The metric DS Invocations represents the number of Domain Shader invocations. The Domain Shader is invoked once per fixed function tessellator output point.
The SimpleBezier11 sample from the Microsoft* DirectX* SDK is a good example to understand Domain Shaders. This sample renders a Mobius strip comprised of 4 patches with 64 control points per patch.
Increasing the Patch Divisions slider increases the tessellation factors of the Hull Shader which results in and increased number of inputs into the Domain Shader. When the Patch Divisions slider is set to 4.0, the DS Invocations value will be 192. When the Patch Divisions slider is set to 5.0, the DS Invocations value will be 320.
The purpose of a Domain Shader is to calculate the vertex positions for subdivided points output by the fixed function tessellator. The best way to improve performance is to minimize the number of DS Invocations. This can be done by decreasing the amount of tessellation performed by either decreasing the number Hull Shader Invocations or decreasing the tessellation factors in the Hull Shader.