HyperODE Offers Zero-Shot Simulation and Inference for Dynamical Systems

Understanding and controlling complex dynamical systems often requires extensive numerical simulations, which are computationally intensive, especially when exploring vast parametric landscapes. Existing machine learning surrogates accelerate simulations but are typically specialized to a single model, requiring costly retraining if the underlying differential equations change. To address this, researchers developed HyperODE, a novel zero-shot surrogate model designed to operate across entire classes of approximately mass-conserving compartmental models without the need for retraining. HyperODE achieves this by mapping the structure of ordinary differential equations (ODEs) into directed hypergraphs, effectively decoupling the functional form of system interactions from the neural network architecture. HyperODE takes an ODE with an arbitrary parameter distribution and transforms it into a hypergraph, outputting the distribution of state trajectories as quantiles. This surrogate can then be used to build an encoder that calibrates the model by taking a noisy trajectory and outputting a parameter distribution in a single pass. The model performs competitively with specialized surrogates on unseen families and system sizes, and can extend to ODEs that break mass conservation or include external forcing, offering rapid simulation and inference in milliseconds.