AI 中文总结
本文提出薛定谔生成器框架，通过分解雅可比结合自适应映射与归一化流变换，实现高维积分采样，在600维以上核量子多体态上表现稳定，可准确复现核子短程关联，为复杂量子系统模拟提供新途径。
AI 中文摘要
高维积分与采样是现代科技的核心挑战之一，支撑着从量子多体物理到贝叶斯推理、人工智能的各类应用。尽管传统蒙特卡洛方法在形式上具备可扩展性，但当高维构型空间中存在强关联或尖锐特征时，其效率会迅速下降。本文提出一种名为薛定谔生成器的新框架，用于基于坐标变换显式优化的积分与采样。该方法将总雅可比分解为两个互补分量：一是通过学习各维度边缘结构最小化估计量方差的自适应映射，二是捕捉目标分布中不可分解关联的基于归一化流的变换。最终的重采样步骤确保即使学习到的变换存在缺陷，仍能生成无偏样本。我们在维度超过600的核量子多体态上验证了该方法的稳定可扩展性能，准确复现了有限核内核子间的短程关联。该框架为高维随机积分与采样提供了物理上可解释的方法，为复杂量子系统的模拟开辟了新可能。
英文摘要
Integration and sampling in high dimensions are among central challenges in modern science and technology, underlying applications ranging from quantum many-body physics to Bayesian inference and artificial intelligence. Although conventional Monte Carlo methods are formally scalable, their efficiency deteriorates rapidly in the presence of strong correlations or sharp features in high-dimensional configuration space. Here we introduce a new framework, termed the Schr"odinger Generator, for integration and sampling based on the explicit optimization of coordinate transformations. The method decomposes the total Jacobian into two complementary components, including an adaptive map that minimizes estimator variance by learning the marginal structure in each dimension, and a normalizing-flow-based transformation that captures non-factorizable correlations in the target distribution. A final resampling step guarantees unbiased sampling even when the learned transformation is imperfect. We demonstrate stable and scalable performance for nuclear quantum many-body states in dimensions exceeding 600. Short-range correlations among nucleons in finite nucleus are faithfully reproduced. The framework offers a physically transparent approach to high-dimensional stochastic integration and sampling, opening new possibilities for simulations of complex quantum systems.
Comments10 pages, 5 figures
