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===Reduction of dynamical models===

===Dynamical model reduction===

An important indicator of causal emergence is the selection of coarse-graining strategies. When the microscopic model is known, coarse-graining the microscopic state is equivalent to performing a '''model reduction''' on the microscopic model. Model reduction is an important subfield in control theory. Antoulas once wrote a related review article <ref name=":15">Antoulas A C. An overview of approximation methods for large-scale dynamical systems[J]. Annual reviews in Control, 2005, 29(2): 181-190.</ref>.

An important indicator of causal emergence is the selection of coarse-graining strategies. When the microscopic model is known, coarse-graining the microscopic state is equivalent to performing a '''model reduction''' on the microscopic model. Model reduction is an important subfield in control theory. Antoulas once wrote a related review article about model reduction for large-scale dynamical systems <ref name=":15">Antoulas A C. An overview of approximation methods for large-scale dynamical systems[J]. Annual reviews in Control, 2005, 29(2): 181-190.</ref>.