Abstract Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode
model equations, like Partial Differential Equations (PDE), as a component of the neural …

Despite great progress in simulating multiphysics problems using the numerical
discretization of partial differential equations (PDEs), one still cannot seamlessly incorporate …

Uncertainty quantification (UQ) methods play a pivotal role in reducing the impact of
uncertainties during both optimization and decision making processes. They have been …

The use of quantum computing for machine learning is among the most exciting prospective
applications of quantum technologies. However, machine learning tasks where data is …

We show that passing input points through a simple Fourier feature mapping enables a
multilayer perceptron (MLP) to learn high-frequency functions in low-dimensional problem …

The effectiveness of machine learning algorithms arises from being able to extract useful
features from large amounts of data. As model and dataset sizes increase, dataset …

Classical machine learning (ML) provides a potentially powerful approach to solving
challenging quantum many-body problems in physics and chemistry. However, the …

We study how neural networks trained by gradient descent extrapolate, ie, what they learn
outside the support of the training distribution. Previous works report mixed empirical results …

The popularity of machine learning (ML), deep learning (DL) and artificial intelligence (AI)
has risen sharply in recent years. Despite this spike in popularity, the inner workings of ML …

A longstanding goal in deep learning research has been to precisely characterize training
and generalization. However, the often complex loss landscapes of neural networks have …