Neural-Network Quantum States have been recently introduced as an Ansatz for describing the wave function of quantum many-body systems. We show that there are strong connections between Neural-Network Quantum States in the form of Restricted Boltzmann Machines and some classes of Tensor-Network states in arbitrary dimensions. In particular we demonstrate that short-range Restricted Boltzmann Machines are Entangled Plaquette States, while fully connected Restricted Boltzmann Machines are String-Bond States with a nonlocal geometry and low bond dimension. These results shed light on the underlying architecture of Restricted Boltzmann Machines and their efficiency at representing many-body quantum states. String-Bond States also provide a generic way of enhancing the power of Neural-Network Quantum States and a natural generalization to systems with larger local Hilbert space. We compare the advantages and drawbacks of these different classes of states and present a method to combine them together. This allows us to benefit from both the entanglement structure of Tensor Networks and the efficiency of Neural-Network Quantum States into a single Ansatz capable of targeting the wave function of strongly correlated systems. While it remains a challenge to describe states with chiral topological order using traditional Tensor Networks, we show that Neural-Network Quantum States and their String-Bond States extension can describe a lattice Fractional Quantum Hall state exactly. In addition, we provide numerical evidence that Neural-Network Quantum States can approximate a chiral spin liquid with better accuracy than Entangled Plaquette States and local String-Bond States. Our results demonstrate the efficiency of neural networks to describe complex quantum wave functions and pave the way towards the use of String-Bond States as a tool in more traditional machine-learning applications.
The Absorption, Distribution, Metabolism, Elimination, and Toxicity (ADMET) properties of drug candidates are estimated to account for up to 50% of all clinical trial failures. Predicting ADMET properties has therefore been of great interest to the cheminformatics and medicinal chemistry communities in recent decades. Traditional cheminformatics approaches, whether the learner is a random forest or a deep neural network, leverage fixed fingerprint feature representations of molecules. In contrast, in this paper, we learn the features most relevant to each chemical task at hand by representing each molecule explicitly as a graph, where each node is an atom and each edge is a bond. By applying graph convolutions to this explicit molecular representation, we achieve, to our knowledge, unprecedented accuracy in prediction of ADMET properties. By challenging our methodology with rigorous cross-validation procedures and prospective analyses, we show that deep featurization better enables molecular predictors to not only interpolate but also extrapolate to new regions of chemical space.
Understanding dynamic fracture propagation is essential to predicting how brittle materials fail. Various mathematical models and computational applications have been developed to predict fracture evolution and coalescence, including finite-discrete element methods such as the Hybrid Optimization Software Suite (HOSS). While such methods achieve high fidelity results, they can be computationally prohibitive: a single simulation takes hours to run, and thousands of simulations are required for a statistically meaningful ensemble. We propose a machine learning approach that, once trained on data from HOSS simulations, can predict fracture growth statistics within seconds. Our method uses deep learning, exploiting the capabilities of a graph convolutional network to recognize features of the fracturing material, along with a recurrent neural network to model the evolution of these features. In this way, we simultaneously generate predictions for qualitatively distinct material properties. Our prediction for total damage in a coalesced fracture, at the final simulation time step, is within 3% of its actual value, and our prediction for total length of a coalesced fracture is within 2%. We also develop a novel form of data augmentation that compensates for the modest size of our training data, and an ensemble learning approach that enables us to predict when the material fails, with a mean absolute error of approximately 15%.
This paper proposes the first step towards a novel unified framework for the analysis of perturbations occurring in nuclear reactors in both Time and Frequency domain. The identification of type and source of such perturbations is fundamental for monitoring core reactors and guarantee safety even while running at nominal conditions. A 3D Convolutional Neural Network (3D-CNN) was employed to analyse perturbations happening in the frequency domain, such as the alteration of an absorber of variable strength or propagating perturbation. Recurrent neural networks (RNN), specifically Long Short-Term Memory (LSTM) was used to study signal sequences related to perturbations induced in the time domain, including the vibrations of fuel assemblies and the fluctuation of thermalhydraulic parameters at the inlet of the reactor coolant loops. 512-dimensional representations were extracted from the 3D-CNN and LSTM architectures, and used as input to a fused multi-sigmoid classification layer to recognise the perturbation type. If the perturbation is frequency domain related, a separate fully-connected layer utilises said representations to regress the coordinates of its source. The results showed that perturbation type can be recognised with high accuracy in both domains, and frequency domain scenario sources can be localised with high precision.
Matter evolved under influence of gravity from minuscule density fluctuations. Non-perturbative structure formed hierarchically over all scales, and developed non-Gaussian features in the Universe, known as the Cosmic Web. To fully understand the structure formation of the Universe is one of the holy grails of modern astrophysics. Astrophysicists survey large volumes of the Universe and employ a large ensemble of computer simulations to compare with the observed data in order to extract the full information of our own Universe. However, to evolve trillions of galaxies over billions of years even with the simplest physics is a daunting task. We build a deep neural network, the Deep Density Displacement Model (hereafter D$^3$M), to predict the non-linear structure formation of the Universe from simple linear perturbation theory. Our extensive analysis, demonstrates that D$^3$M outperforms the second order perturbation theory (hereafter 2LPT), the commonly used fast approximate simulation method, in point-wise comparison, 2-point correlation, and 3-point correlation. We also show that D$^3$M is able to accurately extrapolate far beyond its training data, and predict structure formation for significantly different cosmological parameters. Our study proves, for the first time, that deep learning is a practical and accurate alternative to approximate simulations of the gravitational structure formation of the Universe.