Beyond Static Models: Hypernetworks for Adaptive and Generalizable Forecasting in Complex Parametric Dynamical Systems

TL;DR

This paper introduces PHLieNet, a hypernetwork-based framework that learns to interpolate and extrapolate dynamical system behaviors across parameter spaces, improving forecasting accuracy and capturing long-term dynamics.

Contribution

The work presents a novel hypernetwork architecture that models parametric variability in dynamical systems, enabling smooth interpolation and extrapolation across system parameters.

Findings

Outperforms state-of-the-art baselines in forecast accuracy.

Effectively interpolates in parameter space for unseen dynamics.

Captures long-term features like attractor statistics.

Abstract

Dynamical systems play a key role in modeling, forecasting, and decision-making across a wide range of scientific domains. However, variations in system parameters, also referred to as parametric variability, can lead to drastically different model behavior and output, posing challenges for constructing models that generalize across parameter regimes. In this work, we introduce the Parametric Hypernetwork for Learning Interpolated Networks (PHLieNet), a framework that simultaneously learns: (a) a global mapping from the parameter space to a nonlinear embedding and (b) a mapping from the inferred embedding to the weights of a dynamics propagation network. The learned embedding serves as a latent representation that modulates a base network, termed the hypernetwork, enabling it to generate the weights of a target network responsible for forecasting the system's state evolution conditioned on the previous time history. By interpolating in the space of models rather than observations, PHLieNet facilitates smooth transitions across parameterized system behaviors, enabling a unified model that captures the dynamic behavior across a broad range of system parameterizations. The performance of the proposed technique is validated in a series of dynamical systems with respect to its ability to extrapolate in time and interpolate and extrapolate in the parameter space, i.e., generalize to dynamics that were unseen during training. Our approach outperforms state-of-the-art baselines in both short-term forecast accuracy and in capturing long-term dynamical features such as attractor statistics.