ArticleProceedings of the National Academy of Sciences of the United States of America2019
Data-driven discovery of coordinates and governing equations.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 86 papers.
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Who cites it
86 citing papers in PubMed.
- Data-Driven and Physics-Informed Modeling Perspectives for Soft Manipulators: From SINDy to Hybrid Intelligence.Advanced science (Weinheim, Baden-Wurttemberg, Germany) · 2026Article
- Discovering interpretable low-dimensional dynamics using maximum entropy.Physical review. E · 2026Article
- Identifiable learning of dissipative dynamics.Nature communications · 2026Article
- Explainable AI: learning from the learners.Nature communications · 2026Review
- From data chaos to physically interpretable deterministic mapping.Nature communications · 2026Article
- Chaotic dynamics of Tai Chi public attention revealed by an integrated framework of horizontal visibility graphs, autoencoders, and sparse identification.Scientific reports · 2026Article
- Differentiable land model reveals global environmental controls on latent ecological functions.Nature communications · 2026Article
- Predicting curvature evolution on biological surfaces from clinical imaging-derived area dilation: a closed-form interpretable framework.bioRxiv : the preprint server for biology · 2026Article
- Sparse identification of nonlinear dynamics and Koopman operators with Shallow Recurrent Decoder Networks.Proceedings of the National Academy of Sciences of the United States of America · 2026Article
- A novel spatiotemporal decomposition and identification of sparse equations for human brain deformation.Scientific reports · 2026Article
- Identifying stochastic dynamics from non-sequential data (DyNoSeD).Chaos (Woodbury, N.Y.) · 2026Article
- Data-driven discovery of digital twins in biomedical research.Briefings in bioinformatics · 2026Review
- Discovering Governing Physics in the Presence of Uncertainty.Communications physics · 2026Article
- SINDy-RL for interpretable and efficient model-based reinforcement learning.Nature communications · 2025Article
- Reduced order modeling with shallow recurrent decoder networks.Nature communications · 2025Article
- Sparse identification of nonlinear dynamics applied to the acoustic levitation of acoustically large objects.Scientific reports · 2025Article
- Predicting forced responses of probability distributions via the fluctuation-dissipation theorem and generative modeling.Proceedings of the National Academy of Sciences of the United States of America · 2025Article
- Physics-tailored machine learning reveals unexpected physics in dusty plasmas.Proceedings of the National Academy of Sciences of the United States of America · 2025Article
- Using an ordinary differential equation model to separate rest and task signals in fMRI.Nature communications · 2025Article
- Dynamical systems theory as an organizing principle for single-cell biology.NPJ systems biology and applications · 2025Review
26 more citing papers are in PubMed but not listed here.
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4 authors.
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Abstract
The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions. Advances in sparse regression are currently enabling the tractable identification of both the structure and parameters of a nonlinear dynamical system from data. The resulting models have the fewest terms necessary to describe the dynamics, balancing model complexity with descriptive ability, and thus promoting interpretability and generalizability. This provides an algorithmic approach to Occam's razor for model discovery. However, this approach fundamentally relies on an effective coordinate system in which the dynamics have a simple representation. In this work, we design a custom deep autoencoder network to discover a coordinate transformation into a reduced space where the dynamics may be sparsely represented. Thus, we simultaneously learn the governing equations and the associated coordinate system. We demonstrate this approach on several example high-dimensional systems with low-dimensional behavior. The resulting modeling framework combines the strengths of deep neural networks for flexible representation and sparse identification of nonlinear dynamics (SINDy) for parsimonious models. This method places the discovery of coordinates and models on an equal footing.
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