OPTIMUM SEISMIC, Inc.’s Post

Symplectic Foliation Model of Information Geometry for Statistics and Learning on Lie Groups Video: https://lnkd.in/er7Gqz6N Abstract: https://lnkd.in/eXDWHb7h We present a new symplectic model of Information Geometry [1,2] based on Jean-Marie Souriau's Lie Groups Thermodynamics [3,4]. Souriau model was initially described in chapter IV “Statistical Mechanics” of his book “Structure of dynamical systems” published in 1969. This model gives a purely geometric characterization of Entropy, which appears as an invariant Casimir function in coadjoint representation, characterized by Poisson cohomology. Souriau has proved that we can associate a symplectic manifold to coadjoint orbits of a Lie group by the KKS 2-form (Kirillov, Kostant, Souriau 2-form) in the affine case (affine model of coadjoint operator equivariance via Souriau's cocycle) [5], that we have identified with Koszul-Fisher metric from Information Geometry. Souriau established the generalized Gibbs density covariant under the action of the Lie group. The dual space of the Lie algebra foliates into coadjoint orbits that are also the Entropy level sets that could be interpreted in the framework of Thermodynamics by the fact that dynamics on these symplectic leaves are non-dissipative, whereas transversal dynamics, given by Poisson transverse structure, are dissipative. We will finally introduce Gaussian distribution on the space of Symmetric Positive Definite (SPD) matrices, through Souriau's covariant Gibbs density by considering this space as the pure imaginary axis of the homogeneous Siegel upper half space where Sp(2n,R)/U(n) acts transitively. We will also consider Gibbs density for Siegel Disk where SU(n,n)/S(U(n)xU(n)) acts transitively. Gauss density of SPD matrices is then computed through Souriau's moment map and coadjoint orbits. Souriau’s Lie Groups Thermodynamics model will be further explored in European COST network CaLISTA [6] and European HORIZON-MSCA project CaLIGOLA [7]. Geometry and statistics in data sciences Videos: https://lnkd.in/ecjTvXYU Geometry, Topology and Statistics in Data Sciences https://lnkd.in/eFFEaMpT Videos: https://lnkd.in/eBNDDXV8

AI and physics combine to reveal the 3D structure of a flare erupting around a black hole https://lnkd.in/ey5aP6ze

Engineers at Penn State have advanced an AI approach to predict lab earthquakes, or labquakes, potentially aiding future natural earthquake forecasting. By employing a physics-informed neural network (PINN), the model integrates rate and state friction laws, enhancing prediction accuracy with less data. This method allows for detailed analysis of labquake mechanics, offering insights into fault stability and failure. The PINN model's ability to predict labquakes further into the future and its enhanced transfer learning capabilities suggest promising applications for real-world earthquake prediction. This research builds on previous work published in Nature Communications.

🚀 A Hands-On Introduction to Physics-Informed Neural Networks for Solving Partial Differential Equations Today, I want to share insights from an incredible article by Hubert Baty, titled "A Hands-On Introduction to Physics-Informed Neural Networks for Solving Partial Differential Equations with Benchmark Tests Taken from Astrophysics and Plasma Physics." 🌟 PINNs are a promising method for tackling problems beyond the scope of traditional techniques. They minimize equation residuals directly in the data and excel in: ✅ Complex problems, such as singularities and irregular geometries. ✅ Diverse boundary conditions, including Dirichlet, Neumann, and mixed problems. ✅ Parametric and inverse problems, such as identifying unknown coefficients. Practical cases discussed in the article include: 🔸 Modeling magnetic arcades in the solar corona using the Helmholtz Equation. 🔸 Equilibria of curved loops in tokamaks with the Grad-Shafranov Equation. 🔸 Internal structures of self-gravitating stars via the Lane-Emden Equation. Although PINNs might not match the speed of traditional methods, their flexibility and ability to incorporate complex physical data make them a valuable tool for researchers and engineers. 📂 The article also provides Python-based codes using TensorFlow and PyTorch for those who want to experiment. If you're exploring Machine Learning for Physics or looking for efficient ways to solve PDEs, diving into the world of PINNs is a must! 💡 👉 Have you used PINNs in a project? What were your challenges or discoveries? Let’s discuss in the comments! #PINNs #DeepLearning #Physics #MachineLearning #Astrophysics #DataScience Link for this amazing paper: https://lnkd.in/dneae-2g

