# Manifold meta-learning for reduced-complexity neural system identification

arXiv: https://arxiv.org/abs/2504.11811 · HTML: https://mlsanity.com/paper/2504.11811/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 27 references that are in the map.
- First posted on arXiv 16 Apr 2025.

## Builds on (most cited first, 19 of 19)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [Meta-Learning with Latent Embedding Optimization](https://mlsanity.com/paper/1807.05960/) (2018)
- [Inductive Biases for Deep Learning of Higher-Level Cognition](https://mlsanity.com/paper/2011.15091/) (2020)
- [Continuous-time system identification with neural networks: Model structures and fitting criteria](https://mlsanity.com/paper/2006.02915/) (2020)
- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [Can Transformers Learn Optimal Filtering for Unknown Systems?](https://mlsanity.com/paper/2308.08536/) (2023)
- [From system models to class models: An in-context learning paradigm](https://mlsanity.com/paper/2308.13380/) (2023)
- [Deep Subspace Encoders for Nonlinear System Identification](https://mlsanity.com/paper/2210.14816/) (2022)
- [Meta-Learning of Neural State-Space Models Using Data From Similar Systems](https://mlsanity.com/paper/2211.07768/) (2022)
- [Improved Initialization of State-Space Artificial Neural Networks](https://mlsanity.com/paper/2103.14516/) (2021)
- [Training Recurrent Neural Networks by Sequential Least Squares and the Alternating Direction Method of Multipliers](https://mlsanity.com/paper/2112.15348/) (2021)
- [An L-BFGS-B approach for linear and nonlinear system identification under ℓ1 and group-Lasso regularization](https://mlsanity.com/paper/2403.03827/) (2024)
- [Baseline Results for Selected Nonlinear System Identification Benchmarks](https://mlsanity.com/paper/2405.10779/) (2024)
- [Learning neural state-space models: do we need a state estimator?](https://mlsanity.com/paper/2206.12928/) (2022)
- [Meta-Learning for Physically-Constrained Neural System Identification](https://mlsanity.com/paper/2501.06167/) (2025)
- [Physics-Informed Learning Using Hamiltonian Neural Networks with Output Error Noise Models](https://mlsanity.com/paper/2305.01338/) (2023)
- [MPC of Uncertain Nonlinear Systems with Meta-Learning for Fast Adaptation of Neural Predictive Models](https://mlsanity.com/paper/2404.12097/) (2024)

## Built on by (most cited first, 2 of 2)

- [Meta-Learning Linear Models for Molecular Property Prediction](https://mlsanity.com/paper/2509.13527/) (2025)
- [Variational meta-learning inference for low dimensional neural system identification](https://mlsanity.com/paper/2607.18965/) (2026)

## Abstract (arXiv)

System identification has greatly benefited from deep learning techniques, particularly for modeling complex, nonlinear dynamical systems with partially unknown physics where traditional approaches may not be feasible. However, deep learning models often require large datasets and significant computational resources at training and inference due to their high-dimensional parameterizations. To address this challenge, we propose a meta-learning framework that discovers a low-dimensional manifold within the parameter space of an over-parameterized neural network architecture. This manifold is learned from a meta-dataset of input-output sequences generated by a class of related dynamical systems, enabling efficient model training while preserving the network's expressive power for the considered system class. Unlike bilevel meta-learning approaches, our method employs an auxiliary neural network to map datasets directly onto the learned manifold, eliminating the need for costly second-order gradient computations during meta-training and reducing the number of first-order updates required in inference, which could be expensive for large models. We validate our approach on a family of Bouc-Wen oscillators, which is a well-studied nonlinear system identification benchmark. We demonstrate that we are able to learn accurate models even in small-data scenarios.