标题： 用于Dynare中高维模型的可扩展全局求解技术 显示英文标题

标题： Scalable Global Solution Techniques for High-Dimensional Models in Dynare

摘要： 自三十年前以来，Dynare一直是经济学中动态随机建模的核心工具，主要依赖于基于摄动的局部求解方法。 然而，这些技术在高维、非线性模型中常常失效，需要更全面的方法。 本文表明，通过将自适应稀疏网格（SGs）和高维模型表示（HDMR）引入Dynare，可以准确且快速地计算具有显著异质性和摩擦的经济模型的全局解。 SGs缓解了维度灾难，因为网格点的数量增长比传统张量积笛卡尔网格要慢得多。 此外，自适应性将网格细化集中在梯度陡峭或不可微区域，提高了计算效率。 作为SGs的补充，HDMR通过用低维项的分层展开近似政策函数来处理大的状态空间。 我们使用时间迭代算法，在一个国际实际商业周期模型上对我们的方法进行了基准测试。 我们的结果表明，SGs和HDMR都能缓解维度灾难，使得在标准硬件上相对短时间内就能得到至少100维模型的准确解。 这一进展使Dynare的功能超越了摄动方法，建立了一个多功能平台，用于复杂的非线性模型，并为整合最新的全局求解方法（如机器学习方法）铺平了道路。 显示英文摘要

摘要： For over three decades, Dynare has been a cornerstone of dynamic stochastic modeling in economics, relying primarily on perturbation-based local solution methods. However, these techniques often falter in high-dimensional, non-linear models that demand more comprehensive approaches. This paper demonstrates that global solutions of economic models with substantial heterogeneity and frictions can be computed accurately and swiftly by augmenting Dynare with adaptive sparse grids (SGs) and high-dimensional model representation (HDMR). SGs mitigate the curse of dimensionality, as the number of grid points grows significantly slower than in traditional tensor-product Cartesian grids. Additionally, adaptivity focuses grid refinement on regions with steep gradients or non-differentiabilities, enhancing computational efficiency. Complementing SGs, HDMR tackles large state spaces by approximating policy functions with a hierarchical expansion of low-dimensional terms. Using a time iteration algorithm, we benchmark our approach on an international real business cycle model. Our results show that both SGs and HDMR alleviate the curse of dimensionality, enabling accurate solutions for at least 100-dimensional models on standard hardware in relatively short times. This advancement extends Dynare's capabilities beyond perturbation approaches, establishing a versatile platform for sophisticated non-linear models and paving the way for integrating the most recent global solution methods, such as those from machine learning.