🔍 Exploring a New Geometric Dynamical System Inspired by Billiards! 🎱 In a groundbreaking study, Samuel Everett introduces a novel geometric dynamical system that redefines our understanding of billiard dynamics! This innovative framework utilizes cycling compositions of maps acting on spaces formed by three or more lines in R², drawing parallels with iterated function systems and modified reflection laws in billiards. 📈 Key Highlights: - The system establishes conditions for generating periodic orbits and demonstrates the existence of closed nonsmooth curves that adhere to specific geometric constraints. - The research delves into the complexities of classical billiards, where trajectories reflect off polygonal boundaries. It also investigates scenarios with irregular reflection rules, akin to light passing through cracked glass. - The paper presents rigorous proofs and theorems that assert the existence of periodic trajectories under various conditions. 💡 This work not only advances mathematical theory but also opens avenues for further research into non-conservative dynamics and applications in physics. 🔗 Dive deeper into this fascinating study to uncover how these mathematical principles can reshape our understanding of dynamical systems! #AI #Algorithms #ArtificialIntelligence #Billiards #DL #DS #DataScience #DeepLearning #DynamicalSystems #Geometry #ML #MachineLearning #Mathematics #Physics #ResearchInnovation #Tech #Technology Source: https://lnkd.in/e4vZMCSX

AI and Physics: Revolutionizing Science and Technology A.   AI and Physics: AI aiding black hole simulations, supporting grand theories like the Grand Unified Theory. B.   AI Physics: Merging AI with physics for better predictions in various fields. C.   Particle Physics: AI processing collider data, improving particle detection and discoveries. D.   Materials Science: AI predicting material behaviors, driving innovations in energy and electronics. E.    Astrophysics: AI analyzing astronomical data, identifying rare events like gravitational waves. F.    Physics-Inspired AI: Physics-inspired algorithms enhancing AI’s adaptability and problem-solving. G.   Optimization: Shared optimization concepts between AI and physics, mimicking natural processes. H.   Quantum AI: Quantum AI boosting computational power, especially in optimization and analysis. I.      Ethics: Concerns over unverified AI predictions in physics. J.     Future: AI tackling challenges like dark matter, improving complexity handling. #AIandPhysics #Blackholesimulations #GrandUnifiedTheory #AIPhysics #ParticlePhysics #Colliderdata #Particledetection #MaterialsScience #Materialbehaviors #Energyinnovations #Electronicsinnovations #Astrophysics #Gravitationalwaves #PhysicsInspiredAI #Adaptability #Problemsolving #Optimization #QuantumAI #Computationalpower #Ethics #Darkmatter #Complexityhandling

Artificial Intelligence (AI) is not just a buzzword—it's a transformative force, especially in the field of Physics. The integration of AI in Physics is driving groundbreaking discoveries and pushing the boundaries of our understanding of the universe. AI's ability to analyze vast amounts of data with unprecedented speed and accuracy is revolutionizing research in areas like quantum mechanics, astrophysics, and particle physics. Machine learning algorithms are being used to simulate complex physical systems, predict experimental outcomes, and identify patterns that were previously undetectable. In experimental physics, AI enhances the precision and efficiency of data collection and analysis. For instance, in particle physics, AI helps in processing data from large hadron colliders to identify new particles and understand fundamental forces. In astrophysics, AI algorithms are crucial in analyzing data from telescopes to discover new celestial bodies and phenomena. Moreover, AI-driven simulations and models are providing new insights into materials science, leading to the development of novel materials with extraordinary properties. These advancements have profound implications for technology, energy, and industry. The synergy between AI and Physics is not just advancing our scientific knowledge but also paving the way for practical applications that can address global challenges. As we continue to explore this exciting frontier, the importance of interdisciplinary collaboration and ethical AI development cannot be overstated. Let's embrace the AI revolution in Physics and work together towards a future of discovery and innovation. #ArtificialIntelligence #AI #Physics #Innovation #Technology #Future

(Relation Ships between Data Science & Physics and understanding of the universe secrets ):- *Data Analysis: Data science techniques enable physicists to analyze large and complex datasets, extract meaningful insights, and identify patterns that may not be apparent through traditional methods. *Machine Learning: Machine learning algorithms can be used to develop new physical models, predict experimental outcomes, and accelerate the discovery process. *Data Visualization: Data science tools and techniques can help physicists visualize and interpret complex data, leading to a deeper understanding of physical phenomena. ***Examples of the synergy between Data Science and Physics: -Particle Physics: Data science plays a crucial role in analyzing data from particle accelerators like the Large Hadron Collider, leading to discoveries like the Higgs boson. -Astrophysics: Data science techniques are used to analyze astronomical data, such as images from telescopes, to study the formation and evolution of galaxies and the universe. *Materials Science: Data science can be used to analyze materials data to predict their properties and design new materials with specific characteristics . In conclusion, data science and physics are increasingly intertwined, with each field benefiting from the other's methodologies and insights. This collaboration has the potential to drive significant advancements in both fields and lead to a deeper understanding of the universe.

