相关实验视频

Updated: Apr 13, 2026

Deep Neural Networks for Image-Based Dietary Assessment
13:19

Deep Neural Networks for Image-Based Dietary Assessment

Published on: March 13, 2021

8.9K

部分微分方程与深度神经网络相遇:一项调查

Shudong Huang, Wentao Feng, Chenwei Tang

    IEEE transactions on neural networks and learning systems
    |March 14, 2025
    PubMed
    概括

    深度学习 (DL) 为解决复杂的局部微分方程 (PDEs) 的传统数值方法提供了强大的替代方案. 这项调查系统地审查了各种深度神经网络 (NN) 方法,用于各种科学领域的PDE解决方案.

    更多相关视频

    Author Spotlight: Enhancement of Salient Object Detection for Smart Grid Applications03:31

    Author Spotlight: Enhancement of Salient Object Detection for Smart Grid Applications

    Published on: December 15, 2023

    449
    Author Spotlight: Advancing Alzheimer's Research – Exploring Early Detection and Multi-Omics Approaches09:47

    Author Spotlight: Advancing Alzheimer's Research – Exploring Early Detection and Multi-Omics Approaches

    Published on: December 15, 2023

    933

    相关概念视频

    State Function, Exact and Inexact Differentials01:27

    State Function, Exact and Inexact Differentials

    A state function is a thermodynamic property that depends solely on the current state of a system, irrespective of its history or how it arrived at that state. These functions are represented by capital letters, such as U, H, and S, which stand for internal energy, enthalpy, and entropy, respectively.For instance, the value of internal energy depends on the system's state variables and remains unaffected by the process path. This means that whether the system underwent a linear process or a...
    149
    Introduction to Differential Equations01:20

    Introduction to Differential Equations

    A differential equation is a mathematical expression that establishes a relationship between a function and its derivatives. These equations are fundamental in modeling dynamic systems across various fields of science and engineering. The order of a differential equation is defined by the highest order derivative present in the equation. A first-order differential equation includes only the first derivative, while a second-order differential equation includes up to the second derivative of the...
    435
    Modeling with Differential Equations01:25

    Modeling with Differential Equations

    Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
    278
    Separable Differential Equations01:20

    Separable Differential Equations

    A separable differential equation is a type of first-order differential equation where the derivative dy/dx can be expressed as a product of two functions: one that depends only on x and another that depends only on y. This allows for the rearrangement of the equation so that all terms involving y are on one side, and all terms involving x are on the other. This process, known as the separation of variables, simplifies the process of solving the equation by enabling the integration of both...
    304
    Linear Differential Equations01:27

    Linear Differential Equations

    The integrating factor method provides a systematic way to solve first-order linear differential equations, especially those that cannot be handled by separation of variables. This method is particularly useful in modeling time-dependent physical systems influenced by both constant inputs and resistive forces. A common example is the motion of a car subjected to a constant engine force while experiencing air resistance proportional to its velocity.In such scenarios, Newton’s second law...
    245
    Differential Equations: Problem Solving01:21

    Differential Equations: Problem Solving

    When analyzing the motion of falling objects, it is essential to consider not only the force of gravity but also the opposing force of air resistance. A practical example involves releasing a heavy test weight during a safety check on a ship. As the weight falls from rest, gravity accelerates it downward while air resistance exerts an upward force that increases with velocity. This dynamic interplay of forces is well described by differential equations, which provide a mathematical framework...
    199