Accurately estimating friction coefficients between arbitrary material pairs is critical for robotics, digital fabrication, and physics-based simulation, but exhaustive pairwise testing scales quadratically with the number of materials. We introduce a proxy-based modeling framework that approximates any pairwise friction $f(A,B)$ from a small, fixed set of proxy materials $C=[c_1,\dots,c_k]$ by learning a per-material embedding $z_A = g(f(A,c1),\dots,f(A,ck))$ and a fusion function $p$ such that $f(A,B)\approx p\big(z_A,z_B\big)$. We present deterministic and probabilistic realizations of $g$ and $p$, procedures for selecting diverse proxy sets, and mechanisms for handling missing or noisy proxy measurements. The learned embeddings are compact, interpretable, and enable calibrated uncertainty estimates for downstream decision making. On simulated and measured friction datasets, our approach achieves high predictive accuracy, robust performance with partial observations, and substantial experimental savings by significantly reducing pairwise testing.

翻译：精确估计任意材料对之间的摩擦系数对机器人技术、数字制造和物理仿真至关重要，但穷举配对测试的复杂度随材料数量呈二次方增长。我们提出一种基于代理的建模框架，通过固定且数量较小的代理材料集 $C=[c_1,\dots,c_k]$，学习每种材料的嵌入向量 $z_A = g(f(A,c1),\dots,f(A,ck))$ 与融合函数 $p$，使得任意配对摩擦系数 $f(A,B)$ 可近似表示为 $f(A,B)\approx p\big(z_A,z_B\big)$。我们提出了 $g$ 和 $p$ 的确定性与概率性实现方案、多样代理材料集的选择策略，以及处理缺失或有噪声代理测量数据的机制。所学习的嵌入向量紧凑且可解释，能为下游决策提供带校准的不确定性估计。在仿真与实测摩擦数据集上，本方法实现了高预测精度、对部分观测数据的鲁棒性能，并通过显著减少配对测试量大幅降低实验成本。