用机器学习构建无需正交化的高效密度泛函，提升大体系计算速度。
Surrogate Functionals for Machine-Learned Orbital-Free Density Functional Theory
- 基于密度优化目标设计代理泛函，不依赖能量误差训练。
- 在QM9和QMugs上密度误差优于或媲美现有方法，收敛更快。
- 适合大规模量子体系模拟，尤其关注计算效率的研究者。
我们提出代理泛函：一种基于机器学习的能量泛函，用于无轨域密度泛函理论（OF-DFT）。其定义不追求对物理参考的普遍保真度，仅需确保固定优化流程下能收敛至真实基态密度。训练只需基态密度，无需非基态的能量或梯度。本文提出一种梯度下降改进损失，保证密度指数级收敛，并结合自适应采样策略，聚焦于推理中实际访问的优化轨迹。在QM9和QMugs基准测试中，代理泛函的密度误差达到或超过当前全监督机器学习OF-DFT的最先进水平，且避免了先前方法所需的$O(N^3)$正交化步骤，实现更大体系的更优运行时复杂度。
原文摘要 · Abstract (English)
We introduce surrogate functionals: machine-learned energy functionals for orbital-free density functional theory (OF-DFT) which are defined not by universal fidelity to a physical reference, but merely by the requirement that density optimization with a fixed procedure yields the true ground-state density. Helpfully, training surrogate functionals requires only ground-state densities, no energies or gradients away from the ground state. We here propose a gradient-descent-improvement loss that guarantees exponential convergence of the density to the ground state, and combine it with an adaptive sampling scheme that concentrates learning around the optimization trajectories actually visited during inference. On the QM9 and QMugs benchmarks, surrogate functionals achieve density errors competitive with or improving upon the state of the art for fully supervised machine-learned OF-DFT, while eliminating the need for the $O(N^3)$ orthononormalization step required by prior work, yielding improved runtime scaling for larger systems.
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