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Scaling back the output of neural network (ANN) for multivariate regression?

I do not have any background in machine learning and neural network. I have a panda dataframe in python where one variable is an unknown function of other independent variables: output = func(input1, input2, ...). So when I plot the output vs any of the output I get a scatter plot without any clear relation between the output and input. So I use ANN to try to find the relation.

I have this code:

from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler, MinMaxScaler, Normalizer, RobustScaler
from sklearn.neural_network import MLPRegressor

X = Data[['input1','input2','input3','input4','input5','input6']].values
y = Data[['output']].values

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.15)

scaler = StandardScaler()
scaler.fit(X_train)
X_train_scaled = scaler.transform(X_train)
X_test_scaled = scaler.transform(X_test)

mlp = MLPRegressor(alpha = 1e-5, hidden_layer_sizes = (50,50,50), max_iter = 5000)
mlp.fit(X_train_scaled,y_train)
predictions = mlp.predict(X_test_scaled)
plt.scatter(X_train[:,0], y_train, color = 'green') %column 0 refers to input1
plt.scatter(X_test[:,0], y_test, marker='^', color = "blue")
plt.scatter(X_test[:,0], predictions, marker='x', color = "red")


The output of the code is how the output changes as input1 (and all the other inputs) change:

Green dots show the training dataset, blue triangles the test dataset, and the red marks show what I get from ANN.

The plot is not bad considering that I am new and the code is relatively simple. In the plot, I used the un-scaled (or scaled back) input on x-axis and scaled predictions on y-axis. The question that I have is if I should scale back the predictions or not.
If I use scaled data as input, there will be a horizontal shift in the data represented by the red marks and the plot wont look correct.
If I try to scale back the predictions, I get an error in this case since I have several inputs and only one output so the dimensions do not match. If I only use one input variable, the dimensions match and I do not get any errors, but the red marks in the plot shifts vertically significantly.

Even when I do not scale back the predictions (well, as I said I can't do that anyways in this case even if I want to) still there can be some red marks that are not within the expected bounds.

What should I do here regarding the scaling back (or anything in general) in order to get better results than what is shown in the plot?
Also I would like to know what metrics are available to determine the performance of ANN for regression problems so I don't have to visually inspect the plots (I have too many data and plots)

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