In the year of AI (2025), I was looking back on our work on “Artificial Intelligence models developed jointly with my PH D student Dr Pijush Samui” (now Prof Pijush Samui, Professor and dean at NIT Patna . It was as early as 2004, we ventured in to AI when Pijush joined for his PHD at IISc Bangalore .. We produced two books and many papers with intricate mathematical models applied to geotechnical engineering. Further, Pijush has gone ahead and created many application with AI https://lnkd.in/gRWF5_25 1. Samui, P., & Sitharam, T. G. (2010). Site characterization model using artificial neural network and kriging. International Journal of Geomechanics, 10(5), 171-180. 2. Samui, P., & Sitharam, T. G. (2008). Least‐square support vector machine applied to settlement of shallow foundations on cohesionless soils. International Journal for Numerical and Analytical Methods in Geomechanics, 32(17), 2033-2043. 3. Samui, P., Sitharam, T. G., & Kurup, P. U. (2008). OCR prediction using support vector machine based on piezocone data. Journal of Geotechnical and GeoEnvironmental engineering, 134(6), 894-898. 4. Samui, P., & Sitharam, T. G. (2009). Application of least squares support vector machine in seismic attenuation prediction. ISET Journal of Earthquake Technology, 46(3-4), 147- 155. 5. Samui, P., & Sitharam, T. G. (2010). Applicability of statistical learning algorithms for spatial variability of rock depth. Mathematical Geosciences, 42, 433-446. 6. Samui, P., Kim, D., & Sitharam, T. G. (2011). Support vector machine for evaluating seismic-liquefaction potential using shear wave velocity. Journal of applied geophysics, 73(1), 8-15. 7. Samui, P., & Sitharam, T. G. (2010). Site characterization model using least‐square support vector machine and relevance vector machine based on corrected SPT data (Nc). International journal for numerical and analytical methods in geomechanics, 34(7), 755- 770. 8. Das, S. K., Samui, P., Sabat, A. K., & Sitharam, T. G. (2010). Prediction of swelling pressure of soil using artificial intelligence techniques. Environmental Earth Sciences, 61, 393-403. 9. Samui,Pijush, & Sitharam, T. G. (2011). Determination of liquefaction susceptibility of soil based on field test and artificial intelligence. International journal of earth sciences and engineering, 4(02), 216-222. 10. Samui, P., Bhattacharya, S., & Sitharam, T. G. (2012). Support vector classifiers for prediction of pile foundation performance in liquefied ground during earthquakes. International Journal of Geotechnical Earthquake Engineering (IJGEE), 3(2), 42-59. 11. Sitharam, T. G., Samui, P., & Anbazhagan, P. (2008). Spatial variability of rock depth in Bangalore using geostatistical, neural network and support vector machine models. Geotechnical and Geological Engineering, 26, 503-517. AICTE Pijush Samui

I looked into using the adjoint state optimization method for solving partial differential equations and chose a unique and highly improbable scenario: planets orbiting in a figure-eight pattern in a binary star system. Technology used was C++ and OpenGL. For this method, I explored the Hamiltonian and Lagrange multipliers to define the adjoint equations of motion. To make these equations work, I needed an expected positional equation, which in this case is the figure-eight orbit. I also tried gradient descent methods on this simulation for comparison. In the simulation, there are three planets: - Dark Blue: Planet without optimization. - Light Blue: Planet optimized using adjoint state method. - Red: Planet optimized using gradient descent. Physics setup: - Two fixed suns (yellow) with mass 100 times that of a planet. - Planets interact with the suns but not with each other. - The green figure-eight path is the desired orbit. Observations: - The dark blue planet follows a rough figure-eight pattern but maintains a stable orbit. - The light blue planet stays close to the ideal figure-eight path. - The red planet shows unstable behavior, likely due to the strong gradient descent corrections. Overall, adjoint state optimization seems smoother and more effective than gradient descent for minimizing the cost function, which could be valuable in various machine learning applications. I have spared you all the heavy math technical details but I have provided some non-official and official references for deriving these equations: - https://lnkd.in/g4AqGdMj - https://lnkd.in/gCATas8A - https://lnkd.in/g2iRbu3Z Edit: Maths describing this system in my git repo using Hamiltonians: https://lnkd.in/gydV8Bvs