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This work introduces Neural Chronos Ordinary Differential Equations (NeuralCODE), a deep neural network architecture that fits a continuous-time ODEdynamics for predicting the chronology of a system both forward and backward intime. To train the model, we solve the ODE as an initial value problem and afinal value problem, similar to Neural ODEs. We also explore two approaches tocombining Neural CODE with Recurrent Neural Networks by replacing Neural ODEwith Neural CODE (CODE-RNN), and incorporating a bidirectional RNN for fullinformation flow in both time directions (CODE-BiRNN), and variants with otherupdate cells namely GRU and LSTM: CODE-GRU, CODE-BiGRU, CODE-LSTM, CODE-BiLSTM.  Experimental results demonstrate that Neural CODE outperforms Neural ODE inlearning the dynamics of a spiral forward and backward in time, even withsparser data. We also compare the performance of CODE-RNN/-GRU/-LSTM andCODE-BiRNN/-BiGRU/-BiLSTM against ODE-RNN/-GRU/-LSTM on three real-life timeseries data tasks: imputation of missing data for lower and higher dimensionaldata, and forward and backward extrapolation with shorter and longer timehorizons. Our findings show that the proposed architectures converge faster,with CODE-BiRNN/-BiGRU/-BiLSTM consistently outperforming the otherarchitectures on all tasks.

Neural Chronos ODE: Unveiling Temporal Patterns and Forecasting Future and Past Trends in Time Series Data