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Miscellaneous

Understanding solver logs

The nonlinear solver will log a debug message per iteration with some useful information. Take the following example log:

[polyfem] [debug] [Newton] iter=51 f=-1.06006e-06 ||∇f||=0.006432 ||Δx||=0.0037612 Δx⋅∇f(x)=-6.71732e-08 g=9.69072e-05 tol=1e-05 rate=0.0321861 ||step||=0.000121058

The terms in order they appear are:

  • iter: the iteration number
  • f: the value of the objective function
  • ||∇f||: the \(L^2\)-norm of the gradient of f
  • ||Δx||: the \(L^2\)-norm of the update direction to our optimization variables (e.g., displacements/positions for elasticity)
  • Δx⋅∇f(x): the dot product between these values (this is a measure of how much progress we can expect the optimization can make)
  • g: the convergence criteria (i.e., the optimization stops when g < tol); this depends on the choice of "useGradNorm" solver parameter (for more information see here)
  • tol: the convergence criteria tolerance
  • rate: the step size the line-search produced (i.e. \(x_{i+1} = x_i + \text{rate} * \Delta x\))
  • ||step||: the L2 norm of the step (i.e. \(\|\text{rate} * \Delta x\| = \text{rate} * \|\Delta x\|\))
Last update: 2023-10-03