Speaker
Description
Lagrangian Neural Networks (LNNs) learn mechanical systems directly from trajectory data by parameterizing a scalar Lagrangian and deriving the dynamics through the Euler-Lagrange equations, so that the learned model is strongly biased toward motion that respects the variational structure of mechanics. The interactions studied in this way have so far been pairwise-additive, leaving open whether LNNs can recover an irreducible many-body interaction from motion alone. We investigate this question using the Axilrod-Teller triple-dipole interaction, the leading three-body dispersion contribution, whose dependence on the collective geometry of three particles cannot be represented by any sum of pairwise interactions. Our strategy is to prescribe the kinetic energy exactly and learn only the potential as an unknown function of symmetry-preserving geometric features comprising interparticle distances and angles. Together with a signal-adaptive sampling strategy that concentrates training data where the three-body signal is strongest while preserving coverage of the broader configuration space, we recover the interaction from acceleration observations alone. The learned potential accurately reproduces the radial scaling, angular dependence, and characteristic sign reversal of the Axilrod-Teller interaction, and generates stable trajectories. Embedding this interaction within the standard pairwise Lennard-Jones potential further lets us quantify its observability. The three-body contribution is recovered once its dynamical signature rises above the residual modeling error, and we bracket this transition between the two couplings, recovering it cleanly at amplified coupling while finding it drops below the error floor at the coupling characteristic of a real noble gas. These results demonstrate that LNNs are capable of recovering irreducible three-body interactions directly from trajectory data when their dynamical signature is sufficiently strong, extending their demonstrated capabilities beyond previously studied pairwise-additive systems.