Time series analysis and machine learning studies of biophotovoltaic systems

Abstract

Background. Biophotovoltaics (BPVs) catalysed by photoautotrophs such as cyanobacteria have increasingly gained interest due to their potential to generate low-carbon electricity and chemicals from just sunlight, air and water. The full path of electrons from cyanobacteria photosynthetic and respiratory systems to electrodes remains unknown, slowing efforts towards commercial BPVs. Mathematical expression is useful for testing the conceptual understanding of such complex systems. However, knowledge gaps make it difficult to define robust BPV conceptual models to translate into mathematical mechanistic models. Here, Long Short-Term Memory (LSTM) networks were explored for their ability to replicate complex time-evolving phenomena without a priori knowledge.

Results. Seasonal and trend decomposition using locally estimated scatterplot smoothing (STL) was first used to decompose BPV current density profiles into trend, seasonal and remainder (irregular) components. LSTM networks were then trained to predict the observed and seasonal current densities using current generation and illumination (on/off) histories as predictive variables. LSTMs unsatisfactorily forecast the observed current density, but predicted the seasonal component which lacks irregularities accurately. Mean absolute errors of 0.007, 0.0014 and 0.0013 µA m^{-2} on the training, cross-validation and test data sets were achieved, respectively. Experiments showed that cell size is a good additional predictor for the trend. Cell elongation as Synechococcus elongatus sp. PCC7942 cultures age resulted in larger cell surface area for diffusive flux of electron mediators, partially accounting for the gradual increase in mediated electron export rates over time. To avoid the hard-to-predict STL remainder, the Hilbert-Huang transform (HHT) was applied to decompose current profiles. HHT analysis resulted in more regular and physically meaningful oscillating subcomponents that oscillate with eight discrete time scales. Hypotheses for the genesis of the oscillations were developed by comparing with the decompositions of distinct current profiles obtained with stressed cells cultured in iron-deplete media under air and a 20% v/v CO2 atmosphere. Oscillations consistent with circadian rhythms of key photosynthetic and respiratory system components implicated in cyanobacteria current generation were observed.

Conclusions. Modelling the subcomponents of BPV current profiles using LSTM networks is a compelling alternative to mechanistic modelling. HHT analysis of cyanobacteria current generation inspires new research directions linking chronobiology and bioelectrochemistry. This seminal work is a strong foundation for developing further data-driven models for: (i) pre-modelling experiments and interpreting results; (i) running sensitivity analyses; (iii) hybrid models; and (iv) control software.