Data-driven discovery of spatiotemporal dynamical systems with sparse interpretable neural networks Article Swipe
Siyuan Xing
,
Qing‐Long Han
,
E. G. Charalampidis
,
Ying‐Cheng Lai
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.21203/rs.3.rs-7048656/v1
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.21203/rs.3.rs-7048656/v1
Existing approaches to data-driven model discovery of nonlinear dynamical systems are mainly sparse optimization, symbolic regression, and Kolmogorov-Arnold networks, but they all suffer from the “curse of dimensionality”, i.e., the number of candidate functions grows exponentially with the dimension. Spatiotemporal dynamical systems, when represented by coupled ordinary differential equations, often involve hundreds or even thousands dimensions. Discovering the high-dimensional velocity field using large datasets presents a formidable challenge. We develop a machine-learning framework that integrates an interpretable neural network incorporating the matrix formulation of sparse regression with a specially designed sparsity promoting pruning scheme. Utilizing five paradigmatic spatiotemporal dynamical systems, we demonstrate that our framework is capable of accurately finding the velocity field of more than 100 dimensions and extrapolating to generate the correct coherent structures from untrained data. We further validate the effectiveness of our framework on an empirical dataset from a triple pendulum experiment. Our framework can potentially be scaled up to systems with thousands of dimensions, rendering data-driven model discovery of large complex systems feasible.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- https://doi.org/10.21203/rs.3.rs-7048656/v1
- https://www.researchsquare.com/article/rs-7048656/latest.pdf
- OA Status
- gold
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4412191104
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- OpenAlex ID
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https://openalex.org/W4412191104Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.21203/rs.3.rs-7048656/v1Digital Object Identifier
- Title
-
Data-driven discovery of spatiotemporal dynamical systems with sparse interpretable neural networksWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2025Year of publication
- Publication date
-
2025-07-11Full publication date if available
- Authors
-
Siyuan Xing, Qing‐Long Han, E. G. Charalampidis, Ying‐Cheng LaiList of authors in order
- Landing page
-
https://doi.org/10.21203/rs.3.rs-7048656/v1Publisher landing page
- PDF URL
-
https://www.researchsquare.com/article/rs-7048656/latest.pdfDirect link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
goldOpen access status per OpenAlex
- OA URL
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https://www.researchsquare.com/article/rs-7048656/latest.pdfDirect OA link when available
- Concepts
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Computer science, Artificial neural network, Deep neural networks, Artificial intelligence, Dynamical systems theory, Pattern recognition (psychology), Machine learning, Physics, Quantum mechanicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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