Lennard-Jones
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Learning Permutation-invariant Macroscopic Dynamics
Announce Type: new Abstract: Accurately modeling the macroscopic dynamics of high-dimensional microscopic systems is of broad interest across the sciences. Many data-driven approaches learn a low-dimensional latent state through an autoencoder trained for pointwise input reconstruction. These methods typically assume a fixed ordering of microscopic degrees of freedom in the input.
Learning Permutation-invariant Macroscopic Dynamics
Announce Type: cross Abstract: Accurately modeling the macroscopic dynamics of high-dimensional microscopic systems is of broad interest across the sciences. Many data-driven approaches learn a low-dimensional latent state through an autoencoder trained for pointwise input reconstruction. These methods typically assume a fixed ordering of microscopic degrees of freedom in the input.
Computer-Assisted Proofs for Geometric Optimization: From Crystallization to Carbon Nanotubes
Announce Type: replace Abstract: We present a framework based on computer-assisted proofs that turns geometry optimization simulations for atomistic structures into mathematical proofs. Starting from a numerically computed approximation of a local minimizer or saddle point, we use validated numerical computations to prove the existence of a critical point of the potential energy close to this approximation. We demonstrate this framework in two settings.