EXIT: Extrapolation and Interpolation-based Neural Controlled Differential Equations for Time-series Classification and Forecasting

Deep learning inspired by differential equations is a recent research trend and has marked the state of the art performance for many machine learning tasks. Among them, time-series modeling with neural controlled differential equations (NCDEs) is considered as a breakthrough. In many cases, NCDE-based models not only provide better accuracy than recurrent neural networks (RNNs) but also make it possible to process irregular time-series. In this work, we enhance NCDEs by redesigning their core part, i.e., generating a continuous path from a discrete time-series input. NCDEs typically use interpolation algorithms to convert discrete time-series samples to continuous paths. However, we propose to i) generate another latent continuous path using an encoder-decoder architecture, which corresponds to the interpolation process of NCDEs, i.e., our neural network-based interpolation vs. the existing explicit interpolation, and ii) exploit the generative characteristic of the decoder, i.e., extrapolation beyond the time domain of original data if needed. Therefore, our NCDE design can use both the interpolated and the extrapolated information for downstream machine learning tasks. In our experiments with 5 real-world datasets and 12 baselines, our extrapolation and interpolation-based NCDEs outperform existing baselines by non-trivial margins.Comment: main 8 page

The Effect of Oxygen Supply on the Dual Growth Kinetics of Acidithiobacillus thiooxidans under Acidic Conditions for Biogas Desulfurization

In this study, to simulate a biogas desulfurization process, a modified Monod-Gompertz kinetic model incorporating a dissolved oxygen (DO) effect was proposed for a sulfur-oxidizing bacterial (SOB) strain, Acidithiobacillus thiooxidans, under extremely acidic conditions of pH 2. The kinetic model was calibrated and validated using experimental data obtained from a bubble-column bioreactor. The SOB strain was effective for H2S degradation, but the H2S removal efficiency dropped rapidly at DO concentrations less than 2.0 mg/L. A low H2S loading was effectively treated with oxygen supplied in a range of 2%–6%, but a H2S guideline of 10 ppm could not be met, even with an oxygen supply greater than 6%, when the H2S loading was high at a short gas retention time of 1 min and a H2S inlet concentration of 5000 ppm. The oxygen supply should be increased in the aerobic desulfurization to meet the H2S guideline; however, the excess oxygen above the optimum was not effective because of the decline in oxygen efficiency. The model estimation indicated that the maximum H2S removal rate was approximately 400 ppm/%-O2 at the influent oxygen concentration of 4.9% under the given condition. The kinetic model with a low DO threshold for the interacting substrates was a useful tool to simulate the effect of the oxygen supply on the H2S removal and to determine the optimal oxygen concentration

Development of a two-phase bioreactor for the biological removal of hydrogen sulfide from biogas

AbstractIn this study, a two-phase bioreactor, consisting of an anaerobic absorption column and an aerobic biofilter, was constructed and utilized to determine the removal efficiency of high strength hydrogen sulfide from biogas. A microbial strain of sulfur oxidizing bacteria (SOB), Acidithiobacillus thiooxidans, isolated from earthworm casts was inoculated in the aerobic biofilter. Initially, an inlet concentration of hydrogen sulfide supplied to the two-phase bioreactor was 180ppm, and overall removal efficiencies of hydrogen sulfide were 30 to 60% due to low cell density and activity of the SOB in the bioreactor. As bioreactor operation continued, microbial activity and bioreactor performance increased with sharply decreasing pH levels from 6.3 to 1.5. During the same operational period, the optical density (OD600) increased from 0.05 to 0.4, indicating that the SOB was in an experiential growth stage at the low pH condition. The overall removal efficiency of hydrogen sulfide was found to be greater than 97% from day 8, and the high removal efficiency maintained. On day 30, the inlet concentration of hydrogen sulfide was increased to 400ppm, and the removal efficiency did not decline, showing that the activity of the SOB was high enough to handle the high loading rate of hydrogen sulfide. An interesting finding of the study was that the activity of the SOB strain used in this study was not affected at the extremely low pH values, and no chemical additives were required to maintain the pH. Dissolved oxygen concentrations in the anaerobic column and the aerobic biofilter were maintained at 2 and 8mg/L, respectively. Consequently, the two-phase bioreactor showed advantages over conventional biofilters for the treatment of high strength hydrogen sulfide from biogas