Shivam Barwey’s Post

Here are 10 equations that have significantly impacted various fields and changed the world: 1. **Newton's Law of Universal Gravitation:** \(F = \frac{{G \cdot m_1 \cdot m_2}}{{r^2}}\)   - This equation describes the gravitational force between two objects and laid the foundation for classical mechanics. 2. **Einstein's Theory of Relativity (E=mc²):** \(E = mc^2\)   - This equation relates energy (E) to mass (m) and the speed of light (c), revolutionizing our understanding of space, time, and energy. 3. **Maxwell's Equations:** These four equations describe the behavior of electric and magnetic fields, unifying electricity, magnetism, and light into electromagnetism. 4. **Schrodinger's Wave Equation:** \(i\hbar \frac{\partial \Psi}{\partial t} = -\frac{\hbar^2}{2m} \nabla^2 \Psi + V \Psi\)   - This equation describes the behavior of quantum mechanical systems, forming the basis of quantum mechanics. 5. **The Navier-Stokes Equations:** These equations describe the motion of fluid substances and have widespread applications in fields such as aerodynamics, weather forecasting, and oceanography. 6. **The Black-Scholes Equation:** This partial differential equation revolutionized finance by providing a way to price options, derivatives, and other financial instruments. 7. **The Logistic Equation:** \( \frac{dN}{dt} = rN\left(1 - \frac{N}{K}\right) \)   - This equation models population growth, describing how populations stabilize when resources become limited. 8. **The Fourier Transform:** This mathematical operation decomposes a function into its constituent frequencies, with applications in signal processing, image analysis, and many other fields. 9. **The Heat Equation:** \( \frac{\partial u}{\partial t} = k \nabla^2 u \)   - This equation describes how heat diffuses through a given medium and has applications in physics, engineering, and finance. 10. **The Drake Equation:** \( N = R^* \times f_p \times n_e \times f_l \times f_i \times f_c \times L \)   - Though more speculative, this equation provides a framework for estimating the number of active, communicative extraterrestrial civilizations in the Milky Way galaxy.

Perspective paper on simulations of water with machine learning potentials (Omranpour, Montero De Hijes, Behler & Dellago) https://lnkd.in/d3U5iJjY #MachineLearning #SimulationScience #WaterResearch #ComputationalChemistry #MolecularDynamics #MLPotentials #Chemistry #AIinScience #PhysicalChemistry #MaterialScience

Artifical general intelligence (AGI) is a big goal of modern AI research. One project that we are working on lately is to try to derive the "physics" of such general inference models, by relating the dynamics of model parameters to the statistical mechanics of prediction. A couple of months ago I posted an update on the project and got a lot of great feedback from people. Thanks so much for all your help! I have since reworked the pitch and some derivations of the work. While the project is still far from complete, I think its at a level where I can present it again. Please take a look and let me know what you think! #artificialintelligence #physics #deeplearning #physicsofai #machinelearning #research https://lnkd.in/e2hdrStw

As the heaviest elementary particle in the Standard Model, the top quark is key to understanding the origin of mass. ATLAS researchers are delving deep into the production of the Higgs boson with a top-quark pair ("ttH production"). Although this accounts for only 1% of Higgs bosons produced, it offers a unique chance to measure the interaction between the top quark and the Higgs boson. Using advanced machine learning techniques, ATLAS has achieved the most precise individual measurement of ttH production yet. Read our new briefing to learn more ⤵️

Machine learning and AI - not just for generating odes to your dog. It can also be used to further our understanding of the universe. Brilliant work by the ATLAS Collaboration in gaining even better insights from CERN’s massive ATLAS data sets #AIisMoreThanGenAI

Did you know? An Ising machine is a computational model that has gained a lot of popularity and traction in recent years for showing the potential of solving previously intractable problems. Read QCi’s latest lesson explaining what exactly is an Ising machine, an Ising model, and whether or not they are actually new. #QCiLesson #LessonofWeek #QCi #Ising #IsingModel #Physics #ComputerScience #QuantumMechanics #Optimization

Today I gladly share with my network that our paper entitled "A data-driven turbulence modeling for the Reynolds stress tensor transport equation" has been published at the International Journal for Numerical Methods in Fluids! It is comprised by a significant part of my master's thesis. I co-authored it with Matheus Altomare, MSc., Bernardo Brener and my thesis advisor Roney Thompson. In this work we have introduced a modified transport equation for the Reynolds stress that is driven by a source term predicted by neural networks. The transport equation was coupled with the momentum balance and the SIMPLE algorithm for pressure, forming a full data-driven Reynolds stress model, which was used to correct RANS simulations. DNS simulations for the square-duct flow were used to train the newtork and validate the results. You can access it at https://lnkd.in/dJaB76Ny and it is fully available for free at https://lnkd.in/dZTyKt8H You can also access the model's implementation as an OpenFOAM turbulence model at this repository on Github https://lnkd.in/dpb9UqRm

This is a rather "outside the box" application Feynman's path integrals to score based generative machine learning models. For someone who came to this field from physics it warms my heart to see it being applied in ML. It's more of a toy example as it's not being applied to real image diffusion models but they end up deriving the model equivalent of planks constant, which is funny. Understanding some aspects even the toy model requires using some abstract application of the same mathematics that underpins quantum mechanics, ML just keeps getting more interesting.

A thought after reading the paper: I don’t know if this method would work for some areas where the phenonomena of interest are primarily resonances. The goal of finding narrow resonances often requires fine discretization and almost by definition they exist as special, finely tuned states or modes within the overall space of possible behaviors. Moreover, they are often the result of nonlinear interactions or geometry and often exist in phase space as fragile structures, easily destroyed or distorted by the type of low-resultion sampling this hybrid method uses. That being said, I haven’t tried it and perhaps my intuitions are off. However my experiences modeling resonances in optical microcavities and observing how those resonances shift and degrade, sometimes with very small changes to the parameters, leads me to believe that the claimed speed up may be aspirational in those situations.