基于贝叶斯机器学习的生态模型参数优化方法研究

参数优化方法是准确估计生态模型参数、降低其不确定性的有效手段。本文提出一种基于贝叶斯机器学习的No-U-Turn Sampler（NUTS）生态模型参数优化方法。NUTS是一种高效的参数优化方法,每次取样中利用递归算法生成候选参数集（二叉树）推断参数的后验信息,如果满足约束条件“非U型回转”,不断构建子树更新参数;否则,记录本次抽样的“最优”参数集,并开始下一次取样,直到获取足够样本。该算法在每次取样中充分优化参数,避免因随机游走行为产生冗余抽样,提高了参数优化效率。本文以千烟洲亚热带人工针叶林碳通量模拟为例,基于Pymc3框架利用NUTS参数优化方法实现了碳通量（Net Ecosystem Exchange,NEE）模型参数反演,并与Metropolis-Hastings（MH）方法进行对比。结果表明,本文算法的参数值达到稳定波动时的抽样次数减少了85%左右,参数优化效率提升3倍左右。参数优化后,2种NEE模型中7个参数不确定性降低10%~53%。此外,NEE模拟效果明显提升,模拟值与实测值的R²分别提高23%和17%,RMSE分别降低3%和4%。综上所述,本文提出的参数优化方法对生态领域的参数估计或数据同化工作具有一定的借鉴意义。

Parameters Optimization Method of Ecosystem Model Based on Bayesian Machine Learning

Parameter optimization is an effective means for the accurate estimation of ecosystem model parameters and the reduction of the uncertainty in model predictions. We proposed a method for parameter optimization of the ecosystem model, which is based on the Bayesian machine learning and called No-U-Turn-Sampler (NUTS). As an efficient means of parameter optimization, NUTS uses a recursive algorithm to build a set of candidate points to obtain the posterior information of the parameters. If the constraint condition of “Non-U-Turn” is met, subtrees will be built to update parameters. Otherwise, “the optimal” set of parameters from current sample will be recorded, and then the next sampling begin to run until enough samples are taken. This algorithm avoids sampling redundancy caused by random walk and thus improves the efficiency of parameter optimization. Taking the carbon flux simulations of the Qianyanzhou subtropical coniferous plantation as an example, we implemented the parameter inversion of the carbon flux (Net Ecosystem Exchange, NEE) model using the NUTS method based on the Pymc3 framework. The comparison between the inversion results of NUTS and Metropolis-Hastings (MH) shows that the sampling frequency reduces about 85%, and the optimization efficiency increases about 3 times when the parameter values of the NUTS algorithm reaches convergence. The uncertainties of the seven parameters estimated by NUTS in the two NEE models are reduced by 10%-53% compared to MH. The NEE simulation improved significantly, with the R² between the simulated values and the observed values increased by 23% and 17%, respectively and the RMSE decreased by 3% and 4%, respectively. In sum, the NUTS parameter optimization method proposed in this paper provides an efficient approach for the parameter optimization in ecosystem modeling.