Abstract Complex biological, neuroscience, geoscience and social networks exhibit heterogeneous self-similar higher order topological structures that are usually characterized as being multifractal in nature. However, describing their topological complexity through a compact mathematical description and deciphering their topological governing rules has remained elusive and prevented a comprehensive understanding of networks. To overcome this challenge, we propose a weighted multifractal graph model capable of capturing the underlying generating rules of complex systems and characterizing their node heterogeneity and pairwise interactions. To infer the generating measure with hidden information, we introduce a variational expectation maximization framework. We demonstrate the robustness of the network generator reconstruction as a function of model properties, especially in noisy and partially observed scenarios. The proposed network generator inference framework is able to reproduce network properties, differentiate varying structures in brain networks and chromosomal interactions, and detect topologically associating domain regions in conformation maps of the human genome.
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Learning physics-consistent particle interactions
Interacting particle systems play a key role in science and engineering. Access to the governing particle interaction law is fundamental for a complete understanding of such systems. However, the inherent system complexity keeps the particle interaction hidden in many cases. Machine learning methods have the potential to learn the behavior of interacting particle systems by combining experiments with data analysis methods. However, most existing algorithms focus on learning the kinetics at the particle level. Learning pairwise interaction, e.g., pairwise force or pairwise potential energy, remains an open challenge. Here, we propose an algorithm that adapts the Graph Networks framework, which contains an edge part to learn the pairwise interaction and a node part to model the dynamics at particle level. Different from existing approaches that use neural networks in both parts, we design a deterministic operator in the node part that allows to precisely infer the pairwise interactions that are consistent with underlying physical laws by only being trained to predict the particle acceleration. We test the proposed methodology on multiple datasets and demonstrate that it achieves superior performance in inferring correctly the pairwise interactions while also being consistent with the underlying physics on all the datasets. While the previously proposed approaches are able to be applied as simulators, they fail to infer physically consistent particle interactions that satisfy Newton’s laws. Moreover, the proposed physics-induced graph network for particle interaction also outperforms the other baseline models in terms of generalization ability to larger systems and robustness to significant levels of noise. The developed methodology can support a better understanding and discovery of the underlying particle interaction laws, and hence, guide the design of materials with targeted properties.
more » « less- PAR ID:
- 10384888
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- PNAS Nexus
- Volume:
- 1
- Issue:
- 5
- ISSN:
- 2752-6542
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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