Speaker
Description
Instability-driven pattern formation appears across many nonequilibrium systems, from nanoscale surfaces to larger-scale natural patterns. In the ion-beam community, decades of experiments have revealed a rich variety of surface morphologies, from ripples and dots to faceted structures, and continuum theories can reproduce many of these patterns qualitatively. Yet turning a continuum equation into a quantitatively predictive tool for a specific experiment remains difficult. The evolution laws assume competing mechanisms, such as curvature-dependent erosion, mass redistribution, diffusion, and step-edge barriers, whose strengths are hard to disentangle from sparse, noisy, and misregistered ex situ measurements. Physics-informed neural networks (PINNs) offer a route to closing this theory-experiment gap.
Here, we present an inverse solver that couples a PINN, that recovers the surface dynamics, with a tandem network that accounts for the measurement model. Specifically, we demonstrate the method using just six ex situ atomic force microscopy snapshots of an unstable Ge surface under ion irradiation. The method recovers the full nonlinear evolution equation and turns it into a quantitatively predictive tool. The response of unseen surfaces to ion irradiation can now be predicted with nanometre accuracy. The inferred model can be interpolated beyond the measured spatiotemporal resolution, revealing the continuous transition between experimental snapshots and approaching atomic-scale detail consistent with electron microscopy. Finally, we discuss what these results imply for predictive modelling of instabilities and for bridging experiments with predictive continuum models.