Related papers: Reduced-order Deep Learning for Flow Dynamics

Predicting and understanding the chaotic dynamics in complex systems is essential in various applications. However, conventional approaches, whether full-scale simulations or small-scale omissions, fail to offer a comprehensive solution.…

Current Deep Learning approaches have been very successful using convolutional neural networks (CNN) trained on large graphical processing units (GPU)-based computers. Three limitations of this approach are: 1) they are based on a simple…

Large-scale or high-resolution geologic models usually comprise a huge number of grid blocks, which can be computationally demanding and time-consuming to solve with numerical simulators. Therefore, it is advantageous to upscale geologic…

We propose a combination of machine learning and flux limiting for property-preserving subgrid scale modeling in the context of flux-limited finite volume methods for the one-dimensional shallow-water equations. The numerical fluxes of a…

Model-free deep reinforcement learning algorithms have been shown to be capable of learning a wide range of robotic skills, but typically require a very large number of samples to achieve good performance. Model-based algorithms, in…

This paper studies deep neural networks for solving extremely large linear systems arising from highdimensional problems. Because of the curse of dimensionality, it is expensive to store both the solution and right-hand side vector in such…

This work attempts to interpret modern deep (convolutional) networks from the principles of rate reduction and (shift) invariant classification. We show that the basic iterative gradient ascent scheme for optimizing the rate reduction of…

We propose a convenient matrix-free neural architecture for the multigrid method. The architecture is simple enough to be implemented in less than fifty lines of code, yet it encompasses a large number of distinct multigrid solvers. We…

Molecular dynamics (MD) simulation is essential for various scientific domains but computationally expensive. Learning-based force fields have made significant progress in accelerating ab-initio MD simulation but are not fast enough for…

Deep neural network (DNN) generally takes thousands of iterations to optimize via gradient descent and thus has a slow convergence. In addition, softmax, as a decision layer, may ignore the distribution information of the data during…

Over the past decade a wide spectrum of machine learning models have been developed to model the neurodegenerative diseases, associating biomarkers, especially non-intrusive neuroimaging markers, with key clinical scores measuring the…

Image restoration tasks have achieved tremendous performance improvements with the rapid advancement of deep neural networks. However, most prevalent deep learning models perform inference statically, ignoring that different images have…

We present a deep learning-based iterative approach to solve the discrete heterogeneous Helmholtz equation for high wavenumbers. Combining classical iterative multigrid solvers and convolutional neural networks (CNNs) via preconditioning,…

Training deep neural networks typically relies on backpropagating high dimensional error signals a computationally intensive process with little evidence supporting its implementation in the brain. However, since most tasks involve…

Second-order optimizers hold intriguing potential for deep learning, but suffer from increased cost and sensitivity to the non-convexity of the loss surface as compared to gradient-based approaches. We introduce a coordinate descent method…

In this work, we propose a model order reduction framework to deal with inverse problems in a non-intrusive setting. Inverse problems, especially in a partial differential equation context, require a huge computational load due to the…

Typical topology optimization methods require complex iterative calculations, which cannot meet the requirements of fast computing applications. The neural network is studied to reduce the time of computing the optimization result, however,…

Multimodal medical image fusion is a crucial task that combines complementary information from different imaging modalities into a unified representation, thereby enhancing diagnostic accuracy and treatment planning. While deep learning…

We propose a deep probabilistic-neural-network architecture for learning a minimal and near-orthogonal set of non-linear modes from high-fidelity turbulent-flow-field data useful for flow analysis, reduced-order modeling, and flow control.…

An important application of neural networks to scientific computing has been the learning of non-linear operators. In this framework, a neural network is trained to fit a non-linear map between two infinite dimensional spaces, for example,…