We present a scalable Gaussian Process (GP) method called DSoftKI that can fit and predict full derivative observations. It extends SoftKI, a method that approximates a kernel via softmax interpolation, to the setting with derivatives. DSoftKI enhances SoftKI's interpolation scheme by replacing its global temperature vector with local temperature vectors associated with each interpolation point. This modification allows the model to encode local directional sensitivity, enabling the construction of a scalable approximate kernel, including its first and second-order derivatives, through interpolation. Moreover, the interpolation scheme eliminates the need for kernel derivatives, facilitating extensions such as Deep Kernel Learning (DKL). We evaluate DSoftKI on synthetic benchmarks, a toy n-body physics simulation, standard regression datasets with synthetic gradients, and high-dimensional molecular force field prediction (100-1000 dimensions). Our results demonstrate that DSoftKI is accurate and scales to larger datasets with full derivative observations than previously possible.

翻译：本文提出了一种名为DSoftKI的可扩展高斯过程（GP）方法，能够拟合并预测全导数观测数据。该方法将SoftKI（一种通过软最大插值近似核函数的方法）扩展至包含导数的场景。DSoftKI改进了SoftKI的插值方案，将其全局温度向量替换为与各插值点关联的局部温度向量。这一改进使模型能够编码局部方向敏感性，从而通过插值构建可扩展的近似核函数及其一阶与二阶导数。此外，该插值方案无需计算核函数导数，便于实现深度核学习（DKL）等扩展。我们在合成基准测试、玩具n体物理模拟、含合成梯度的标准回归数据集以及高维分子力场预测（100-1000维）任务上评估DSoftKI。实验结果表明，DSoftKI在保持精度的同时，能够处理比以往方法更大规模的全导数观测数据集。