(542d) Nonlinear Data Fusion from Heterogeneous Partial Observation Sets

Our understanding of physical processes can be greatly advanced by informative low-dimensional embeddings of high-dimensional data, such as those arising from molecular dynamics simulations or stochastic simulations of chemically reacting systems. Here we consider the problem of combining multiple data sets, each arising from different partial observations of the same system. We can imagine different “experts” observing the system in different ways, but each expert only sees part of the data. We can calibrate our experts’ observations to appropriately discovered intrinsic system states (e.g., from the covariance of short noisy simulation bursts at each data point, the so-called Mahalanobis metric^[1,2]). This filters out the effect of different observation functions, allowing us to estimate distances between data points in an intrinsic low-dimensional embedding of the system. We demonstrate our approach on stochastic simulation data for an enzyme reaction network with multiple time scales. This framework does not require that any expert to see all the data, nor that any data point be seen by all the experts. We also discuss a neural network architecture (Gappy Local Conformal Autoencoder^[3]) capable of solving this problem. The latter work is in collaboration with Ofir Lindenbaum and Matan Gavish.

[1] A. Singer and R.R. Coifman. Non-linear independent component analysis with diffusion maps. Applied and Computational Harmonic Analysis, 25(2):226-239, 2008.

[2] C. J. Dsilva, R. Talmon, N. Rabin, R.R. Coifman, and I.G. Kevrekidis. Nonlinear intrinsic variables and state reconstruction in multiscale simulations. J. Chem. Phys, 139, 184109, 2013.

[3] E. Peterfreund, O. Lindenbaum, F. Dietrich, T. Bertalan, M. Gavish, I.G. Kevrekidis, and R.R. Coifman. Local conformal autoencoder for standardized data coordinates. PNAS, 117(49), 2020.