Related papers: Parametric Nonlinear Volterra Series via Machine L…
Statistical learning methods show great promise in providing an accurate prediction of materials and molecular properties, while minimizing the need for computationally demanding electronic structure calculations. The accuracy and…
We propose the introduction of nonlinear operation into the feature generation process in convolutional neural networks. This nonlinearity can be implemented in various ways. First we discuss the use of nonlinearities in the process of data…
Unstructured point clouds with varying sizes are increasingly acquired in a variety of environments through laser triangulation or Light Detection and Ranging (LiDAR). Predicting a scalar response based on unstructured point clouds is a…
Machine learning has revolutionized the high-dimensional representations for molecular properties such as potential energy. However, there are scarce machine learning models targeting tensorial properties, which are rotationally covariant.…
Most machine learning techniques are based upon statistical learning theory, often simplified for the sake of computing speed. This paper is focused on the uncertainty aspect of mathematical modeling in machine learning. Regression analysis…
A vortex-lattice method for wing aerodynamics that uses nonlinear airfoil data is presented. Two applications of this procedure are presented: Direct Design of a Flying Wing and Inverse Identification from wind tunnel measurements with…
A regression-based framework for interpretable multi-way data imputation, termed Kernel Regression via Tensor Trains with Hadamard overparametrization (KReTTaH), is introduced. KReTTaH adopts a nonparametric formulation by casting…
Aerodynamic performance evaluation is an important part of the aircraft aerodynamic design optimization process; however, traditional methods are costly and time-consuming. Despite the fact that various machine learning methods can achieve…
The simulation of nanophotonic structures relies on electromagnetic solvers, which play a crucial role in understanding their behavior. However, these solvers often come with a significant computational cost, making their application in…
The success of the current wave of artificial intelligence can be partly attributed to deep neural networks, which have proven to be very effective in learning complex patterns from large datasets with minimal human intervention. However,…
We develop a novel data-driven approach to modeling the atmospheric boundary layer. This approach leads to a nonlocal, anisotropic synthetic turbulence model which we refer to as the deep rapid distortion (DRD) model. Our approach relies on…
There have been increasing interests on the Volterra series identification with the kernel-based regularization method. The major difficulties are on the kernel design and efficiency of the corresponding implementation. In this paper, we…
In this paper, a class of high order numerical schemes is proposed to solve the nonlinear parabolic equations with variable coefficients. This method is based on our previous work [10] for convection-diffusion equations, which relies on a…
Strongly coupled hidden sector theories predict collider production of invisible, composite dark matter candidates mixed with standard model hadrons in the form of semivisible jets. Classical mass reconstruction techniques may not be…
Effectively predicting transonic unsteady flow over an aerofoil poses inherent challenges. In this study, we harness the power of deep neural network (DNN) models using the attention U-Net architecture. Through efficient training of these…
This paper presents a novel machine-learning framework for reconstructing low-order gust-encounter flow field and lift coefficients from sparse, noisy surface pressure measurements. Our study thoroughly investigates the time-varying…
In this document, a neural network is employed in order to estimate the solution of the initial value problem in the context of non linear trajectories. Such trajectories can be subject to gravity, thrust, drag, centrifugal force,…
We propose a data-driven control design method for nonlinear systems that builds on kernel-based interpolation. Under some assumptions on the system dynamics, kernel-based functions are built from data and a model of the system, along with…
Given the widespread availability of grids of models for stellar atmospheres, it is necessary to recover intermediate atmospheric models by means of accurate techniques that go beyond simple linear interpolation and capture the intricacies…
In this paper, we focus on the data-driven discovery of a general second-order particle-based model that contains many state-of-the-art models for modeling the aggregation and collective behavior of interacting agents of similar size and…