Related papers: Fourier neural operator for learning solutions to …

The precise simulation of turbulent flows is of immense importance in a variety of scientific and engineering fields, including climate science, freshwater science, and the development of energy-efficient manufacturing processes. Within the…

The application of deep learning toward discovery of data-driven models requires careful application of inductive biases to obtain a description of physics which is both accurate and robust. We present here a framework for discovering…

We propose the Inverse Neural Operator (INO), a two-stage framework for recovering hidden ODE parameters from sparse, partial observations. In Stage 1, a Conditional Fourier Neural Operator (C-FNO) with cross-attention learns a…

The rapid development of autonomous vehicles (AVs) holds vast potential for transportation systems through improved safety, efficiency, and access to mobility. However, the progression of these impacts, as AVs are adopted, is not well…

Macroscopic traffic models are necessary for simulation and study of traffic's complex macro-scale dynamics, and are often used by practitioners for road network planning, integrated corridor management, and other applications. These models…

High-fidelity simulations of laser welding capture complex thermo-fluid phenomena, including phase change, free-surface deformation, and keyhole dynamics, however their computational cost limits large-scale process exploration and real-time…

To ensure frequency security in power systems, both the rate of change of frequency (RoCoF) and the frequency nadir (FN) must be explicitly accounted for in real-time frequency-constrained optimal power flow (FCOPF). However, accurately…

This article introduces a novel approach to learning monotone neural networks through a newly defined penalization loss. The proposed method is particularly effective in solving classes of variational problems, specifically monotone…

We develop a deep learning model to predict traffic flows. The main contribution is development of an architecture that combines a linear model that is fitted using $\ell_1$ regularization and a sequence of $\tanh$ layers. The challenge of…

Neural operators (NOs) are designed to learn maps between infinite-dimensional function spaces. We propose a novel reframing of their use. By introducing an auxiliary base-space, any finite-dimensional function can be viewed as an operator…

Machine learning applied to computer vision and signal processing is achieving results comparable to the human brain on specific tasks due to the great improvements brought by the deep neural networks (DNN). The majority of state-of-the-art…

Recent researches show that machine learning has the potential to learn better heuristics than the one designed by human for solving combinatorial optimization problems. The deep neural network is used to characterize the input instance for…

Numerically solving partial differential equations typically requires fine discretization to resolve necessary spatiotemporal scales, which can be computationally expensive. Recent advances in deep learning have provided a new approach to…

This paper presents a novel learning-based trajectory planning framework for quadrotors that combines model-based optimization techniques with deep learning. Specifically, we formulate the trajectory optimization problem as a quadratic…

Supervised deep learning methods typically require large datasets and high-quality labels to achieve reliable predictions. However, their performance often degrades when trained on imperfect labels. To address this challenge, we propose a…

Space-time visualizations of macroscopic or microscopic traffic variables is a qualitative tool used by traffic engineers to understand and analyze different aspects of road traffic dynamics. We present a deep learning method to learn the…

An encoder-decoder neural network has been used to examine the possibility for acceleration of a partial integro-differential equation, the Fokker-Planck-Landau collision operator. This is part of the governing equation in the massively…

Neural Operators that directly learn mappings between function spaces, such as Deep Operator Networks (DONs) and Fourier Neural Operators (FNOs), have received considerable attention. Despite the universal approximation guarantees for DONs…

We consider solving partial differential equations (PDEs) with Fourier neural operators (FNOs), which operate in the frequency domain. Since the laws of physics do not depend on the coordinate system used to describe them, it is desirable…

With massive advancements in sensor technologies and Internet-of-things, we now have access to terabytes of historical data; however, there is a lack of clarity in how to best exploit the data to predict future events. One possible…