(658b) Manifold Learning for Measurements across Several Sensors: Alternating Diffusion, Data Fusion and Constructing Nonlinear Observers for Complex Chemical Reaction Networks

We study the problem of reconciling measurements from different observations of simultaneously occurring uncoupled phenomena – e.g. several simultaneous but noninteracting reaction networks occurring in an isothermal stirred tank (or, for that matter, in a cell). One needs to first understand which sets of variables ``belong together”, and should therefore constitute an irreducible building block. Novel data mining/ manifold learning techniques (in particular, Alternating Diffusion [1]) make this possible.

Once the several constituent building blocks (different reaction networks) are identified, it is possible to use data mining (diffusion maps) to fuse the information from different partial sensors of the same building block. It is also possible to exploit semi-supervised learning or even AI techniques (like deep neural networks or deep Gaussian processes) to reconstruct, from partial observations, the full state, including quantities that are difficult to measure. We implement and demonstrate these tools on ensembles of concentration measurements from several simultaneously occurring biochemical reactions.

[1] R. R. Lederman, R. Talmon, Learning the geometry of common latent variables using alternating-diffusion, Applied and Computational Harmonic Analysis, 44 (3) (2018), pp. 509-536, https://doi.org/10.1016/j.acha.2015.09.002.