Related papers: Ab-Initio Potential Energy Surfaces by Pairing GNN…

The quantum Monte Carlo (QMC) is one of the most promising many-body electronic structure approaches. It employs stochastic techniques for solving the stationary Schr\" odinger equation and for evaluation of expectation values. The key…

It was recently shown that the Madelung equations, that is, a hydrodynamic form of the Schr\"odinger equation, can be derived from a canonical ensemble of neural networks where the quantum phase was identified with the free energy of hidden…

To overcome these obstacles and improve computational accuracy and efficiency, this paper presents the Randomized Radial Basis Function Neural Network (RRNN), an innovative approach explicitly crafted for solving multiscale elliptic…

While Annealing Machines (AM) have shown increasing capabilities in solving complex combinatorial problems, positioning themselves as a more immediate alternative to the expected advances of future fully quantum solutions, there are still…

The Non-Markovian Stochastic Schrodinger Equation (NMSSE) offers a promising approach for open quantum simulations, especially in large systems, owing to its low scaling complexity and suitability for parallel computing. However, its…

The paper uses statistical and differential geometric motivation to acquire prior information about the learning capability of an artificial neural network on a given dataset. The paper considers a broad class of neural networks with…

Deep neural networks have been shown as a potentially powerful ansatz in variational Monte Carlo for solving quantum many-body problems. We propose two improvements in this direction. The first is graph neural ansatz (GNA), which is a…

We introduce the concept of a Graph-Informed Neural Network (GINN), a hybrid approach combining deep learning with probabilistic graphical models (PGMs) that acts as a surrogate for physics-based representations of multiscale and…

We present a simple, yet general, end-to-end deep neural network representation of the potential energy surface for atomic and molecular systems. This methodology, which we call Deep Potential, is "first-principle" based, in the sense that…

One of the main challenges in using deep learning-based methods for simulating physical systems and solving partial differential equations (PDEs) is formulating physics-based data in the desired structure for neural networks. Graph neural…

Predicting the structure of quantum many-body systems from the first principles of quantum mechanics is a common challenge in physics, chemistry, and material science. Deep machine learning has proven to be a powerful tool for solving…

Quantum mechanics has introduced a new theoretical framework for the study of molecules, enabling the prediction of properties and dynamics through the solution of the Schr\"odinger equation applied to these systems. However, solving this…

Surface wave tomography uses measured dispersion properties of surface waves to infer the spatial distribution of subsurface properties such as shear-wave velocities. These properties can be estimated vertically below any geographical…

By conceiving physical systems as 3D many-body point clouds, geometric graph neural networks (GNNs), such as SE(3)/E(3) equivalent GNNs, have showcased promising performance. In particular, their effective message-passing mechanics make…

Neural quantum states (NQS) have gained prominence in variational quantum Monte Carlo methods in approximating ground-state wavefunctions. Despite their success, they face limitations in optimization, scalability, and expressivity in…

The main approach to hybrid quantum-classical neural networks (QNN) is employing quantum computing to build a neural network (NN) that has quantum features, which is then optimized classically. Here, we propose a different strategy: to use…

We present a Graph Neural Network (GNN) that accurately simulates a multidisperse suspension of interacting spherical particles. Our machine learning framework is built upon the recent work of Sanchez-Gonzalez et al. ICML, PMLR, 119,…

Bayesian Neural Networks (BNNs) provide a promising framework for modeling predictive uncertainty and enhancing out-of-distribution robustness (OOD) by estimating the posterior distribution of network parameters. Stochastic Gradient Markov…

The goal of this work is to train a neural network which approximates solutions to the Navier-Stokes equations across a region of parameter space, in which the parameters define physical properties such as domain shape and boundary…

The application of deep learning to symbolic domains remains an active research endeavour. Graph neural networks (GNN), consisting of trained neural modules which can be arranged in different topologies at run time, are sound alternatives…