# Continuous-time system identification with neural networks: Model structures and fitting criteria

arXiv: https://arxiv.org/abs/2006.02915 · HTML: https://mlsanity.com/paper/2006.02915/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2020.

## Built on by (most cited first, 30 of 30)

- [Learning a Single Near-hover Position Controller for Vastly Different Quadcopters](https://mlsanity.com/paper/2209.09232/) (2022)
- [From system models to class models: An in-context learning paradigm](https://mlsanity.com/paper/2308.13380/) (2023)
- [On the adaptation of recurrent neural networks for system identification](https://mlsanity.com/paper/2201.08660/) (2022)
- [Deep Subspace Encoders for Nonlinear System Identification](https://mlsanity.com/paper/2210.14816/) (2022)
- [Sparse Bayesian Deep Learning for Dynamic System Identification](https://mlsanity.com/paper/2107.12910/) (2021)
- [Synthesis of Stabilizing Recurrent Equilibrium Network Controllers](https://mlsanity.com/paper/2204.00122/) (2022)
- [Few-Shot Learning by Dimensionality Reduction in Gradient Space](https://mlsanity.com/paper/2206.03483/) (2022)
- [Baseline Results for Selected Nonlinear System Identification Benchmarks](https://mlsanity.com/paper/2405.10779/) (2024)
- [On the adaptation of in-context learners for system identification](https://mlsanity.com/paper/2312.04083/) (2023)
- [Continuous-time identification of dynamic state-space models by deep subspace encoding](https://mlsanity.com/paper/2204.09405/) (2022)
- [Stable Linear Subspace Identification: A Machine Learning Approach](https://mlsanity.com/paper/2311.03197/) (2023)
- [On the effectiveness of Randomized Signatures as Reservoir for Learning Rough Dynamics](https://mlsanity.com/paper/2201.00384/) (2022)
- [ASV Station Keeping under Wind Disturbances using Neural Network Simulation Error Minimization Model Predictive Control](https://mlsanity.com/paper/2310.07892/) (2023)
- [Manifold meta-learning for reduced-complexity neural system identification](https://mlsanity.com/paper/2504.11811/) (2025)
- [Stable-by-Design Neural Network-Based LPV State-Space Models for System Identification](https://mlsanity.com/paper/2510.24757/) (2025)
- [SOLIS: Physics-Informed Learning of Interpretable Neural Surrogates for Nonlinear Systems](https://mlsanity.com/paper/2604.14879/) (2026)
- [Deep learning with transfer functions: new applications in system identification](https://mlsanity.com/paper/2104.09839/) (2021)
- [Likelihood-based generalization of Markov parameter estimation and multiple shooting objectives in system identification](https://mlsanity.com/paper/2212.13902/) (2022)
- [A Physiologically-Constrained Neural Network Digital Twin Framework for Replicating Glucose Dynamics in Type 1 Diabetes](https://mlsanity.com/paper/2508.05705/) (2025)
- [Tuning the burn-in phase in training recurrent neural networks improves their performance](https://mlsanity.com/paper/2602.10911/) (2026)
- [The Dynamic-Probabilistic Consistency Gap in Chaotic Surrogate Modeling](https://mlsanity.com/paper/2605.31547/) (2026)
- [Learning Flow Functions from Data with Applications to Nonlinear Oscillators](https://mlsanity.com/paper/2303.16656/) (2023)
- [On the improvement of model-predictive controllers](https://mlsanity.com/paper/2308.15157/) (2023)
- [State Derivative Normalization for Continuous-Time Deep Neural Networks](https://mlsanity.com/paper/2401.02902/) (2024)
- [SINDy vs Hard Nonlinearities and Hidden Dynamics: a Benchmarking Study](https://mlsanity.com/paper/2403.00578/) (2024)
- [A neural network-based approach to hybrid systems identification for control](https://mlsanity.com/paper/2404.01814/) (2024)
- [Beyond Prediction: Interval Neural Networks for Uncertainty-Aware System Identification](https://mlsanity.com/paper/2605.11460/) (2026)
- [Online learning of neural state-space models](https://mlsanity.com/paper/2607.17614/) (2026)
- [In-Context Learning for System Identification: Probabilistic Formulation, Long-Sequence Handling, and Benchmark Validation](https://mlsanity.com/paper/2610.13411/) (2026)
- [Scalable Identification of Physics-Based and Neural Dynamics from Partial Measurements](https://mlsanity.com/paper/2610.16559/) (2026)

## Abstract (arXiv)

This paper presents tailor-made neural model structures and two custom fitting criteria for learning dynamical systems. The proposed framework is based on a representation of the system behavior in terms of continuous-time state-space models. The sequence of hidden states is optimized along with the neural network parameters in order to minimize the difference between measured and estimated outputs, and at the same time to guarantee that the optimized state sequence is consistent with the estimated system dynamics. The effectiveness of the approach is demonstrated through three case studies, including two public system identification benchmarks based on experimental data.