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AbstractReconstructing dynamics of complex systems from sparse, incomplete time series data is a challenging problem with applications in various domains. Here, we develop an iterative heuristic method to infer the underlying network structure and parameters governed by Ising dynamics from incomplete spin configurations based on sparse and small-sized samples. Our method iterates between imputing missing spin states given current coupling strengths and re-estimating couplings from completed spin state data. Central to our approach is the novel application of adaptive $$l_1$$

l
1

regularization on updating coupling strengths, which features an automatic adjustment of the regularization strength throughout the iterative inference process. By doing so, we aim at preventing over-fitting and enforcing the sparsity of couplings without access to ground truth parameters. We demonstrate that this approach accurately recovers parameters and imputes missing spins even with substantial missing data and short time series, providing improvements in the inference of Ising model parameters even for relatively small sample sizes.

Folowing presentation describes the pretreatment for adhesive bonding of titanium in aerospace. This project has received funding from the Clean Sky 2 Joint Undertaking (JU) under grant agreement No 807097. The JU receives support from the European Union's Horizon 2020 research and innovation programme and the Clean Sky 2 JU members other than the Union. The results, opinions, conclusions, etc. presented in this work are those of the author(s) only and do not necessarily represent the position of the JU; the JU is not responsible for any use made of the information contained herein.