如何让神经网络算法收敛以完成绘图？R代码报错求助

我使用R语言的nnet和neuralnet包进行破产预测，编写并运行了以下代码：

library(nnet)
library(neuralnet)
bank.nnet <- nnet(Bankrupt ~ .,data = test.set, size = 1, maxit = 500, type='class')
prob.nnet = predict(bank.nnet, test.set)
pred.nnet = as.numeric(prob.nnet > 0.06)

table(test.set$Bankrupt, pred.nnet, dnn = c("Observation", "Prediction"))
mean(ifelse(test.set$Bankrupt != pred.nnet, 1, 0))

n=6
bank.nnet.tune <- nnet(Bankrupt ~ ., 
                       size = n, data = train.set, maxit=1000, decay=0.006, linout = TRUE)   
prob.nnet.tune.train = predict(bank.nnet.tune, train.set)
pred.nnet.tune.train = as.numeric(prob.nnet.tune.train > 0.06)
#table(bank.test$DLRSN, pred.nnet.tune.train, dnn = c("Observation", "Prediction"))
table(train.set$Bankrupt, pred.nnet.tune.train, dnn = c("Observation", "Prediction"))
mean(ifelse(train.set$Bankrupt != pred.nnet.tune.train, 1, 0))

#outofsample
prob.nnet.tune = predict(bank.nnet.tune, train.set)
pred.nnet.tune = as.numeric(prob.nnet.tune > 0.06)
table(train.set$Bankrupt, pred.nnet.tune, dnn = c("Observation", "Prediction"))
mean(ifelse(train.set$Bankrupt != pred.nnet.tune, 1, 0))

library(verification)
data$Bankrupt=as.factor(data$Bankrupt)
#roc.plot(bank.test$DLRSN == "1", pred.nnet.tune)

nn <- neuralnet(Bankrupt ~ X1+X2+X3+X4+X5+X6+X7+X8+X9+X10,
                data=train.set,hidden=c(8,1),linear.output=T) 
plot(nn)

运行最后一行plot(nn)时，出现以下警告和错误：

Warning message:
Algorithm did not converge in 1 of 1 repetition(s) within the stepmax.

Error in plot.nn(nn) : weights were not calculated

我尝试将linear.output设置为FALSE，但问题仍未解决，请问如何优化算法使其收敛，从而完成神经网络的绘图？

优化方案及代码调整 #

针对算法不收敛的问题，可以从以下几个维度调整参数和数据处理方式：

1. 数据标准化 #

神经网络对特征尺度极度敏感，先将所有输入特征标准化到统一尺度（如均值为0、方差为1），消除尺度差异对训练的影响：

# 标准化训练集特征（仅针对输入变量）
train_scaled <- train.set
feature_cols <- c("X1","X2","X3","X4","X5","X6","X7","X8","X9","X10")
train_scaled[, feature_cols] <- scale(train_scaled[, feature_cols])

2. 调整神经网络结构 #

当前设置的hidden=c(8,1)属于双隐藏层结构，参数较多易导致收敛困难。先简化为单隐藏层，减少神经元数量：

# 改为单隐藏层，5个神经元
hidden = c(5)

3. 增大迭代步数 #

neuralnet默认的stepmax为100000，若算法未收敛，可手动调大该值，给模型足够的迭代次数：

stepmax = 1e6  # 增大到100万步

4. 调整学习率 #

学习率过大易导致训练震荡，过小则收敛过慢。设置适中的学习率（如0.01）平衡收敛速度与稳定性：

learningrate = 0.01

5. 匹配问题类型设置参数 #

破产预测是二分类问题，需将linear.output设为FALSE，配合合适的激活函数（如tanh或默认的logistic）输出概率值：

linear.output = FALSE
act.fct = "tanh"  # 可选，替换默认的logistic激活函数

修改后的完整训练代码 #

library(neuralnet)

# 数据标准化
train_scaled <- train.set
feature_cols <- c("X1","X2","X3","X4","X5","X6","X7","X8","X9","X10")
train_scaled[, feature_cols] <- scale(train_scaled[, feature_cols])

# 训练优化后的神经网络
nn <- neuralnet(Bankrupt ~ X1+X2+X3+X4+X5+X6+X7+X8+X9+X10,
                data=train_scaled,
                hidden=c(5),
                linear.output=FALSE,
                stepmax=1e6,
                learningrate=0.01,
                act.fct="tanh")

# 绘图
plot(nn)

内容的提问来源于stack exchange，提问作者Emily Paula