Related papers: Model reduction, machine learning based global opt…

Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…

In this article we propose a new deep learning approach to approximate operators related to parametric partial differential equations (PDEs). In particular, we introduce a new strategy to design specific artificial neural network (ANN)…

Deep learning models hold state of the art performance in many fields, yet their design is still based on heuristics or grid search methods that often result in overparametrized networks. This work proposes a method to analyze a trained…

Partial differential equation (PDE)-constrained optimization arises in many scientific and engineering domains, such as energy systems, fluid dynamics and material design. In these problems, the decision variables (e.g., control inputs or…

In many areas of engineering, nonlinear numerical analysis is playing an increasingly important role in supporting the design and monitoring of structures. Whilst increasing computer resources have made such formerly prohibitive analyses…

A variety of modeling techniques have been developed in the past decade to reduce the computational expense and improve the accuracy of modeling. In this study, a new framework of modeling is suggested. Compared with other popular methods,…

Artificial neural networks (ANNs) are highly flexible predictive models. However, reliably quantifying uncertainty for their predictions is a continuing challenge. There has been much recent work on "recalibration" of predictive…

High-fidelity physics simulations are powerful tools in the design and optimization of charged particle accelerators. However, the computational burden of these simulations often limits their use in practice for design optimization and…

General circulation models are essential tools in weather and hydrodynamic simulation. They solve discretized, complex physical equations in order to compute evolutionary states of dynamical systems, such as the hydrodynamics of a lake.…

Deep Neural Networks have achieved remarkable success relying on the developing availability of GPUs and large-scale datasets with increasing network depth and width. However, due to the expensive computation and intensive memory,…

We present a new scientific machine learning method that learns from data a computationally inexpensive surrogate model for predicting the evolution of a system governed by a time-dependent nonlinear partial differential equation (PDE), an…

The diverse world of machine learning applications has given rise to a plethora of algorithms and optimization methods, finely tuned to the specific regression or classification task at hand. We reduce the complexity of algorithm design for…

Model predictive control (MPC) has established itself as the primary methodology for constrained control, enabling general-purpose robot autonomy in diverse real-world scenarios. However, for most problems of interest, MPC relies on the…

We propose using machine learning and artificial neural networks (ANNs) to enhance residual-based stabilization methods for advection-dominated differential problems. Specifically, in the context of the finite element method, we consider…

Evolutionary artificial neural networks (EANNs) refer to a special class of artificial neural networks (ANNs) in which evolution is another fundamental form of adaptation in addition to learning. Evolutionary algorithms are used to adapt…

The objective of this study is to evaluate whether the number of requisite training samples can be reduced with the use of various transfer learning models for predicting, for example, the chemical source terms of the data-driven…

This work proposes a systematic model reduction approach based on rank adaptive tensor recovery for partial differential equation (PDE) models with high-dimensional random parameters. Since the standard outputs of interest of these models…

Algebraic multigrid (AMG) methods are among the most efficient solvers for linear systems of equations and they are widely used for the solution of problems stemming from the discretization of Partial Differential Equations (PDEs). The most…

Automated design methods for convolutional neural networks (CNNs) have recently been developed in order to increase the design productivity. We propose a neuroevolution method capable of evolving and optimizing CNNs with respect to the…

Artificial neural networks are trained by a standard backpropagation learning algorithm with regularization to model and predict the systematics of -decay of heavy and superheavy nuclei. This approach to regression is implemented in two…