Deriving Physical Laws with Neural Networks

Max Fusté Costa

February 2023

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

M.Raissia, P.Perdikarisb,∗, G.E.Karniadakisa

aDivision of Applied Mathematics, Brown University, Providence, RI, 02912, USA

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bDepartment of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA, 19104, USA

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Universal Physics-Informed Neural Networks: Symbolic Differential Operator Discovery with Sparse Data

Lena Podina * 1 Brydon Eastman * 2 Mohammad Kohandel

CS598: Physics-Informed Neural Networks:

A deep learning framework for solving forward and inverse

problems involving nonlinear PDEs

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M. Raissi, P. Perdikaris, GE. Karniadakis

Bhavesh Shrimali

November 18, 2021

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FACULTY OF SCIENCE AND TECHNOLOGY

MASTER THESIS

Study programme / specialisation:

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Applied Data Science

The spring semester, 2022

Open / Confidential

Author:

Lars Belbo Lukerstuen

…………………………………………

(signature author)

Course coordinator:

Supervisor(s):

Aksel Hiorth

Thesis title:

A Study on Physics Informed Neural Networks,

with Applications for Compartment Models

Credits (ECTS):

30

Keywords:

PiNN, Machine Learning,

Numerical Computation,

Physics Informed Learning

Pages: 77

+ appendix: 104

Stavanger, 13/06/2022

date/year

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Modeling, Monitoring and Control Based on Neural Networks

Chi Yung Fu

Publication presented at

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Materials Research Society Spring Meeting

San Francisco, California

April 17-21,1995

April 14,1995

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本文为爱思唯尔收费报告。西班牙格拉纳达大学研究人员系统梳理神经网络历史，从模型、模拟器到实现几方面阐释神经网络发展，展示了随时间推移，神经网络如何催生了计算神经学、神经工程学、计算智能和机器学习等学科。论文还探讨了与脑科学相关的信息处理研究，介绍了欧洲人类大脑计划、美国脑计划等各国神经网络相关重大科研项目，是对神经网络和计算神经科学的发展进行系统和全局理解的好资料。

作者：Alberto Prieto, Beatriz Prieto , Eva Martinez Ortigosa , Eduardo Ros , Francisco Pelayo , Julio Ortega , Ignacio Rojas

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摘要

本文从模型、模拟器及实现这几方面深入神经网络发展历程，发展神经网络有两个目的，一是弄清神经系统的运作机制，二是制造在功能上与之相似的系统，论文展示了随时间推移，神经网络如何催生了计算神经学、神经工程学、计算智能和机器学习等学科。更深入地理解人脑被视为本世纪的一大难题，论文还介绍了各国神经网络相关的重大科研项目。对神经网络和计算神经科学的发展有更系统和全局的理解。

神经网络：早期研究、当前框架和新的挑战

1. 神经网络（ANN）研究和目标简介

2. ANN 相关话题

2.1 模型、结构和算法

2.2 模拟器和专用硬件

2.2.1 模拟器

2.2.2 模拟器平台及神经硬件

2.2.2.1 通用平台

2.2.2.2 神经硬件

2.2.2.3 神经形态电路

2.2.2.4 神经加速器

2.2.2.5 神经形态计算机和系统

2.2.2.6 嵌入式神经形态系统

2.2.2.7 其他技术和趋势

3. 现实世界应用领域

4. 当前框架

5. 理解大脑生理结构面临的问题

6. 结论

7. 致谢

8. 参考文献

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Techniques and Systems for Training Large Neural Networks Quickly

Jeff Dean

Google

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Joint work with many colleagues at Google

How Can We Build More Intelligent Computer

Systems?

Need to perceive and understand the world

Basic speech and vision capabilities

Language understanding

User behavior prediction

…

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