ArticleNature communications2023
Discovering conservation laws using optimal transport and manifold learning.
Article in Nature communications, 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
What it found
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The trial behind it
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Who cites it
2 citing papers in PubMed.
- MANIFOLD LEARNING IN METRIC SPACES.Applied and computational harmonic analysis · 2026Article
- Discovering conservation laws using optimal transport and manifold learning.Nature communications · 2023Article
Corrections and comments
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Authors and funding
3 authors.
Funding
Abstract
Conservation laws are key theoretical and practical tools for understanding, characterizing, and modeling nonlinear dynamical systems. However, for many complex systems, the corresponding conserved quantities are difficult to identify, making it hard to analyze their dynamics and build stable predictive models. Current approaches for discovering conservation laws often depend on detailed dynamical information or rely on black box parametric deep learning methods. We instead reformulate this task as a manifold learning problem and propose a non-parametric approach for discovering conserved quantities. We test this new approach on a variety of physical systems and demonstrate that our method is able to both identify the number of conserved quantities and extract their values. Using tools from optimal transport theory and manifold learning, our proposed method provides a direct geometric approach to identifying conservation laws that is both robust and interpretable without requiring an explicit model of the system nor accurate time information.
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Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.