Learning theory for inferring interaction kernels in second-order interacting agent systems
Learning theory for inferring interaction kernels in second-order interacting agent systems
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DOI：
10.1007/s43670-023-00055-9
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发表时间：
2020-10
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影响因子：
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通讯作者：
Jason Miller;Sui Tang;Ming Zhong;M. Maggioni
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文献类型：
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作者：
Jason Miller;Sui Tang;Ming Zhong;M. Maggioni
对粒子或代理系统的复杂相互作用进行建模是从物理学和生物学到经济学和社会科学的一个基本问题。在这项工作中，我们考虑二阶，异构，多变量模型的相互作用剂或粒子，在简单的环境。我们描述了一个非参数推理框架，以有效地估计潜在的相互作用内核驱动这些动态系统。我们开发了一个学习理论，建立强一致性和最佳的非参数最小-最大收敛率的估计，以及可证明准确的预测轨迹。最优速率仅取决于相互作用的内在维度，其通常远小于环境维度。我们的论点是基于一个bavity条件，确保相互作用内核可以估计在稳定的方式。建立估计的数值算法是可并行的，在高维问题上表现良好，其性能在各种复杂的动力系统上进行了测试。
Modeling the complex interactions of systems of particles or agents is a fundamental problem across the sciences, from physics and biology, to economics and social sciences. In this work, we consider second-order, heterogeneous, multivariable models of interacting agents or particles, within simple environments. We describe a nonparametric inference framework to efficiently estimate the latent interaction kernels which drive these dynamical systems. We develop a learning theory which establishes strong consistency and optimal nonparametric min–max rates of convergence for the estimators, as well as provably accurate predicted trajectories. The optimal rates only depends on intrinsic dimension of interactions, which is typically much smaller than the ambient dimension. Our arguments are based on a coercivity condition which ensures that the interaction kernels can be estimated in stable fashion. The numerical algorithm presented to build the estimators is parallelizable, performs well on high-dimensional problems, and its performance is tested on a variety of complex dynamical systems.