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The connection of Taylor maps and polynomial neural networks (PNN) to solve ordinary differential equations (ODEs) numerically is considered. Having the system of ODEs, it is possible to calculate weights of PNN that simulates the dynamics…

We introduce a quantum Monte Carlo method to simulate the reversible dynamics of correlated many-body systems. Our method is based on the Laplace transform of the time-evolution operator which, as opposed to most quantum Monte Carlo…

Computational fluid dynamics (CFD) simulations of viscous fluids described by the Navier-Stokes equations are considered. Depending on the Reynolds number of the flow, the Navier-Stokes equations may exhibit a highly nonlinear behavior. The…

We propose a neural network based approach for extracting models from dynamic data using ordinary and partial differential equations. In particular, given a time-series or spatio-temporal dataset, we seek to identify an accurate governing…

This paper presents a data driven universal ball trajectory prediction method integrated with physics equations. Existing methods are designed for specific ball types and struggle to generalize. This challenge arises from three key factors.…

Neural Ordinary Differential Equations (NODEs) use a neural network to model the instantaneous rate of change in the state of a system. However, despite their apparent suitability for dynamics-governed time-series, NODEs present a few…

Exact numerical simulations of dynamics of open quantum systems often require immense computational resources. We demonstrate that a deep artificial neural network comprised of convolutional layers is a powerful tool for predicting…

Unraveling the dynamical motions of biomolecules is essential for bridging their structure and function, yet it remains a major computational challenge. Molecular dynamics (MD) simulation provides a detailed depiction of biomolecular…

Here we present a parametric model for dynamic textures. The model is based on spatiotemporal summary statistics computed from the feature representations of a Convolutional Neural Network (CNN) trained on object recognition. We demonstrate…

Deep learning involves a difficult non-convex optimization problem, which is often solved by stochastic gradient (SG) methods. While SG is usually effective, it may not be robust in some situations. Recently, Newton methods have been…

Accurate molecular force fields are of paramount importance for the efficient implementation of molecular dynamics techniques at large scales. In the last decade, machine learning methods have demonstrated impressive performances in…

The presented work demonstrates the training of recurrent neural networks (RNNs) from distributions of atom coordinates in solid state structures that were obtained using ab initio molecular dynamics (AIMD) simulations. AIMD simulations on…

This paper explores the application of tensor networks (TNs) to the simulation of material deformations within the framework of linear elasticity. Material simulations are essential computational tools extensively used in both academic…

We describe collective-move Monte Carlo algorithms designed to approximate the overdamped dynamics of self-assembling nanoscale components equipped with strong, short-ranged and anisotropic interactions. Conventional Monte Carlo simulations…

Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…

The advancement of human healthspan and bioengineering relies heavily on predicting the behavior of complex biological systems. While high-throughput multiomics data is becoming increasingly abundant, converting this data into actionable…

We study the applicability of a Deep Neural Network (DNN) approach to simulate one-dimensional non-relativistic fluid dynamics. Numerical fluid dynamical calculations are used to generate training data-sets corresponding to a broad range of…

Molecular dynamics (MD) simulations are used in biochemistry, physics, and other fields to study the motions, thermodynamic properties, and the interactions between molecules. Computational limitations and the complexity of these problems,…

Recurrent neural networks (RNNs) have been used extensively and with increasing success to model various types of sequential data. Much of this progress has been achieved through devising recurrent units and architectures with the…

We have proposed new algorithms for the numerical integration of the equations of motion for classical spin systems. In close analogy to symplectic integrators for Hamiltonian equations of motion used in Molecular Dynamics these algorithms…