Fig. 4: Learned potential energy landscape.
From: Constructing custom thermodynamics using deep learning
a–f, We plot V projected onto the Z1–Z2 (a,d), Z1–Z3 (b,e) and Z2–Z3 (c,f) planes. a–c are contour plots and d–f are surface plots to visualize the landscape. Insets: stable and unstable directions of the saddle points, corresponding to positive (top left inset) and negative (bottom right inset) Z3 values. Projection is computed via minimization (for example, \(V({Z}_{1},{Z}_{2})=\mathop{\min }\limits_{{Z}_{3}}V({Z}_{1},{Z}_{2},{Z}_{3})\)), which at low temperatures closely approximates marginalizing with respect to the Boltzmann distribution. The stable and saddle points are marked on the energy landscape, and their corresponding reconstructed fully extended and folded states are shown. A pair of each exists due to reflection symmetry in the flow direction. Example ‘fast’ (red) and ‘slow’ (blue) trajectories from the training dataset are overlaid on the landscape. The fast trajectory avoids the saddle points and goes directly towards a stable minimum, whereas the slow trajectory gets trapped for long times near saddle 2, before finally escaping through its unstable manifold. For b and e, the stable manifolds of the saddles closely align with Z2, and hence are not visible due to minimization (marginalization). g–i, Scatterplots in the Z1–Z2 (g), Z1–Z3 (h) and Z2–Z3 (i) planes, together with predicted isotherms (solid lines) capturing typical fluctuations around a fully stretched state Zstable,1. Insets: magnified views of the fluctuating trajectories around the stretched state over the energy landscape.
