Analytic Gaussian Convolution for Faster Molecular Optimization and Sampling

For macromolecular structure optimization over internal torsion angles, the rugged, highly non-convex Lennard–Jones (LJ) potential poses a major obstacle. Our novel contribution lies in applying analytic Gaussian convolution to the LJ potential as a linear, shift-invariant smoothing operator that uniquely guarantees monotonic reduction of non-convexity without introducing new extrema. By deriving closed-form radial integrals and exact gradients in $\mathbb{R}^{3N}\$, our method enables efficient, rotation- and translation-invariant smoothing. Across systems of 3 to 500 particles, we observe up to a 56\% reduction in the optimization gap to the global minimum and over 75\% closure of the sampling gap in toy benchmarks, translating into orders-of-magnitude higher probabilities of visiting near-optimal configurations. This framework opens a new avenue for scaling advanced neural samplers in biomolecular modeling.