论文标题
使用随机增强拉格朗日方法在身体约束下训练神经网络
Training neural networks under physical constraints using a stochastic augmented Lagrangian approach
论文作者
论文摘要
我们研究了XGC中5维动力学融合模拟中的fokker-planck-landau碰撞操作员的编码器折叠神经网络的物理受限训练。为了训练该网络，我们提出了一种随机增强的拉格朗日方法，该方法利用Pytorch的天然随机梯度下降方法来求解内部无约束的最小值子问题，并与外部增强的Lagranged Lagrangian Loop中的惩罚因素和Lagrange倍增器进行了启发式更新。我们针对单个离子物种病例的训练结果，具有自我收集和对电子的碰撞，表明所提出的随机增强Lagrangian方法比使用固定的应用程序问题训练可以实现更高的模型预测准确性，并且对于我们的应用程序问题的固定惩罚方法，其准确性足以实现动力学模拟的实际应用。
We investigate the physics-constrained training of an encoder-decoder neural network for approximating the Fokker-Planck-Landau collision operator in the 5-dimensional kinetic fusion simulation in XGC. To train this network, we propose a stochastic augmented Lagrangian approach that utilizes pyTorch's native stochastic gradient descent method to solve the inner unconstrained minimization subproblem, paired with a heuristic update for the penalty factor and Lagrange multipliers in the outer augmented Lagrangian loop. Our training results for a single ion species case, with self-collisions and collision against electrons, show that the proposed stochastic augmented Lagrangian approach can achieve higher model prediction accuracy than training with a fixed penalty method for our application problem, with the accuracy high enough for practical applications in kinetic simulations.
