We present the performances of our mathematical deep learning (MathDL) models for D3R Grand Challenge 4 (GC4). This challenge involves pose prediction, affinity ranking, and free energy estimation for beta secretase 1 (BACE) as well as affinity ranking and free energy estimation for Cathepsin S (CatS). We have developed advanced mathematics, namely differential geometry, algebraic graph, and/or algebraic topology, to accurately and efficiently encode high dimensional physical/chemical interactions into scalable low-dimensional rotational and translational invariant representations. These representations are integrated with deep learning models, such as generative adversarial networks (GAN) and convolutional neural networks (CNN) for pose prediction and energy evaluation, respectively. Overall, our MathDL models achieved the top place in pose prediction for BACE ligands in Stage 1a. Moreover, our submissions obtained the highest Spearman correlation coefficient on the affinity ranking of 460 CatS compounds, and the smallest centered root mean square error on the free energy set of 39 CatS molecules. It is worthy to mention that our method on docking pose predictions has significantly improved from our previous ones.

中文翻译：

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MathDL：D3R Grand Challenge 4 的数学深度学习。


我们展示了我们的数学深度学习 (MathDL) 模型在 D3R Grand Challenge 4 (GC4) 中的表现。该挑战涉及 β 分泌酶 1 (BACE) 的姿势预测、亲和力排名和自由能估计，以及组织蛋白酶 S (CatS) 的亲和力排名和自由能估计。我们开发了高等数学，即微分几何、代数图和/或代数拓扑，以准确有效地将高维物理/化学相互作用编码为可扩展的低维旋转和平移不变表示。这些表示与深度学习模型集成，例如分别用于姿态预测和能量评估的生成对抗网络（GAN）和卷积神经网络（CNN）。总体而言，我们的 MathDL 模型在第 1a 阶段的 BACE 配体姿势预测中名列前茅。此外，我们提交的材料在 460 个 CatS 化合物的亲和力排名上获得了最高的 Spearman 相关系数，在 39 个 CatS 分子的自由能集上获得了最小的中心均方根误差。值得一提的是，我们的对接姿势预测方法比之前的方法有了显着改进。