Early-warning the compact-to-dendritic transition via spatiotemporal learning of two-dimensional growth images

TL;DR

This paper develops a spatiotemporal deep learning approach to predict the transition from compact to dendritic growth in electrodeposition, enabling early warnings of morphological instabilities in nonequilibrium systems.

Contribution

It introduces an end-to-end learning framework that jointly captures spatial and temporal features from growth images to forecast morphological transitions.

Findings

End-to-end spatiotemporal learning improves prediction accuracy.

A low-dimensional surrogate variable tracks destabilization.

Transferability of the model is limited across different reaction rates.

Abstract

Transitions between distinct dynamical regimes are ubiquitous in nonequilibrium systems. As a prototypical example, deposition growth is often accompanied by irreversible morphological instabilities. Forecasting such transitions from pre-transition configurations remains fundamentally challenging, as early precursors are weak, spatially heterogeneous, and masked by inherent fluctuations. Here, we investigate compact-to-dendritic transitions (CDTs) in a two-dimensional particle-based electrodeposition model and formulate a horizon-based early-warning task using trajectory-resolved transition points. We demonstrate that anticipating the CDT is intrinsically a spatiotemporal problem: neither static morphological descriptors nor temporal learning applied to predefined features alone yields reliable predictive signals. In contrast, end-to-end learning of jointly optimized spatial and temporal representations from growth images enables robust anticipation across a wide range of prediction horizons. Analysis of the learned latent dynamics reveals the emergence of a low-dimensional surrogate variable that tracks progressive morphological destabilization and undergoes reorganization near the transition. We further show that the learned spatiotemporal representation exhibits limited but systematic transferability across reaction-rate conditions, with predictive performance degrading as the inference condition departs from the training condition, consistent with changes in the latent-state dynamics. Overall, our results establish a general formulation for forecasting incipient instabilities in nonequilibrium interfacial growth, with implications for the predictive monitoring and control of pattern-forming driven systems.