Neural Networks Struggle with Out-of-Distribution Physical Rule Learning.

Neural networks are increasingly employed to deduce underlying physical structures from observed dynamic data. However, a critical question remains: does their performance on unseen, out-of-distribution data truly reflect an understanding of transferable physical rules? This research addresses this by examining the inverse problem of reconstructing interaction graphs in a kinetic Ising model using magnetization trajectories. The study evaluated various neural architectures, including convolutional, graph, Transformer, and hybrid models. It revealed that data-driven training leads to distinct and consistent statistical strategies when faced with shifts in topology or temperature. For instance, Transformer-based models tended to maintain the link density observed in their training data, while convolutional models often collapsed to sparse or no-link predictions, appearing robust by exploiting the prevalence of no-link classes. These findings suggest that achieving high accuracy on training data and seemingly robust performance on out-of-distribution data does not necessarily mean the network has learned the underlying dynamics-to-structure rule. Instead, the reconstruction process can be heavily influenced by statistical priors inherent to the specific neural network architecture. This highlights a significant failure mode in standard data-driven learning for physical inverse problems and underscores the need for rule-guided principles in machine learning for scientific discovery.