的ODE或PDE的结构被内置到NN中。这对于高维系统是非常有利的。该项目的目标是应用PINN来求解Boltzmann方程，并将其扩展到复杂的领域;经过训练，NN可以为这个非常具有挑战性的方程提供几乎即时的解决方案。