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

arXiv: https://arxiv.org/abs/2506.19609 · HTML: https://mlsanity.com/paper/2506.19609/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 39 of its 89 references that are in the map.
- First posted on arXiv 24 Jun 2025.

## Builds on (most cited first, 30 of 39)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Generating Sequences With Recurrent Neural Networks](https://mlsanity.com/paper/1308.0850/) (2013)
- [Convolutional Neural Operators for robust and accurate learning of PDEs](https://mlsanity.com/paper/2302.01178/) (2023)
- [HyperStyle: StyleGAN Inversion with HyperNetworks for Real Image Editing](https://mlsanity.com/paper/2111.15666/) (2021)
- [Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks](https://mlsanity.com/paper/1802.07486/) (2018)
- [Enhancing Computational Fluid Dynamics with Machine Learning](https://mlsanity.com/paper/2110.02085/) (2021)
- [Backpropagation Algorithms and Reservoir Computing in Recurrent Neural Networks for the Forecasting of Complex Spatiotemporal Dynamics](https://mlsanity.com/paper/1910.05266/) (2019)
- [Dynamic mode decomposition with control](https://mlsanity.com/paper/1409.6358/) (2014)
- [Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances](https://mlsanity.com/paper/2105.12221/) (2021)
- [Transformers for Modeling Physical Systems](https://mlsanity.com/paper/2010.03957/) (2020)
- [A Brief Review of Hypernetworks in Deep Learning](https://mlsanity.com/paper/2306.06955/) (2023)
- [POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition](https://mlsanity.com/paper/2101.11845/) (2021)
- [Weight-space symmetry in deep networks gives rise to permutation saddles, connected by equal-loss valleys across the loss landscape](https://mlsanity.com/paper/1907.02911/) (2019)
- [On conditional diffusion models for PDE simulations](https://mlsanity.com/paper/2410.16415/) (2024)
- [DHP: Differentiable Meta Pruning via HyperNetworks](https://mlsanity.com/paper/2003.13683/) (2020)
- [Generalizing to New Physical Systems via Context-Informed Dynamics Model](https://mlsanity.com/paper/2202.01889/) (2022)
- [Hypernetwork-based Meta-Learning for Low-Rank Physics-Informed Neural Networks](https://mlsanity.com/paper/2310.09528/) (2023)
- [LEADS: Learning Dynamical Systems that Generalize Across Environments](https://mlsanity.com/paper/2106.04546/) (2021)
- [HyperPINN: Learning parameterized differential equations with physics-informed hypernetworks](https://mlsanity.com/paper/2111.01008/) (2021)
- [Parameterized Physics-informed Neural Networks for Parameterized PDEs](https://mlsanity.com/paper/2408.09446/) (2024)
- [Hierarchical Deep Learning of Multiscale Differential Equation Time-Steppers](https://mlsanity.com/paper/2008.09768/) (2020)
- [Meta-Auto-Decoder for Solving Parametric Partial Differential Equations](https://mlsanity.com/paper/2111.08823/) (2021)
- [Hypersolvers: Toward Fast Continuous-Depth Models](https://mlsanity.com/paper/2007.09601/) (2020)
- [Quadratic Approximation Manifold for Mitigating the Kolmogorov Barrier in Nonlinear Projection-Based Model Order Reduction](https://mlsanity.com/paper/2204.02462/) (2022)
- [Meta-PDE: Learning to Solve PDEs Quickly Without a Mesh](https://mlsanity.com/paper/2211.01604/) (2022)
- [Supervised and Unsupervised Learning of Parameterized Color Enhancement](https://mlsanity.com/paper/2001.05843/) (2019)

## Abstract (arXiv)

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.