# Meta-Learning for Physically-Constrained Neural System Identification

arXiv: https://arxiv.org/abs/2501.06167 · HTML: https://mlsanity.com/paper/2501.06167/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 69 references that are in the map.
- First posted on arXiv 10 Jan 2025.

## Builds on (most cited first, 30 of 34)

- [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)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (2014)
- [Meta-Learning with Implicit Gradients](https://mlsanity.com/paper/1909.04630/) (2019)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Rapid Learning or Feature Reuse? Towards Understanding the Effectiveness of MAML](https://mlsanity.com/paper/1909.09157/) (2019)
- [How to train your MAML](https://mlsanity.com/paper/1810.09502/) (2018)
- [Meta Networks](https://mlsanity.com/paper/1703.00837/) (2017)
- [Searching for Activation Functions](https://mlsanity.com/paper/1710.05941/) (2017)
- [Advances and Challenges in Meta-Learning: A Technical Review](https://mlsanity.com/paper/2307.04722/) (2023)
- [Generalization Bounds For Meta-Learning: An Information-Theoretic Analysis](https://mlsanity.com/paper/2109.14595/) (2021)
- [Adaptive-Control-Oriented Meta-Learning for Nonlinear Systems](https://mlsanity.com/paper/2103.04490/) (2021)
- [Constructing Neural Network-Based Models for Simulating Dynamical Systems](https://mlsanity.com/paper/2111.01495/) (2021)
- [Nonlinear state-space identification using deep encoder networks](https://mlsanity.com/paper/2012.07697/) (2020)
- [dynoNet: a neural network architecture for learning dynamical systems](https://mlsanity.com/paper/2006.02250/) (2020)
- [On Correctness of Automatic Differentiation for Non-Differentiable Functions](https://mlsanity.com/paper/2006.06903/) (2020)
- [Model structures and fitting criteria for system identification with neural networks](https://mlsanity.com/paper/1911.13034/) (2019)
- [From system models to class models: An in-context learning paradigm](https://mlsanity.com/paper/2308.13380/) (2023)
- [Identifying the Dynamics of a System by Leveraging Data from Similar Systems](https://mlsanity.com/paper/2204.05446/) (2022)
- [Deep Identification of Nonlinear Systems in Koopman Form](https://mlsanity.com/paper/2110.02583/) (2021)
- [On the Initialization of Nonlinear LFR Model Identification with the Best Linear Approximation](https://mlsanity.com/paper/2004.05040/) (2020)
- [Physics-Informed Neural State Space Models via Learning and Evolution](https://mlsanity.com/paper/2011.13497/) (2020)
- [Meta Learning MPC using Finite-Dimensional Gaussian Process Approximations](https://mlsanity.com/paper/2008.05984/) (2020)
- [On the adaptation of in-context learners for system identification](https://mlsanity.com/paper/2312.04083/) (2023)
- [Learning neural state-space models: do we need a state estimator?](https://mlsanity.com/paper/2206.12928/) (2022)
- [Optimizing Closed-Loop Performance with Data from Similar Systems: A Bayesian Meta-Learning Approach](https://mlsanity.com/paper/2211.00077/) (2022)
- [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, 6 of 6)

- [Manifold meta-learning for reduced-complexity neural system identification](https://mlsanity.com/paper/2504.11811/) (2025)
- [Point Cloud Sequence Encoding for Material-conditioned Graph Network Simulators](https://mlsanity.com/paper/2605.20978/) (2026)
- [Meta-Learning for Rapid Adaptation in Reference Tracking of Uncertain Nonlinear Systems](https://mlsanity.com/paper/2605.22513/) (2026)
- [Learning Dynamical Systems from Multiple Sparse Datasets: A Hierarchical Bayesian Modeling Approach](https://mlsanity.com/paper/2606.24966/) (2026)
- [Variational meta-learning inference for low dimensional neural system identification](https://mlsanity.com/paper/2607.18965/) (2026)
- [In-Context Learning for System Identification: Probabilistic Formulation, Long-Sequence Handling, and Benchmark Validation](https://mlsanity.com/paper/2610.13411/) (2026)

## Abstract (arXiv)

We present a gradient-based meta-learning framework for rapid adaptation of neural state-space models (NSSMs) for black-box system identification. When applicable, we also incorporate domain-specific physical constraints to improve the accuracy of the NSSM. The major benefit of our approach is that instead of relying solely on data from a single target system, our framework utilizes data from a diverse set of source systems, enabling learning from limited target data, as well as with few online training iterations. Through benchmark examples, we demonstrate the potential of our approach, study the effect of fine-tuning subnetworks rather than full fine-tuning, and report real-world case studies to illustrate the practical application and generalizability of the approach to practical problems with physical-constraints. Specifically, we show that the meta-learned models result in improved downstream performance in model-based state estimation in indoor localization and energy systems.