Fig. 3: Comparing predictions at 200ns for different values of the symmetry parameter κ.
From: Path sampling of recurrent neural networks by incorporating known physics
Here we show that ps-LSTM learns the correct symmetry κ. The original training data is a 20ns Aib9 trajectory generated from MD simulation at 500K, where (a) shows its calculated free energy profile has an asymmetry of population between L and R helix states. The snapshots of L and R configurations at χ = 5.2 and χ = − 5.31 are also displayed as insets above the free energy profile. Training LSTM model with this asymmetric data and using it to predict what would happen at 200ns leads to the result shown in (b), where the LSTM predictions retain and even enhance the undesired free energy asymmetry while the free energies calculated from a longer 200ns trajectory shows the desired symmetric profile. In (c), we show that ps-LSTM trained as described in Section ”Equilibrium constraint on Aib9” can not only predict the correct symmetry, but also deviate less from the true free energy calculated from the reference 200ns data. The table in (d) shows the κ values defined in Eq. (9) for different trajectories. The free energy profiles and the κ values in (b) and (c) are averaged over 10 independent training processes. The corresponding error bars are calculated as standard errors and filled with transparent colors.
