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I am trying

DensityPlot[output, {input1, 0.41, 1.16}, {input2, -0.4, 0.37}, 
  ColorFunction -> "SunsetColors", 
  PlotLegends -> Automatic, 
  Mesh -> 16, 
  AxesLabel -> {"input1", "input2"}]

but the addition of AxesLabel -> {"input1", "input2"} does not label the axes as usual, is there an alternative way or am I doing something wrong?

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Use FrameLabel instead. AxesLabel requires the origin to be present (and Axes -> True if you move the origin with AxesOrigin, unless AxesLabel -> Automatic).

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