(350b) Some of the Variables, Some of the Times, with Some Things Known: Identification with Partial Information

Experimental data often consists of variables measured independently at different sampling rates, such that the Δt between successive measurements of a variable is non-uniform, and that at a specific time point only a subset of all variables are sampled. Previous methods to learn dynamical systems from such data use interpolation, imputation and/or sub-sampling to re-organize or modify the training data prior to learning [1, 2]. We present an approach using a multi-layer perceptron embedded in a Runge-Kutta numerical integrator template to learn the right-hand side of the underlying governing ODEs [3]. This neural-network model is iterated step-wise through time on a batch of trajectories with loss calculated at the time points data is available, allowing for learning from data sampled at arbitrary time points without data modification. Finally, we show how this network can be integrated with physics-informed ‘grey-boxes’ to learn kinetic rate or microbial growth functions and fit experimental parameters simultaneously to learning the dynamical system.

[1] Che, Zhengping, et al. "Recurrent neural networks for multivariate time series with missing values." Scientific reports 8.1 (2018): 1-12.

[2] Dimri, V. P., and M. Ravi Prakash. "Scaling of power spectrum of extinction events in the fossil record." Earth and Planetary Science Letters 186.3-4 (2001): 363-370.

[3] Rico-Martinez, R., et al. "Discrete-vs. continuous-time nonlinear signal processing of Cu electrodissolution data." Chemical Engineering Communications 118.1 (1992): 25-48.