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Deep Learning methods have seen a wide range of successful applications across different industries. Up until now, applications to physical simulations such as CFD (Computational Fluid Dynamics), have been limited to simple test-cases of…
Many large scale problems in computational fluid dynamics such as uncertainty quantification, Bayesian inversion, data assimilation and PDE constrained optimization are considered very challenging computationally as they require a large…
Although more layers and more parameters generally improve the accuracy of the models, such big models generally have high computational complexity and require big memory, which exceed the capacity of small devices for inference and incurs…
In several problems involving fluid flows, Computational Fluid Dynamics (CFD) provides detailed quantitative information, and often allows the designer to successfully optimize the system, by minimizing a cost function. Sometimes, however,…
Large machine learning models trained on diverse data have recently seen unprecedented success. Federated learning enables training on private data that may otherwise be inaccessible, such as domain-specific datasets decentralized across…
In-context learning (ICL) has shown impressive results in few-shot learning tasks, yet its underlying mechanism is still not fully understood. A recent line of work suggests that ICL performs gradient descent (GD)-based optimization…
Deep learning (DL) has recently emerged as a candidate for closure modeling of large-eddy simulation (LES) of turbulent flows. High-fidelity training data is typically limited: it is computationally costly (or even impossible) to…
While deep learning has shown tremendous success in a wide range of domains, it remains a grand challenge to incorporate physical principles in a systematic manner to the design, training, and inference of such models. In this paper, we aim…
Understanding the advantages of deep neural networks trained by gradient descent (GD) compared to shallow models remains an open theoretical challenge. In this paper, we introduce a class of target functions (single and multi-index Gaussian…
Rapid and accurate simulations of fluid dynamics around complicated geometric bodies are critical in a variety of engineering and scientific applications, including aerodynamics and biomedical flows. However, while scientific machine…
Computational Fluid Dynamics (CFD) is the main approach to analyzing flow field. However, the convergence and accuracy depend largely on mathematical models of flow, numerical methods, and time consumption. Deep learning-based analysis of…
The design and implementation of Deep Learning (DL) models is currently receiving a lot of attention from both industrials and academics. However, the computational workload associated with DL is often out of reach for low-power embedded…
This paper aims to explore the potential of combining Deep Reinforcement Learning (DRL) with Knowledge Distillation (KD) by distilling various DRL algorithms and studying their distillation effects. By doing so, the computational burden of…
Deep learning (DL) allows computer models to learn, visualize, optimize, refine, and predict data. To understand its present state, examining the most recent advancements and applications of deep learning across various domains is…
Numerical simulators are essential tools in the study of natural fluid-systems, but their performance often limits application in practice. Recent machine-learning approaches have demonstrated their ability to accelerate spatio-temporal…
A finite element method for solving nonlinear differential equations on a grid, with potential applicability to computational fluid dynamics (CFD), is developed and tested. The current method facilitates the computation of solutions of a…
Water distribution systems (WDS) are an integral part of critical infrastructure which is pivotal to urban development. As 70% of the world's population will likely live in urban environments in 2050, efficient simulation and planning tools…
Deep Learning (DL) algorithms are the central focus of modern machine learning systems. As data volumes keep growing, it has become customary to train large neural networks with hundreds of millions of parameters to maintain enough capacity…
Computational fluid dynamics (CFD) simulations of viscous fluids described by the Navier-Stokes equations are considered. Depending on the Reynolds number of the flow, the Navier-Stokes equations may exhibit a highly nonlinear behavior. The…
Computational fluid dynamics (CFD) simulations are broadly applied in engineering and physics. A standard description of fluid dynamics requires solving the Navier-Stokes (N-S) equations in different flow regimes. However, applications of…