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Deep Abstractions of Chemical Reaction Networks

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Computational Methods in Systems Biology (CMSB 2018)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 11095))

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Abstract

Multi-scale modeling of biological systems, for instance of tissues composed of millions of cells, are extremely demanding to simulate, even resorting to High Performance Computing (HPC) facilities, particularly when each cell is described by a detailed model of some intra-cellular pathways and cells are coupled and interacting at the tissue level. Model abstraction can play a crucial role in this setting, by providing simpler models of intra-cellular dynamics that are much faster to simulate so to scale better the analysis at the tissue level. Abstractions themselves can be very challenging to build ab-initio. A more viable strategy is to learn them from single cell simulation data.

In this paper, we explore this direction, constructing abstract models of chemical reaction networks in terms of Discrete Time Markov Chains on a continuous space, learning transition kernels using deep neural networks. This allows us to obtain accurate simulations, greatly reducing the computational burden.

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Notes

  1. 1.

    A node is said to be hidden if it does not belong to the input or the output layer. A layer is, roughly, a collection of nodes at the same depth level with respect to the input layer. A layer composed of hidden nodes is called hidden layer.

  2. 2.

    Rectified Linear Unit: \(f(x)=\max \{0, x\}\), cfr. [12].

  3. 3.

    We generated training and validation sets with the same number of datapoints. A t each epoch, we subsample from these sets without replacement (until the whole dataset has been consumed) to have a finer control on overfitting using early stopping regularization.

  4. 4.

    As in the SIR case, training set and validation set have the same number of datapoints, and we subsample without replacement at each epoch to have a finer control on overfitting using early stopping regularization.

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Correspondence to Luca Bortolussi .

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Bortolussi, L., Palmieri, L. (2018). Deep Abstractions of Chemical Reaction Networks. In: Češka, M., Šafránek, D. (eds) Computational Methods in Systems Biology. CMSB 2018. Lecture Notes in Computer Science(), vol 11095. Springer, Cham. https://doi.org/10.1007/978-3-319-99429-1_2

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  • DOI: https://doi.org/10.1007/978-3-319-99429-1_2

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