Conformal Prediction for Time-Dependent PDEs
Even arbitrarily small shifts in time can make exact conformal coverage guarantees impossible for PDE surrogate models.
The authors prove that distributions at arbitrarily close times can be mutually singular in a function-space setting. On discretized grids, they show that total variation distance often saturates exponentially fast as resolution increases, requiring restrictions on spatial discretization to preserve coverage. For certain settings, weighted conformal prediction restores finite-sample coverage guarantees over growing time horizons.
ArXiv · AI/CL/LG's note
The authors prove that distributions at arbitrarily close times can be mutually singular in a function-space setting. On discretized grids, they show that total variation distance often saturates exponentially fast as resolution increases, requiring restrictions on spatial discretization to preserve coverage. For certain settings, weighted conformal prediction restores finite-sample coverage guarantees over growing time horizons.
ArXiv · AI/CL/LG's note
score 4