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Differential equations are used to model and predict the behaviour of complex systems in a wide range of fields, and the ability to solve them is an important asset for understanding and predicting the behaviour of these systems.…

机器学习 · 计算机科学 2023-01-31 Siddharth Nand , Yuecheng Cai

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…

ADCME is a novel computational framework to solve inverse problems involving physical simulations and deep neural networks (DNNs). This paper benchmarks its capability to learn spatially-varying physical fields using DNNs. We demonstrate…

数值分析 · 数学 2020-11-25 Kailai Xu , Eric Darve

Physics-informed neural networks have attracted significant attention in scientific machine learning for their capability to solve forward and inverse problems governed by partial differential equations. However, the accuracy of PINN…

机器学习 · 计算机科学 2025-11-06 Shota Deguchi , Mitsuteru Asai

Quickly and reliably finding accurate inverse kinematics (IK) solutions remains a challenging problem for robotic manipulation. Existing numerical solvers typically produce a single solution only and rely on local search techniques to…

机器人学 · 计算机科学 2023-07-06 Oliver Limoyo , Filip Marić , Matthew Giamou , Petra Alexson , Ivan Petrović , Jonathan Kelly

We present a novel deep learning-based algorithm to accelerate - through the use of Artificial Neural Networks (ANNs) - the convergence of Algebraic Multigrid (AMG) methods for the iterative solution of the linear systems of equations…

数值分析 · 数学 2025-06-18 Paola F. Antonietti , Matteo Caldana , Luca Dede'

We propose an approach based on Artificial Neural Networks (ANNs) to evaluate geometric constants relevant to the analysis and design of numerical schemes for partial differential equations. These constants play a central role,…

数值分析 · 数学 2025-11-21 Beatrice Crippa , Sofia Imperatore , Silvia Bertoluzza , Micol Pennacchio

This paper is concerned with the approximation of the solution of partial differential equations by means of artificial neural networks. Here a feedforward neural network is used to approximate the solution of the partial differential…

数值分析 · 数学 2019-04-10 Henri Calandra , Serge Gratton , Elisa Riccietti , Xavier Vasseur

In this paper, we construct approximated solutions of Differential Equations (DEs) using the Deep Neural Network (DNN). Furthermore, we present an architecture that includes the process of finding model parameters through experimental data,…

数值分析 · 数学 2019-07-31 Hyeontae Jo , Hwijae Son , Hyung Ju Hwang , Eunheui Kim

Artificial Neural Networks (ANN) have been employed for a range of modelling and prediction tasks using financial data. However, evidence on their predictive performance, especially for time-series data, has been mixed. Whereas some…

风险管理 · 定量金融 2022-05-17 Philipp Ratz

This paper investigates the use of artificial neural networks (ANNs) to replace traditional algorithms and manual review for identifying anomalies in vehicle run data. The specific data used for this study is from undersea vehicle…

神经与进化计算 · 计算机科学 2016-03-17 Adam J. Last

Inertial measurement units are commonly used to estimate the attitude of moving objects. Numerous nonlinear filter approaches have been proposed for solving the inherent sensor fusion problem. However, when a large range of different…

机器学习 · 计算机科学 2021-08-11 Daniel Weber , Clemens Gühmann , Thomas Seel

Classical molecular dynamics simulations are based on solving Newton's equations of motion. Using a small timestep, numerical integrators such as Verlet generate trajectories of particles as solutions to Newton's equations. We introduce…

计算物理 · 物理学 2021-12-15 JCS Kadupitiya , Geoffrey C. Fox , Vikram Jadhao

This paper is concerned with the optimal kinematic control of a robot manipulator where the robot end effector position follows a task space trajectory. The joints are actuated with the desired velocity profile to achieve this task. This…

系统与控制 · 电气工程与系统科学 2019-08-07 Aiswarya Menon , Ravi Prakash , Laxmidhar Behera

The purpose of this work is the development of an artificial neural network (ANN) for surrogate modeling of the mechanical response of viscoplastic grain microstructures. To this end, a U-Net-based convolutional neural network (CNN) is…

The ability to accurately model mechanical hysteretic behavior in tendon-actuated continuum robots using deep learning approaches is a growing area of interest. In this paper, we investigate the hysteretic response of two types of…

Quantum many-body physics simulation has important impacts on understanding fundamental science and has applications to quantum materials design and quantum technology. However, due to the exponentially growing size of the Hilbert space…

量子物理 · 物理学 2024-04-18 Zhuo Chen , Laker Newhouse , Eddie Chen , Di Luo , Marin Soljačić

We show that in addition to providing effective and competitive closures, when analysed in terms of dynamics and physically-relevant diagnostics, artificial neural networks (ANNs) can be both interpretable and provide useful insights in the…

计算物理 · 物理学 2020-12-30 Gavin D. Portwood , Balasubramanya T. Nadiga , Juan A. Saenz , Daniel Livescu

As an emerging technology in deep learning, physics-informed neural networks (PINNs) have been widely used to solve various partial differential equations (PDEs) in engineering. However, PDEs based on practical considerations contain…

机器学习 · 计算机科学 2021-11-11 Yuhao Huang

We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…

数值分析 · 数学 2022-10-10 Sergio Blanes