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

2025-06-24

AI Summary

To address poor generalization in parametric dynamical systems caused by parameter variability, this paper proposes PHLieNet—a physics-informed hypernetwork framework. PHLieNet learns a nonlinear embedding of the parameter space via a hypernetwork and dynamically generates weights for a Lie group–based physical propagation network, enabling adaptive prediction across diverse parameter configurations. Crucially, it performs interpolation in model weight space—not observation space—thereby supporting smooth cross-parameter transfer and robust extrapolation/interpolation. The framework unifies parameter-conditioned weight generation, nonlinear parameter embedding learning, and sequential modeling to construct a tunable foundational dynamics network. Evaluated on canonical parametric systems—including Lorenz-96 and Kuramoto–Sivashinsky equations—PHLieNet achieves state-of-the-art or competitive performance in both short-term forecasting accuracy and long-term statistical fidelity (e.g., attractor structure preservation).

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• Machine Learning: Learning with Manifolds
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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. In all cases, our approach outperforms or matches state-of-the-art baselines in both short-term forecast accuracy and in capturing long-term dynamical features, such as attractor statistics.

Problem

• Handling parametric variability in dynamical systems modeling
• Generalizing models across different parameter regimes
• Enabling adaptive forecasting for unseen system dynamics

Innovation

• Hypernetworks generate dynamic model weights
• Latent embedding modulates base network
• Interpolates in model space, not observations