NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations

Time series forecasting has become a very intensive field of research, which is even increasing in recent years. Deep neural networks have proved to be powerful and are achieving high accuracy in many application fields. For these reasons, they are one of the most widely used methods of machine learning to solve problems dealing with big data nowadays. In this work, the time series forecasting problem is initially formulated along with its mathematical fundamentals. Then, the most common deep learning architectures that are currently being successfully applied to predict time series are described, highlighting their advantages and limitations. Particular attention is given to feed forward networks, recurrent neural networks (including Elman, long-short term memory, gated recurrent units, and bidirectional networks), and convolutional neural networks. Practical aspects, such as the setting of values for hyper-parameters and the choice of the most suitable frameworks, for the successful application of deep learning to time series are also provided and discussed. Several fruitful research fields in which the architectures analyzed have obtained a good performance are reviewed. As a result, research gaps have been identified in the literature for several domains of application, thus expecting to inspire new and better forms of knowledge.

Deep Learning for Time Series Forecasting: A Survey.

For over a century, reduced order models (ROMs) have been a fundamental discipline of theoretical fluid mechanics. Early examples include Galerkin models inspired by the Orr–Sommerfeld stability equation and numerous vortex models, of which the von Karman vortex street is one of the most prominent. Subsequent ROMs typically relied on first principles, like mathematical Galerkin models, weakly nonlinear stability theory, and two- and three-dimensional vortex models. Aubry et al. [J. Fluid Mech. 192, 115–173 (1988)] pioneered the data-driven proper orthogonal decomposition (POD) modeling. In early POD modeling, available data were used to build an optimal basis, which was then utilized in a classical Galerkin procedure to construct the ROM, but data have made a profound impact on ROMs beyond the Galerkin expansion. In this paper, we take a modest step and illustrate the impact of data-driven modeling on one significant ROM area. Specifically, we focus on ROM closures, which are correction terms that are added to the classical ROMs in order to model the effect of the discarded ROM modes in under-resolved simulations. Through simple examples, we illustrate the main modeling principles used to construct the classical ROMs, motivate and introduce modern ROM closures, and show how data-driven modeling, artificial intelligence, and machine learning have changed the standard ROM methodology over the last two decades. Finally, we outline our vision on how the state-of-the-art data-driven modeling can continue to reshape the field of reduced order modeling.

On closures for reduced order models—A spectrum of first-principle to machine-learned avenues

Temporal convolutional network with soft thresholding and attention mechanism for machinery prognostics

For over a century, reduced order models (ROMs) have been a fundamental discipline of theoretical fluid mechanics. Early examples include Galerkin models inspired by the Orr-Sommerfeld stability equation (1907) and numerous vortex models, of which the von Karman vortex street (1911) is one of the most prominent. Subsequent ROMs typically relied on first principles, like mathematical Galerkin models, weakly nonlinear stability theory, and two- and three-dimensional vortex models. Aubry et al. (1988) pioneered, with the proper orthogonal decomposition (POD) model of the turbulent boundary layer, a new data-driven paradigm, which has become the most popular avenue. In early POD modeling, available data was used to build an optimal basis, which was then utilized in a classical Galerkin procedure to construct the ROM. But data has made a profound impact on ROMs beyond the Galerkin expansion. In this paper, we take a modest step and illustrate the impact of data-driven modeling on one significant ROM area. Specifically, we focus on ROM closures, which are correction terms that are added to classical ROMs in order to model the effect of the discarded ROM modes in under-resolved simulations. Through simple examples, we illustrate the main modeling principles used to construct classical ROMs, motivate and introduce modern ROM closures, and show how data-driven modeling, artificial intelligence, and machine learning have changed the standard ROM methodology over the last two decades. Finally, we outline our vision on how state-of-the-art data-driven modeling can continue to reshape the field of reduced order modeling.

On closures for reduced order models $-$ A spectrum of first-principle to machine-learned avenues

Data-driven reduced order model with temporal convolutional neural network

Fast data assimilation (FDA): Data assimilation by machine learning for faster optimize model state

Multi-premise natural language inference provides important technical support for automatic question answering, machine reading comprehension and other application fields. Existing approaches for Multiple Premises Entailment (MPE) task are to convert MPE data into Single Premise Entailment (SPE) data format, then MPE is handled in the same way as SPE. This process ignores the unique characteristics of multi-premise, which will result in loss of semantics. This paper proposes a mechanism based on Attention and Gate Fusion Network (AGNet). AGNet adopts a “Local Matching-Integration” strategy to consider the characteristics of multi-premise. In this process, an attention mechanism combined with a matching gate mechanism can fully describe the relationship between the premise and hypothesis. A self-attention mechanism and a fusion gate mechanism can deeply exploit the relationship from the multi-premise. In order to avoid over-fitting problem, we propose a pre-training method for our model. In terms of computational complexity, AGNet has good parallelism, reduces the time complexity to O(1) in the process of matching. The experiments show that our model has achieved new state-of-the-art results on MPE test set.

Multiple premises entailment recognition based on attention and gate mechanism

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Data-driven reduced order model with temporal convolutional neural network

Fast data assimilation (FDA): Data assimilation by machine learning for faster optimize model state

Multiple premises entailment recognition based on attention and gate mechanism