Deterministically solving charged particle transport problems at a sufficient spatial and angular resolution is often prohibitively expensive, especially due to their highly forward peaked scattering. We propose a model order reduction approach which evolves the solution on a low-rank manifold in time, making computations feasible at much higher resolutions and reducing the overall run-time and memory footprint. For this, we use a hybrid dynamical low-rank approach based on a collided-uncollided split, i.e., the transport equation is split through a collision source method. Uncollided particles are described using a ray tracer, facilitating the inclusion of boundary conditions and straggling, whereas collided particles are represented using a moment method combined with the dynamical low-rank approximation. Here the energy is treated as a pseudo-time and a rank adaptive integrator is chosen to dynamically adapt the rank in energy. We can reproduce the results of a full-rank reference code at a much lower rank and thus computational cost and memory usage. The solution further achieves comparable accuracy with respect to TOPAS MC as previous deterministic approaches.

翻译：确定性地求解带电粒子输运问题在足够的空间和角度分辨率下通常计算成本过高，尤其因其高度前向峰化的散射特性。我们提出一种模型降阶方法，在时间维度上将解演化于低秩流形上，从而在更高分辨率下实现可行计算，并降低总体运行时间和内存占用。该方法采用基于碰撞-非碰撞分裂的混合动力学低秩框架，即通过碰撞源方法对输运方程进行分解。非碰撞粒子采用射线追踪器描述，便于边界条件和能量离散效应的处理；而碰撞粒子则采用矩方法结合动力学低秩近似进行表征。其中能量维度被视作伪时间变量，并选用秩自适应积分器动态调整能量维度的秩。我们能在更低秩数（即更低计算成本与内存占用）下复现全秩参考代码的结果。该解决方案相较于先前的确定性方法，进一步实现了与TOPAS蒙特卡罗模拟相当的精度。