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Given access to accurate solutions of the many-electron Schr\"odinger equation, nearly all chemistry could be derived from first principles. Exact wavefunctions of interesting chemical systems are out of reach because they are NP-hard to…

Recently developed neural network-based \emph{ab-initio} solutions (Pfau et. al arxiv:1909.02487v2) for finding ground states of fermionic systems can generate state-of-the-art results on a broad class of systems. In this work, we improve…

Metasurfaces have become a promising means for manipulating optical wavefronts in flat and high-performance optical devices. Conventional metasurface device design relies on trial-and-error methods to obtain target electromagnetic (EM)…

Variational quantum Monte Carlo (QMC) is an ab-initio method for solving the electronic Schr\"odinger equation that is exact in principle, but limited by the flexibility of the available ansatzes in practice. The recently introduced deep…

Neural-network quantum states offer a flexible route to compact many-electron wave functions, but their practical accuracy depends strongly on how fermionic antisymmetry, electron correlation, and optimization noise are treated. Here we…

In this paper we consider the limiting case of neural networks (NNs) architectures when the number of neurons in each hidden layer and the number of hidden layers tend to infinity thus forming a continuum, and we derive approximation errors…

Finding reliable approximations to the quantum many-body problem is one of the central challenges of modern physics. Elemental to this endeavor is the development of advanced numerical techniques pushing the limits of what is tractable. One…

NeuroNet is a deep convolutional neural network mimicking multiple popular and state-of-the-art brain segmentation tools including FSL, SPM, and MALPEM. The network is trained on 5,000 T1-weighted brain MRI scans from the UK Biobank Imaging…

In open data sets of functional magnetic resonance imaging (fMRI), the heterogeneity of the data is typically attributed to a combination of factors, including differences in scanning procedures, the presence of confounding effects, and…

Solving variational image segmentation problems with hidden physics is often expensive and requires different algorithms and manually tunes model parameter. The deep learning methods based on the U-Net structure have obtained outstanding…

This paper introduces the Neural Differential Manifold (NDM), a novel neural network architecture that explicitly incorporates geometric structure into its fundamental design. Departing from conventional Euclidean parameter spaces, the NDM…

Uniform-precision neural network quantization has gained popularity since it simplifies densely packed arithmetic unit for high computing capability. However, it ignores heterogeneous sensitivity to the impact of quantization errors across…

Motivated by the famous and pioneering mathematical works by Perelman, Hamilton, and Thurston, we introduce the concept of using modern geometrical mathematical classifications of multi-dimensional manifolds to characterize electronic…

This paper presents a physics-informed neural network approach for dynamic modeling of saturable synchronous machines, including cases with spatial harmonics. We introduce an architecture that incorporates gradient networks directly into…

We develop a Mean-Field (MF) view of the learning dynamics of overparametrized Artificial Neural Networks (NN) under data symmetric in law wrt the action of a general compact group $G$. We consider for this a class of generalized shallow…

Automated brain tissue segmentation into white matter (WM), gray matter (GM), and cerebro-spinal fluid (CSF) from magnetic resonance images (MRI) is helpful in the diagnosis of neuro-disorders such as epilepsy, Alzheimer's, multiple…

Interpretable deep learning models have received widespread attention in the field of image recognition. Due to the unique multi-instance learning of medical images and the difficulty in identifying decision-making regions, many…

This paper demonstrates a method for tensorizing neural networks based upon an efficient way of approximating scale invariant quantum states, the Multi-scale Entanglement Renormalization Ansatz (MERA). We employ MERA as a replacement for…

The architecture of a neural network and the selection of its activation function are both fundamental to its performance. Equally vital is ensuring these two elements are well-matched, as their alignment is key to achieving effective…

Convolutional neural network (CNN) has achieved impressive success in computer vision during the past few decades. The image convolution operation helps CNNs to get good performance on image-related tasks. However, it also has high…