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Solving Differential Equations With Neural Networks

How Neural Networks are strong tools for solving differential equations without the use of training dataPhoto by Linus Mimietz on UnsplashDifferential equations are one of the protagonists in physical sciences, with vast applications in engineering, biology, economy, and even social sciences. Roughly speaking, they tell us how a quantity varies in time (or some other parameter, but usually we are interested in time variations). We can understand how a population, or a stock price, or even how the opinion of some society…

A Bird’s Eye View of Linear Algebra: Systems of Equations, Linear Regression, and Neural Networks

The humble matrix multiplication along with its inverse is almost exclusively what’s going on in many simple ML modelsContinue reading on Towards Data Science » The humble matrix multiplication along with its inverse is almost exclusively what’s going on in many simple ML modelsContinue reading on Towards Data Science » FOLLOW US ON GOOGLE NEWS Read original article here Denial of responsibility! Techno Blender is an automatic aggregator of the all world’s media. In each content, the hyperlink…

The Simpsons Invented This Surprisingly Tough Geometry Task

Hidden amid its trademark satire of average American life, The Simpsons is riddled with mathematical Easter eggs. The show’s writing staff has boasted an impressive pedigree of Ivy League mathheads who couldn’t resist infusing America’s longest-running sitcom with inside jokes, scattered about like sprinkles on Homer’s doughnuts.The Hunger Games Director Francis Lawrence on Adapting a PrequelAs early as the opening shot of the show’s second episode, the perpetually one-year old baby, Maggie, stacks her alphabet blocks to…

Linear Algebra 4: Matrix Equations

Solving matrix equations Ax= bPrefaceWelcome back to the fourth edition of my ongoing series on the basics of Linear Algebra, the foundational math behind machine learning. In my previous article, I introduced vectors, linear combinations, and vector spans. This essay will take a look at the matrix equation Ax = b and we’ll see how the very principle of solving a system of linear equations is linked to the matrix equation.This article would best serve readers if read in accompaniment with Linear Algebra and Its…

Differential Equations as a Pytorch Neural Network Layer | by Kevin Hannay | Apr, 2023

How to use differential equations layers in pytorchDifferential equations are the mathematical foundation for most of modern science. They describe the state of a system using an equation for the rate of change (differential). It is remarkable how many systems can be well described by equations of this form. For example, the physical laws describing motion, electromagnetism and quantum mechanics all take this form. More broadly, differential equations describe chemical reaction rates through the law of mass action,…

Microsoft makes Bing chatbot better at math equations, here’s how

Microsoft has been upgrading Bing Chat’s artificial intelligence (AI) prowess since its launch. Apart from releasing it to more services, it has also expanded the use cases of the AI chatbot. In the latest development, the company has now added support for LaTeX markup that will enable Bing chat to correctly display complex mathematical expressions. “We shipped support for LaTeX markup—allowing Bing chat to correctly display complex mathematical expressions. This makes Bing chat an even more useful tool for learning math…

New method for deriving approximate linear equations to complicated nonlinear problems

Credit: Kryshtofor Volodymyr/Shutterstock Researchers at the University of Tsukuba have created a new method for deriving approximate linear equations to complicated nonlinear problems. Using simulation results, they show that the model derived using their proposed pseudo-linearization approach yields responses that are closer to those of the well-known alternative method. This work can help scientists and engineers predict…

A New Computer Proof ‘Blows Up’ Centuries-Old Fluid Equations

For centuries, mathematicians have sought to understand and model the motion of fluids. The equations that describe how ripples crease the surface of a pond have also helped researchers to predict the weather, design better airplanes, and characterize how blood flows through the circulatory system. These equations are deceptively simple when written in the right mathematical language. However, their solutions are so complex that making sense of even basic questions about them can be prohibitively difficult.Perhaps the…

From 100,000 to 4 Equations, AI is Making Quantum Physics Problems Simple

Artificial Intelligence Reduces A 100,000 Equation to 4 Equations to Solve Quantum Physics ProblemsUsing artificial intelligence, physicists have solved daunting quantum physics problems. Studies show that new properties of complex quantum materials are much more manageable. This computational feat could help tackle one of quantum physics’ most difficult problems, the ‘many-electron’ problem, which attempts to describe systems containing large numbers of interacting electrons.The team believes that the “dimensionality…