ArticleNature communications2022
Learning emergent partial differential equations in a learned emergent space.
Article in Nature communications, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 5 papers.
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Who cites it
5 citing papers in PubMed.
- From disorganized data to emergent dynamic models: Questionnaires to partial differential equations.PNAS nexus · 2025Article
- Finding emergence in data by maximizing effective information.National science review · 2025Article
- On learning what to learn: Heterogeneous observations of dynamics and establishing possibly causal relations among them.PNAS nexus · 2024Article
- Limits of entrainment of circadian neuronal networks.Chaos (Woodbury, N.Y.) · 2023Article
- Prevalence and Early Prediction of Diabetes Using Machine Learning in North Kashmir: A Case Study of District Bandipora.Computational intelligence and neuroscience · 2022Article
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Authors and funding
7 authors.
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Abstract
We propose an approach to learn effective evolution equations for large systems of interacting agents. This is demonstrated on two examples, a well-studied system of coupled normal form oscillators and a biologically motivated example of coupled Hodgkin-Huxley-like neurons. For such types of systems there is no obvious space coordinate in which to learn effective evolution laws in the form of partial differential equations. In our approach, we accomplish this by learning embedding coordinates from the time series data of the system using manifold learning as a first step. In these emergent coordinates, we then show how one can learn effective partial differential equations, using neural networks, that do not only reproduce the dynamics of the oscillator ensemble, but also capture the collective bifurcations when system parameters vary. The proposed approach thus integrates the automatic, data-driven extraction of emergent space coordinates parametrizing the agent dynamics, with machine-learning assisted identification of an emergent PDE description of the dynamics in this parametrization.
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