The paper, which appeared in Physics of Fluids, presents a new approach for improving the accuracy of predictions for advection-dominated dynamical systems.

These systems are common in applications such as engineering design, oceanography, and Earth sciences. Since accuracy is critical in these applications, various proposals have been made to use machine learning techniques. Typically, such techniques involve reducing the problem dimensions and then using time series and sequential learning methods to predict the evolution of the reduced problem. Often, however, these machine-learned predictions suffer from stability issues.

To address these issues, the Argonne researchers have developed a non-autoregressive approach for predicting linear-reduced-basis time histories.

“Autoregressive methods – methods in which the outputs of the network are fed back to be used for predicting the next step – are commonly used for time-series learning. But these methods can lead to error propagation during recursive predictions,” said Prasanna Balaprakash, a computer scientist in Argonne’s Mathematics and Computer Science Division with a joint appointment in the Leadership Computing Facility. ​“Instead, we use non-autoregressive methods that give direct prediction.”

Specifically, the researchers devised a non-autoregressive variant of the long short-term memory (LSTM) network method that performs bidirectional gating. ​“By switching the gating dimension, for example, we interpret the dataset to be sequential in space rather than in time,” said Romit Maulik, Margret Butler Fellow in the Leadership Computing Facility and the lead author of the study.

In an evaluation on the shallow water equations – a system of equations widely used for geophysical flows – the new non-autoregressive LSTM method was compared with two traditional LSTM methods, five non-autoregressive methods, and the equation-based Galerkin projection method. The Argonne team demonstrated that their approach results in fewer testing and reconstruction errors as well as significant improvement in model stability compared with that of the traditional LSTM. For many applications, using the new non-autoregressive approach also reduces the inference time by several orders of magnitude in comparison with the benchmark Gaussian projection method and autoregressive methods. Furthermore, the model size of the new non-autoregressive bidirectional LSTM is less than that of the other non-autoregressive methods.

The award-winning  paper is available on the web: R. Maulik, B. Lusch, and P. Balaprakash, ​“Non-auto-regressive time-series methods for stable parametric reduced-order models,” Physics of Fluids, 32(8), 2020.