Figure 5
From: Investigating molecular transport in the human brain from MRI with physics-informed neural networks
Adaptive training point refinement is needed to fulfill the PDE in all timepoints. (a) Average PDE residual in \(\Omega _P\) over time for different optimization schemes. Vertical lines (dashed) indicate the times where data is available. In all cases, the learning rate decays exponentially from \(10^{-3}\) to \(10^{-4}\). (b,c) Distribution of PDE points during training with RAR (b) and RAE (c). Starting from a uniform distribution of points (in time), more points are added at 7, 24 and 46Â h where data is available.
