批量波前扫描用于线性输运不确定性量化
Batched Wavefront Sweeps for Linear Transport Uncertainty Quantification
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中文总结 AI 辅助
本文提出图兼容的批量波前扫描算法，用于线性输运DG离散，实现跨通道并行与伴随一致性，并在GPU上显著加速不确定性量化计算。
中文摘要 AI 辅助
我们为线性输运的上风间断伽辽金离散提出了一种图兼容的批量波前公式。对于可扫描的离散，在定向迎风依赖图的拓扑排序下，单元方程形成一个块下三角系统。这种因果结构可以在局部算子、源项和入流数据变化的固定源问题族之间共享。我们利用这一观察，将具有共同依赖图的通道分组为图兼容的扫描类，并将样本、右端项、能量组和符号兼容的角方向作为张量维度纳入共同的波前调度中。我们证明了所得的批量波前算法在代数上等价于对类中每个通道独立执行经典DG扫描，同时在波前单元和通道维度上暴露并行性。我们将该公式实现为基于批量单元局部求解的GPU张量程序，并量化其工作量、深度和存储需求，包括样本微批处理引入的吞吐量-内存权衡。我们进一步在固定面符号分支上刻画离散的参数到可观测映射，并表明通过波前算法的反向模式微分再现了相应的离散伴随作用。数值实验验证了预期的DG收敛性和伴随一致性，展示了样本批处理带来的显著GPU执行增益，并在材料遮蔽不确定性量化问题和耦合多群C5G7/KAIST启发的幂迭代工作负载中说明了该方法。
英文摘要
We develop a graph-compatible batched wavefront formulation for upwind discontinuous Galerkin discretisations of linear transport. For sweepable discretisations, the cell equations form a block lower-triangular system under a topological ordering of the directed upwind dependency graph. This causal structure can be shared across families of fixed-source problems whose local operators, sources and inflow data vary. We exploit this observation by grouping channels with a common dependency graph into graph-compatible sweep classes and carrying samples, right-hand sides, energy groups and sign-compatible angular ordinates as tensor dimensions within a common wavefront schedule. We prove that the resulting batched wavefront algorithm is algebraically equivalent to independent classical DG sweeps for every channel in a class, while exposing parallelism simultaneously across wavefront cells and channel dimensions. We realise the formulation as a GPU tensor program based on batched cell-local solves and quantify its work, depth and storage requirements, including the throughput--memory tradeoff introduced by sample microbatching. We further characterise the discrete parameter-to-observable map on fixed face-sign branches and show that reverse-mode differentiation through the wavefront algorithm reproduces the corresponding discrete adjoint action. Numerical experiments verify the expected DG convergence and adjoint consistency, demonstrate substantial GPU execution gains from sample batching, and illustrate the method in a material-shadowing uncertainty-quantification problem and a coupled multigroup C5G7/KAIST-inspired power-iteration workload.
发表机构
- University of Bath（巴斯大学）
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