We design a deterministic particle method for the solution of the spatially homogeneous Landau equation with uncertainty. The deterministic particle approximation is based on the reformulation of the Landau equation as a formal gradient flow on the set of probability measures, whereas the propagation of uncertain quantities is computed by means of a sg representation of each particle. This approach guarantees spectral accuracy in uncertainty space while preserving the fundamental structural properties of the model: the positivity of the solution, the conservation of invariant quantities, and the entropy production. We provide a regularity results for the particle method in the random space. We perform the numerical validation of the particle method in a wealth of test cases.

翻译：我们设计了一种确定性粒子方法，用于求解含不确定性的空间均匀Landau方程。该确定性粒子近似基于Landau方程在概率测度集上形式梯度流的重新表述，而不确定量的传播则通过每个粒子的随机变量表示来计算。该方法在不确定性空间中保证了谱精度，同时保留了模型的基本结构性质：解的正定性、不变量的守恒性以及熵产生。我们给出了随机空间中粒子方法的正则性结果，并通过大量算例对该粒子方法进行了数值验证。