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Performing machine learning on structured data is complicated by the fact that such data does not have vectorial form. Therefore, multiple approaches have emerged to construct vectorial representations of structured data, from kernel and…

Data-driven methods have changed the way we understand and model materials. However, while providing unmatched flexibility, these methods have limitations such as reduced capacity to extrapolate, overfitting, and violation of physics…

Recently, there has been growing interest in using physics-informed neural networks (PINNs) to solve differential equations. However, the preservation of structure, such as energy and stability, in a suitable manner has yet to be…

Neural networks are increasingly used in complex (data-driven) simulations as surrogates or for accelerating the computation of classical surrogates. In many applications physical constraints, such as mass or energy conservation, must be…

Recurrent neural networks (RNNs) have recently been extensively applied to model the time-evolution in fluid dynamics, weather predictions, and even chaotic systems thanks to their ability to capture temporal dependencies and sequential…

Seismic wave velocity of underground rock plays important role in detecting internal structure of the Earth. Rock physics models have long been the focus of predicting wave velocity. However, construction of a theoretical model requires…

This paper aims to discuss and analyze the potentialities of Recurrent Neural Networks (RNN) in control design applications. The main families of RNN are considered, namely Neural Nonlinear AutoRegressive eXogenous, (NNARX), Echo State…

Computational efficiency and robustness are essential in process modeling, optimization, and control for real-world engineering applications. While neural network-based approaches have gained significant attention in recent years,…

Predictive models in acute care settings must be able to immediately recognize precipitous changes in a patient's status when presented with data reflecting such changes. Recurrent neural networks (RNNs) have become common for training and…

This paper proposes a physics-informed learning framework for a class of recurrent neural networks tailored to large-scale and networked systems. The approach aims to learn control-oriented models that preserve the structural and stability…

Countless learning tasks require dealing with sequential data. Image captioning, speech synthesis, and music generation all require that a model produce outputs that are sequences. In other domains, such as time series prediction, video…

Stochastic recurrent neural networks with latent random variables of complex dependency structures have shown to be more successful in modeling sequential data than deterministic deep models. However, the majority of existing methods have…

Non-Newtonian rheology is widely acknowledged in subsurface fluids, yet its presence and effects are largely ignored in current fracture-flow studies. Here, we simulate fracture flow of non-Newtonian polymer solutions on a several…

We develop a method to learn physical systems from data that employs feedforward neural networks and whose predictions comply with the first and second principles of thermodynamics. The method employs a minimum amount of data by enforcing…

We propose a deep neural network architecture designed such that its output forms an invertible symplectomorphism of the input. This design draws an analogy to the real-valued non-volume-preserving (real NVP) method used in normalizing flow…

Fluid thermodynamics underpins atmospheric dynamics, climate science, industrial applications, and energy systems. However, direct numerical simulations (DNS) of such systems can be computationally prohibitive. To address this, we present a…

Substitution of well-grounded theoretical models by data-driven predictions is not as simple in engineering and sciences as it is in social and economic fields. Scientific problems suffer most times from paucity of data, while they may…

The transformative impact of machine learning, particularly Deep Learning (DL), on scientific and engineering domains is evident. In the context of computational fluid dynamics (CFD), Physics-Informed Neural Networks (PINNs) represent a…

Recurrent neural networks (RNNs) are a class of nonlinear dynamical systems often used to model sequence-to-sequence maps. RNNs have excellent expressive power but lack the stability or robustness guarantees that are necessary for many…

Neural networks can emulate nonlinear physical systems with high accuracy, yet they may produce physically-inconsistent results when violating fundamental constraints. Here, we introduce a systematic way of enforcing nonlinear analytic…