Related papers: A general framework for knowledge integration in m…

The capability of Deep Neural Networks (DNNs) to recognize objects in orientations outside the distribution of the training data is not well understood. We present evidence that DNNs are capable of generalizing to objects in novel…

Deep neural networks (DNNs) have been quite successful in solving many complex learning problems. However, DNNs tend to have a large number of learning parameters, leading to a large memory and computation requirement. In this paper, we…

We develop a mathematically rigorous framework for multilayer neural networks in the mean field regime. As the network's widths increase, the network's learning trajectory is shown to be well captured by a meaningful and dynamically…

Deep learning has the potential to revolutionize quantum chemistry as it is ideally suited to learn representations for structured data and speed up the exploration of chemical space. While convolutional neural networks have proven to be…

We propose a neural network-based meta-learning method to efficiently solve partial differential equation (PDE) problems. The proposed method is designed to meta-learn how to solve a wide variety of PDE problems, and uses the knowledge for…

We introduce Effective Field Neural Networks (EFNNs), a new architecture based on continued functions -- mathematical tools used in renormalization to handle divergent perturbative series. Our key insight is that neural networks can…

Physical networks, such as biological neural networks, can learn desired functions without a central processor, using local learning rules in space and time to learn in a fully distributed manner. Learning approaches such as equilibrium…

Real-world data contains aleatoric uncertainty - irreducible noise arising from imperfect measurements or from incomplete knowledge about the data generation process. Mean-variance estimation networks can learn this type of uncertainty but…

Transfer learning for feature extraction can be used to exploit deep representations in contexts where there is very few training data, where there are limited computational resources, or when tuning the hyper-parameters needed for training…

In Hezaveh et al. 2017 we showed that deep learning can be used for model parameter estimation and trained convolutional neural networks to determine the parameters of strong gravitational lensing systems. Here we demonstrate a method for…

Learning with kernels is an important concept in machine learning. Standard approaches for kernel methods often use predefined kernels that require careful selection of hyperparameters. To mitigate this burden, we propose in this paper a…

Compressing neural nets is an active research problem, given the large size of state-of-the-art nets for tasks such as object recognition, and the computational limits imposed by mobile devices. We give a general formulation of model…

Machine learning has emerged as a powerful tool in materials discovery, enabling the rapid design of novel materials with tailored properties for countless applications, including in the context of energy and sustainability. To ensure the…

A myriad of phenomena in materials science and chemistry rely on quantum-level simulations of the electronic structure in matter. While moving to larger length and time scales has been a pressing issue for decades, such large-scale…

This dissertation studies a fundamental open challenge in deep learning theory: why do deep networks generalize well even while being overparameterized, unregularized and fitting the training data to zero error? In the first part of the…

Microstructures, i.e., architected materials, are designed today, typically, by maximizing an objective, such as bulk modulus, subject to a volume constraint. However, in many applications, it is often more appropriate to impose constraints…

We study norm-based uniform convergence bounds for neural networks, aiming at a tight understanding of how these are affected by the architecture and type of norm constraint, for the simple class of scalar-valued one-hidden-layer networks,…

Deriving governing equations in Electromagnetic (EM) environment based on first principles can be quite tough when there are some unknown sources of noise and other uncertainties in the system. For nonlinear multiple-physics electromagnetic…

Nanophotonics enables unprecedented control over light-matter interactions, yet conventional isotropic materials limit the spectral range and mode response in subwavelength structures. Anisotropic nanoparticles -- ubiquitous in natural and…

Despite the successful implementations of physics-informed neural networks in different scientific domains, it has been shown that for complex nonlinear systems, achieving an accurate model requires extensive hyperparameter tuning, network…