The field of dynamic modeling and physics-informed learning is rapidly advancing, with a focus on developing innovative methods for efficient and accurate modeling of complex systems. Recent developments have seen a shift towards the integration of machine learning and physics-based approaches, enabling the discovery of underlying governing equations and the modeling of high-dimensional systems. Notably, the use of neural networks and deep learning algorithms has improved the efficiency and accuracy of dynamic modeling, particularly in cases where data is limited or noisy. Furthermore, the development of hierarchical and graph-based methods has enabled the modeling of complex motion hierarchies and the discovery of interpretable motion relationships.

Some noteworthy papers in this area include: TRASE-NODEs, which proposes a trajectory-sensitivity-aware approach for efficient dynamic modeling. Hierarchical Physics-Embedded Learning, which introduces a two-level architecture for forward spatiotemporal prediction and inverse discovery of physical laws. Neural Stochastic Flows, which enables solver-free modeling and inference for SDE solutions. Curly Flow Matching, which learns non-gradient field dynamics by designing and solving a Schrödinger bridge problem. HEIR, which learns graph-based motion hierarchies and provides an adaptable, data-driven hierarchical modeling paradigm.