让我震惊：利用稀疏微分以O(N)时间从局部MLIP精确计算分子Hessian矩阵！
Colour me shocked: Exact Molecular Hessians from local MLIPs in O(N) time using sparse differentiation!
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- University of Toronto（多伦多大学）
- Vector Institute for Artificial Intelligence（Vector人工智能研究所）
- Acceleration Consortium（加速联盟）
- Canadian Institute for Advanced Research（加拿大高级研究院）
- NVIDIA（英伟达）
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中文总结 AI 辅助
本文提出利用闭式稀疏模式和稀疏自动微分，将局部机器学习原子间势的Hessian计算成本降至O(N)，在烷烃链、水团簇及Aβ40等体系上实现2-15倍加速，使蛋白质等大体系的高精度Hessian计算成为可能。
中文摘要 AI 辅助
能量相对于核位置的Hessian矩阵在原子建模中不可或缺。然而，构建该矩阵需要O(N)次Hessian向量积，传统上限制了高精度Hessian计算只能用于小体系。机器学习原子间势（MLIPs）通过以O(N)成本提供高精度的能量和力，加速了原子建模，但由此产生的O(N^2)成本的Hessian计算仍是大体系的实际瓶颈。基于我们可以闭式推导MLIP的Hessian稀疏模式这一见解，本文展示了如何利用稀疏自动微分技术，将局部MLIP的Hessian计算成本降低到与体系大小无关的Hessian向量积次数，从而在不作任何近似的情况下实现总体O(N)的总成本。我们在从烷烃链到水团簇再到Aβ40构象体的多种体系上对我们的方法进行了基准测试。根据MLIP配置的不同，我们已在相对较小的体系上实现了线性标度区域，从而为这些体系带来了2倍至15倍的大幅运行时间缩减。这为将高精度MLIP Hessian计算扩展到非常大的体系（如以前无法触及的蛋白质）开辟了可能性。
英文摘要
The Hessian of the energy with respect to the nuclear positions is indispensable in atomistic modelling. However, constructing this matrix requires $O(N)$ Hessian vector products, traditionally limiting high-accuracy Hessians to small systems. Machine learning interatomic potentials (MLIPs) have accelerated atomistic modelling by providing highly accurate energies and forces at $O(N)$ cost, yet the resulting $O(N^2)$ cost of Hessians remains a practical bottleneck for large systems. Based on the insight that we can derive the sparsity pattern for an MLIP's Hessians in closed form, we show in this paper how to use techniques from sparse automatic differentiation to reduce the cost of a local MLIP's Hessians to a system-size-independent number of Hessian-vector products, yielding overall $O(N)$ total cost without any approximations. We benchmark our approach on a variety of systems ranging from alkane chains to water clusters to $A\beta40$ conformers. Depending on the MLIP configuration, we achieve the linear scaling regime already on relatively small systems, resulting in large runtime reductions between 2$\times$-15$\times$ for these systems. This opens up the possibility of scaling high-accuracy MLIP Hessians to very large systems, such as proteins that were previously inaccessible.
