相关论文: Solving Newton's Equations of Motion with Large Ti…

We develop a randomized Newton's method for solving differential equations, based on a fully connected neural network discretization. In particular, the randomized Newton's method randomly chooses equations from the overdetermined nonlinear…

Modern power systems require fast and accurate dynamic simulations for stability assessment, digital twins, and real-time control, but classical ODE solvers are often too slow for large-scale or online applications. We propose a…

Training of convolutional neural networks is a high dimensional and a non-convex optimization problem. At present, it is inefficient in situations where parametric learning rates can not be confidently set. Some past works have introduced…

Initial value problems -- a system of ordinary differential equations and corresponding initial conditions -- can be used to describe many physical phenomena including those arise in classical mechanics. We have developed a novel approach…

The emergence of collective dynamics in neural networks is a mechanism of the animal and human brain for information processing. In this paper, we develop a computational technique using distributed processing elements in a complex network,…

Physics-informed neural networks solve partial differential equations by training neural networks. Since this method approximates infinite-dimensional PDE solutions with finite collocation points, minimizing discretization errors by…

Dual descent methods are commonly used to solve network optimization problems because their implementation can be distributed through the network. However, their convergence rates are typically very slow. This paper introduces a family of…

We develop data-driven models to predict the dynamics of a freely settling sphere in a quiescent Newtonian fluid using experimentally obtained trajectories. Particle tracking velocimetry was used to obtain a comprehensive dataset of…

In this work we present an application of modern deep learning methodologies to the numerical solution of partial differential equations in transport models. More specifically, we employ a supervised deep neural network that takes into…

Diverse optimization algorithms correctly identify, in finite time, intrinsic constraints that must be active at optimality. Analogous behavior extends beyond optimization to systems involving partly smooth operators, and in particular to…

Partial differential equations have a wide range of applications in modeling multiple physical, biological, or social phenomena. Therefore, we need to approximate the solutions of these equations in computationally feasible terms. Nowadays,…

A class of algorithms comprised by certain semismooth Newton and active-set methods is able to solve convex minimization problems involving sparsity-inducing regularizers very rapidly; the speed advantage of methods from this class is a…

Efficient simulation of the Navier-Stokes equations for fluid flow is a long standing problem in applied mathematics, for which state-of-the-art methods require large compute resources. In this work, we propose a data-driven approach that…

One of the biggest challenges for simulating the Boltzmann equation is the evaluation of fivefold collision integral. Given the recent successes of deep learning and the availability of efficient tools, it is an obvious idea to try to…

In numerous contexts, high-resolution solutions to partial differential equations are required to capture faithfully essential dynamics which occur at small spatiotemporal scales, but these solutions can be very difficult and slow to obtain…

Exascale computing holds great opportunities for molecular dynamics (MD) simulations. However, to take full advantage of the new possibilities, we must learn how to focus computational power on the discovery of complex molecular mechanisms,…

We discuss the structure of the equation of motion that governs nucleation processes at first order phase transitions. From the underlying microscopic dynamics of a nucleating system, we derive by means of a non-equilibrium projection…

Recent advances at the intersection of control theory, neuroscience, and machine learning have revealed novel mechanisms by which dynamical systems perform computation. These advances encompass a wide range of conceptual, mathematical, and…

The three body problem is a special case of the n body problem where one takes the initial positions and velocities of three point masses and attempts to predict their motion over time according to Newtonian laws of motion and universal…

Spatio-temporal dynamics of physical processes are generally modeled using partial differential equations (PDEs). Though the core dynamics follows some principles of physics, real-world physical processes are often driven by unknown…