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Modeling of conservative systems with neural networks is an area of active research. A popular approach is to use Hamiltonian neural networks (HNNs) which rely on the assumptions that a conservative system is described with Hamilton's…
The objective of this paper is to design novel multi-layer neural network architectures for multiscale simulations of flows taking into account the observed data and physical modeling concepts. Our approaches use deep learning concepts…
Neural Networks (NNs) have been successfully employed to represent the state evolution of complex dynamical systems. Such models, referred to as NN dynamic models (NNDMs), use iterative noisy predictions of NN to estimate a distribution of…
Stability certification and identifying a safe and stabilizing initial set are two important concerns in ensuring operational safety, stability, and robustness of dynamical systems. With the advent of machine-learning tools, these issues…
A promising approach to improve climate-model simulations is to replace traditional subgrid parameterizations based on simplified physical models by machine learning algorithms that are data-driven. However, neural networks (NNs) often lead…
Recurrent neural networks have gained widespread use in modeling sequential data. Learning long-term dependencies using these models remains difficult though, due to exploding or vanishing gradients. In this paper, we draw connections…
The ability to store and manipulate information is a hallmark of computational systems. Whereas computers are carefully engineered to represent and perform mathematical operations on structured data, neurobiological systems perform…
We demonstrate several techniques to encourage practical uses of neural networks for fluid flow estimation. In the present paper, three perspectives which are remaining challenges for applications of machine learning to fluid dynamics are…
Large neural networks are typically trained for a fixed computational budget, creating a rigid trade-off between performance and efficiency that is ill-suited for deployment in resource-constrained or dynamic environments. Existing…
State estimation is key to both analyzing physical mechanisms and enabling real-time control of fluid flows. A common estimation approach is to relate sensor measurements to a reduced state governed by a reduced-order model (ROM). (When…
Machine learning is playing an increasing role in hydrology, supplementing or replacing physics-based models. One notable example is the use of recurrent neural networks (RNNs) for forecasting streamflow given observed precipitation and…
The weights of a deep neural network model are optimized in conjunction with the governing flow equations to provide a model for sub-grid-scale stresses in a temporally developing plane turbulent jet at Reynolds number $Re_0=6\,000$. The…
The theory-guided convolutional neural network (TgCNN) framework, which can incorporate discretized governing equation residuals into the training of convolutional neural networks (CNNs), is extended to two-phase porous media flow problems…
We propose a neural entropy-stable conservative flux form neural network (NESCFN) for learning hyperbolic conservation laws and their associated entropy functions directly from solution trajectories, without requiring any predefined…
The recurrent neural network and its variants have shown great success in processing sequences in recent years. However, this deep neural network has not aroused much attention in anomaly detection through predictively process monitoring.…
This paper proposes a novel algorithm for training recurrent neural network models of nonlinear dynamical systems from an input/output training dataset. Arbitrary convex and twice-differentiable loss functions and regularization terms are…
We propose a general framework to extract microscopic interactions from raw configurations with deep neural networks. The approach replaces the modeling Hamiltonian by the neural networks, in which the interaction is encoded. It can be…
A properly designed controller can help improve the quality of experimental measurements or force a dynamical system to follow a completely new time-evolution path. Recent developments in deep reinforcement learning have made steep advances…
Normalizing Flows are a promising new class of algorithms for unsupervised learning based on maximum likelihood optimization with change of variables. They offer to learn a factorized component representation for complex nonlinear data and,…
Neural networks have become a powerful tool as surrogate models to provide numerical solutions for scientific problems with increased computational efficiency. This efficiency can be advantageous for numerically challenging problems where…