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> ...unstable singularities are exceptionally elusive; they require initial conditions tuned with infinite precision, being in a state of instability whereby infinitesimal perturbations immediately divert the solution from its blow-up trajectory.

Can one "find" an unstable singularity if writing it down requires an endless computational process to produce the incremental digits as one marches towards infinite precision? It sounds like chasing a set of measure zero.

Anyone have an ELI5? I can't quite put my finger on what's happening here. It sounds like the PINNs are being used as fancy discrete basis functions to solve similarity transformed fluid equations so they can chase the unstable solutions comprising a set of measure zero. I don't know how one thinks about grid convergence in these settings. Does one need PINNs or could traditional discretization approaches accomplish the same?