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

The dynamics of physical systems is often constrained to lower dimensional sub-spaces due to the presence of conserved quantities. Here we propose a method to learn and exploit such symmetry constraints building upon Hamiltonian Neural…

Equations governing physico-chemical processes are usually known at microscopic spatial scales, yet one suspects that there exist equations, e.g. in the form of Partial Differential Equations (PDEs), that can explain the system evolution at…

It is well known that physical phenomena may be of great help in computing some difficult problems efficiently. A typical example is prime factorization that may be solved in polynomial time by exploiting quantum entanglement on a quantum…

One of the most significant challenges involved in efforts to understand the effects of repeated earthquake cycle activity are the computational costs of large-scale viscoelastic earthquake cycle models. Computationally intensive…

Differential equations parameterized by neural networks become expensive to solve numerically as training progresses. We propose a remedy that encourages learned dynamics to be easier to solve. Specifically, we introduce a differentiable…

Isaac Newton formulated the central difference algorithm (Eur. Phys. J. Plus (2020) 135:267) when he derived his second law. The algorithm is under various names ("Verlet, leap-frog,...") the most used algorithm in simulations of complex…

Simulating the dynamics of ions near polarizable nanoparticles (NPs) using coarse-grained models is extremely challenging due to the need to solve the Poisson equation at every simulation timestep. Recently, a molecular dynamics (MD) method…

Massively parallel hardware (GPUs) and long sequence data have made parallel algorithms essential for machine learning at scale. Yet dynamical systems, like recurrent neural networks and Markov chain Monte Carlo, were thought to suffer from…

In this paper, we present an~algorithm that computes funnels along trajectories of systems of ordinary differential equations. A funnel is a time-varying set of states containing the given trajectory, for which the evolution from within the…

Neural operators, which emerge as implicit solution operators of hidden governing equations, have recently become popular tools for learning responses of complex real-world physical systems. Nevertheless, the majority of neural operator…

Data-driven modeling of human motions is ubiquitous in computer graphics and computer vision applications, such as synthesizing realistic motions or recognizing actions. Recent research has shown that such problems can be approached by…

A revised version of the quaternion approach for numerical integration of the equations of motion for rigid polyatomic molecules is proposed. The modified approach is based on a formulation of the quaternion dynamics with constraints. This…

Most computer simulations of molecular dynamics take place under equilibrium conditions--in a closed, isolated system, or perhaps one held at constant temperature or pressure. Sometimes, extra tensions, shears, or temperature gradients are…

Deep neural networks (DNNs), especially physics-informed neural networks (PINNs), have recently become a new popular method for solving forward and inverse problems governed by partial differential equations (PDEs). However, these methods…

In recent years, machine learning methods have been widely used to study physical systems that are challenging to solve with governing equations. Physicists and engineers are framing the data-driven paradigm as an alternative approach to…

The variability of renewable energy generation and the unpredictability of electricity demand create a need for real-time economic dispatch (ED) of assets in microgrids. However, solving numerical optimization problems in real-time can be…

Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…

Data-driven simulation of pedestrian dynamics is an incipient and promising approach for building reliable microscopic pedestrian models. We propose a methodology based on generalized regression neural networks, which does not have to deal…

This paper proposes a computational procedure that applies a quantum algorithm to train classical artificial neural networks. The goal of the procedure is to apply quantum walk as a search algorithm in a complete graph to find all synaptic…

Forecasting time series and time-dependent data is a common problem in many applications. One typical example is solving ordinary differential equation (ODE) systems $\dot{x}=F(x)$. Oftentimes the right hand side function $F(x)$ is not…