Fig. 1
From: A continuous-time MaxSAT solver with high analog performance
MaxSAT solver dynamics. The Max 3-SAT formula used here has N = 10, M = 80 (clauses given in the Supplementary Data 1). a The potential V, b the radius \(R = \sqrt {\mathop {\sum}\nolimits_i {\kern 1pt} s_i^2}\), and c the number of unsatisfied clauses (energy) E as function of analog time t for the original dynamics corresponding to b = 0 (red) and the modified dynamics with b = 0.0725 (black). d–g Colormaps of the potential V(s(t), a(t)) in the plane (s1, s2). At a given time instant t we fix all values sj(t), j = 3, …, N and am(t), ∀m and change only s1, s2 in the [−1, 1] × [−1, 1] plane, showing the instantaneous potential energy landscape V in this plane. The curves indicate the projection of the trajectory onto (s1, s2) up to the indicated time t. In t = 0, s1 = s2 = −1. For b = 0, the dynamics converges to s = 0, which is the centre of a deep well in the potential landscape. For b = 0.0725, the centre is not a minimum anymore and at time t = 10 the orthant with minimal energy Emin = 3 is found (the solution), shown as a blue dotted line in the E(t) figure
