Graphs are a convenient representation of high dimensional data that provides access to their geometry and other structures. Many machine learning tasks are formulated as minimizing objective functionals or as dynamical processes on graphs. Such objective functionals and evolutions on graphs have close connections to continuum functionals studied in calculus of variations and to partial differential equations. We will explore connections between the discrete and continuum worlds. In particular we will highlight some of the shared structures, establish properties that of equations on graphs, and indicate some of the differences. Furthermore we will investigate in which regimes are the equations on graphs a good approximation of the continuum PDE.

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