# Structure is information: structural identifiability mappings for machine learning with partially observed dynamical systems

arXiv: https://arxiv.org/abs/2502.04131 · HTML: https://mlsanity.com/paper/2502.04131/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 53 references that are in the map.
- First posted on arXiv 6 Feb 2025.

## Builds on (most cited first, 13 of 13)

- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Deep learning for time series classification: a review](https://mlsanity.com/paper/1809.04356/) (2018)
- [When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learning](https://mlsanity.com/paper/2203.16797/) (2022)
- [Reservoir computing approaches for representation and classification of multivariate time series](https://mlsanity.com/paper/1803.07870/) (2018)
- [On structural and practical identifiability](https://mlsanity.com/paper/2102.05100/) (2021)
- [On the Identifiability of Switching Dynamical Systems](https://mlsanity.com/paper/2305.15925/) (2023)
- [Differential elimination for dynamical models via projections with applications to structural identifiability](https://mlsanity.com/paper/2111.00991/) (2021)
- [Web-based Structural Identifiability Analyzer](https://mlsanity.com/paper/2106.15066/) (2021)
- [Learned Regularization for Inverse Problems: Insights from a Spectral Model](https://mlsanity.com/paper/2312.09845/) (2023)
- [A Dynamic Systems Approach to Modelling Human-Machine Rhythm Interaction](https://mlsanity.com/paper/2407.09538/) (2024)
- [A Classification Framework for Partially Observed Dynamical Systems](https://mlsanity.com/paper/1607.02085/) (2016)
- [Benchmarking tools for a priori identifiability analysis](https://mlsanity.com/paper/2207.09745/) (2022)

## Built on by (most cited first, 4 of 4)

- [FieldFormer: Locality-Aware Transformers for Spatio-Temporal Modeling on Sparse Sensor Networks](https://mlsanity.com/paper/2510.03589/) (2025)
- [NeuronDiscover: Agent-in-Twin for Mechanistic Discovery in Neuronal Microenvironments with World Action Models](https://mlsanity.com/paper/2609.35338/) (2026)
- [Identifiability of a dissipative knowledge-dynamics model: exact recovery under designed excitation, degeneration on observational data](https://mlsanity.com/paper/2610.09889/) (2026)
- [LLM-IDEA: Identifiability-Driven Experimental Agent for Autonomous Discovery of Mechanistic World Models](https://mlsanity.com/paper/2610.11253/) (2026)

## Abstract (arXiv)

The successful application of modern machine learning for time series classification is often hampered by limitations in quality and quantity of available training data. To overcome these limitations, domain knowledge can be leveraged in the form of parameterised mechanistic dynamical models, whereby time series observations may be represented as instances of a predefined class of dynamical systems. Provided the dynamical models are interpretable in terms of domain-specific variables and their dynamic interaction, the learning process becomes interpretable as well and enables the modeller to handle sparsely and irregularly sampled data naturally. However, the internal processes of a dynamical model are often only partially observed. This can lead to ambiguity regarding which particular model realization best explains a given time series observation. This problem is well-known in the literature, and a dynamical model with this issue is referred to as structurally unidentifiable. Training a classifier that ignores knowledge about a structurally unidentifiable dynamical model can negatively influence classification performance. To address this issue, we employ structural identifiability analysis to explicitly relate parameter configurations that are associated with identical system outputs. Using the derived relations in classifier training, we demonstrate that this method significantly improves the classifier's ability to generalize to unseen data on a number of example models from the biomedical domain. This effect is especially pronounced when the number of training instances is limited. Our results demonstrate the importance of structural identifiability, a topic that has received relatively little attention from the machine learning community.