Tensor network methods provide a scalable solution to represent high-dimensional data. However, their efficacy is often limited by static, expert-defined structures that fail to adapt to evolving data correlations. We address this limitation by formalizing the tensor network structural rounding problem and introducing the hierarchical structure search algorithm HISS, which automatically identifies near-optimal structures and index reshaping for arbitrary tree networks. To navigate the combinatorial explosion of the structural search space, HISS integrates stochastic sub-network sampling with hierarchical refinement. This approach utilizes entropy-guided index clustering to reduce dimensionality and targeted reshaping to expose latent data correlations. Numerical experiments on analytical functions and real-world physics applications, including thermal radiation transport, neutron diffusion, and computational fluid dynamics, demonstrate that HISS exhibits empirical polynomial scaling with dimensionality relative to the sampling budget, bypassing the scalability barriers in prior work. HISS achieves compression ratios $2.5\times$ to $100\times$ higher than standard fixed formats such as Tensor Trains and Hierarchical Tuckers~(peaking at $1000\times$). Furthermore, HISS discovers structures that generalize effectively: applying a structure optimized for one data instance to a related target data typically maintains compression performance within $10\%$ of the result obtained by performing structure search on that target data. These results highlight HISS as a robust, automated tool for adaptive data representation and high-dimensional simulation compression with tensor network methods.

翻译：张量网络方法为高维数据的表示提供了一种可扩展的解决方案。然而，其有效性常常受限于静态的、由专家定义且无法适应数据关联动态变化的结构。为解决此问题，我们形式化了张量网络结构舍入问题，并引入了层级化结构搜索算法HISS，该算法能自动为任意树形网络识别近乎最优的结构和指标重塑方案。为应对结构搜索空间中组合爆炸的挑战，HISS将随机子网络采样与层级化精炼相结合。该方法利用熵引导的指标聚类来降低维度，并通过有针对性的重塑来揭示潜在的数据关联。在解析函数以及包含热辐射输运、中子扩散和计算流体动力学在内的实际物理应用上的数值实验表明，相对于采样预算，HISS的经验计算复杂度随维度呈多项式增长，从而突破了先前工作中存在的可扩展性瓶颈。与张量列车、层级化Tucker等标准固定格式相比（后者最高可达1000倍），HISS所能实现的压缩比高出2.5倍至100倍。此外，HISS发现的结构具有良好的泛化能力：将通过优化一个数据实例获得的结构应用于相关目标数据，其压缩性能通常可维持在直接对目标数据进行结构搜索结果性能的10%以内。这些结果凸显了HISS作为稳健自动化工具，在张量网络方法中用于自适应数据表示和高维仿真压缩的价值。