AI 中文总结
针对不规则微粒的斯托克斯阻力张量预测，提出SO(3)等变神经网络，从球谐表面表示直接输出完整张量块，精度高且快4-5个数量级，揭示标量近似丢失的取向效应。
AI 中文摘要
不规则微粒的斯托克斯流水动力学由其总阻力矩阵编码，这是一个6x6张量，其平移和旋转块（A和C）控制沉降、扩散和取向输运。经验阻力相关性将这些张量压缩为单个标量，丢弃了阻力的取向依赖性和旋转响应。我们提出了一种SO(3)等变神经网络，从粒子的球谐表面表示预测完整的对称正定A和C块，该网络通过构造在浮点精度内等变。在从近球形到非常粗糙的1.1x10^5个随机形状上训练，并设有18,000个形状的密封测试集，它在两个块上实现了1.4%和2.7%的平均相对误差，同时每个形状的评估速度比生成其标签的正则化斯托克斯求解器快4-5个数量级。一项谱收敛研究确认了表示的保真性：在球谐度15处截断一个形状，其阻力中位数变化为0.14%（平移）和0.38%（旋转），而训练形状在度15处带限生成，不携带截断误差。在1.16x10^6个取向采样的沉降、旋转和扩散事件中，该代理模型揭示了高达11度的横向漂移、高达46度的旋转错位，以及形状引起的扩散扩展为30%（平移）和2.4倍（旋转），这些在标量或椭球降维下均完全为零。即使是相关性所针对的取向平均标量摩擦，准确度在中位数1.7-2.8%（均值2.2-3.2%），也不携带张量取向，而代理模型以约1%的准确度重现该标量，同时提供完整的各向异性张量。一个快速、等变的张量代理模型可以在大气尘埃输运、微塑料归宿和胶体布朗动力学中替代求解器和标量近似。
英文摘要
The Stokes-flow hydrodynamics of an irregular microparticle is encoded by its grand resistance matrix, a 6x6 tensor whose translational and rotational blocks (A and C) govern settling, diffusion, and orientational transport. Empirical drag correlations compress these tensors to a single scalar, discarding drag's orientation dependence and the rotational response. We present an SO(3)-equivariant neural network that predicts the full symmetric positive-definite A and C blocks from a particle's spherical-harmonic surface representation, equivariant by construction to floating-point precision. Trained on 1.1x10^5 random shapes from near-spherical to very rough, with a sealed test set of 18,000, it achieves 1.4% and 2.7% mean relative error on the two blocks while evaluating each shape 4-5 orders of magnitude faster than the regularised-Stokeslet solver that generated its labels. A spectral-convergence study confirms the representation is faithful: truncating a shape at spherical-harmonic degree 15 changes its resistance by a median of 0.14% (translation) and 0.38% (rotation), while the training shapes, generated band-limited at degree 15, carry no truncation error. Across 1.16x10^6 orientation-sampled settling, rotation and diffusion events, the surrogate reveals lateral drift up to 11 deg, rotational misalignment up to 46 deg, and shape-induced diffusion spreads of 30% (translational) and 2.4x (rotational), all identically zero under any scalar or spheroid reduction. Even the orientation-averaged scalar friction the correlations target, accurate to 1.7-2.8% (median; 2.2-3.2% mean), carries no tensor orientation, whereas the surrogate reproduces that scalar to ~1% while supplying the full anisotropic tensors. A fast, equivariant tensor surrogate can replace both solver and scalar approximation in atmospheric dust transport, microplastic fate and colloidal Brownian dynamics.
