论文标题
部分可观测时空混沌系统的无模型预测
Approximate Bayesian Computation Based on Maxima Weighted Isolation Kernel Mapping
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
Motivation: A branching processes model yields an unevenly stochastically distributed dataset that consists of sparse and dense regions. This work addresses the problem of precisely evaluating parameters for such a model. Applying a branching processes model to an area such as cancer cell evolution faces a number of obstacles, including high dimensionality and the rare appearance of a result of interest. We take on the ambitious task of obtaining the coefficients of a model that reflects the relationship of driver gene mutations and cancer hallmarks on the basis of personal data regarding variant allele frequencies. Results: An approximate Bayesian computation method based on Isolation Kernel is developed. The method involves the transformation of row data to a Hilbert space (mapping) and the measurement of the similarity between simulated points and maxima weighted Isolation Kernel mapping related to the observation point. We also design a heuristic algorithm for parameter estimation that requires no calculation and is dimension independent. The advantages of the proposed machine learning method are illustrated using multidimensional test data as well as a specific example focused on cancer cell evolution.
