Regularization parameter selection (RPS) is one of the most important tasks in solving inverse problems. The most common approaches seek the optimal regularization parameter (ORP) from a sequence of candidate values. However, these methods are often time-consuming because they need to conduct the estimation process on all candidate values, and they are always restricted to solve certain problem types. In this paper, we propose a novel machine learning-based prediction framework (MLBP) for the RPS problem. The MLBP first generates a large number of synthetic data by varying the inputs with different noise conditions. Then, MLBP extracts some pre-defined features to represent the input data and computes the ORP of each synthetic example by using true models. The pairs of ORP and extracted features construct a training set, which is used to train a regression model to describe the relationship between the ORP and input data. Therefore, for newly practical inverse problems, MLBP can predict their ORPs directly with the pre-trained regression model, avoiding wasting computational resources on improper regularization parameters. The numerical results also show that MLBP requires significantly less computing time and provides more accurate solutions for different tasks than traditional methods. Especially, even though the MLBP trains the regression model on synthetic data, it can also achieve satisfying performance when directly applied to field data.

正则化参数选择（RPS）是解决逆问题中最重要的任务之一。最常见的方法是从一系列候选值中寻求最佳正则化参数（ORP）。但是，这些方法通常很耗时，因为它们需要对所有候选值进行估计过程，并且始终受限于解决某些问题类型。在本文中，我们针对RPS问题提出了一种新颖的基于机器学习的预测框架（MLBP）。MLBP首先通过改变具有不同噪声条件的输入来生成大量合成数据。然后，MLBP提取一些预定义的特征来表示输入数据，并使用真实模型计算每个综合示例的ORP。成对的ORP和提取的特征构成训练集，它用于训练回归模型来描述ORP和输入数据之间的关系。因此，对于新出现的实际反问题，MLBP可以使用预训练的回归模型直接预测其ORP，避免将计算资源浪费在不正确的正则化参数上。数值结果还表明，与传统方法相比，MLBP需要更少的计算时间，并为不同任务提供了更准确的解决方案。特别是，即使MLBP在合成数据上训练回归模型，当直接应用于现场数据时，它也可以实现令人满意的性能。避免将计算资源浪费在不正确的正则化参数上。数值结果还表明，与传统方法相比，MLBP需要更少的计算时间，并为不同任务提供了更准确的解决方案。特别是，即使MLBP在合成数据上训练回归模型，当直接应用于现场数据时，它也可以实现令人满意的性能。避免将计算资源浪费在不正确的正则化参数上。数值结果还表明，与传统方法相比，MLBP需要更少的计算时间，并为不同任务提供了更准确的解决方案。特别是，即使MLBP在合成数据上训练回归模型，当直接应用于现场数据时，它也可以实现令人满意的性能。