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Energy Manifold Natural Gradient Descent: From Riemannian Optimization to Modern Neuroscience, NeuroAI and Quantum Physics

Dr. Rishabh Pathak
When Geometry, Energy, Artificial Intelligence and Neuroscience Converge Modern Artificial Intelligence is rapidly moving beyond the idea that learning simply means minimizing an error function. Increasingly, researchers are asking a deeper question: what is the structure of the space in which learning takes place? This question becomes particularly important when the system being modelled is constrained, nonlinear, dynamic, or governed by physical principles. A recent work titled “Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers” , by Zhangyong Liang and Huanhuan Gao, introduces Energy Manifold Natural Gradient Descent (EMNGD) , a mathematical framework that extends energy-based natural-gradient optimization from unconstrained Euclidean parameter spaces to constrained Riemannian parameter manifolds . At its core, the framework proposes a simple but powerful principle: An optimization algorithm should not only determine how to reduce error; it sh...
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What is Bio-Mechanics?

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Dr. Rishabh Pathak


Biomechanics is the study of the mechanical aspects of living organisms, particularly the human body, and how they interact with their surroundings. It combines principles of biology and mechanics to understand how biological systems function, move, and respond to external forces. In the context of human movement, biomechanics focuses on analyzing the structure and function of the musculoskeletal system and how it generates and controls movement.

Key aspects of biomechanics include:


1.   Kinematics: Kinematics is the branch of biomechanics that deals with the description of motion, including the position, velocity, and acceleration of body segments during movement. By analyzing kinematic data, researchers can understand the patterns and characteristics of human motion.

2.  Kinetics: Kinetics is the branch of biomechanics that focuses on the forces that cause motion. By studying the forces acting on the human body during movement, researchers can assess muscle activity, joint loading, and energy transfer within the body.

3.   Muscle Mechanics: Muscle mechanics involves studying the properties and behavior of muscles during contraction and relaxation. Understanding muscle mechanics is essential for analyzing movement efficiency, strength, and power generation.

4.  Biomechanical Modeling: Biomechanical modeling involves creating mathematical and computational models to simulate and analyze human movement. These models help researchers predict the effects of different variables on performance and injury risk.

5.  Gait Analysis: Gait analysis is a common application of biomechanics that involves studying the patterns of walking and running. By analyzing gait parameters such as stride length, step width, and joint angles, researchers can assess gait abnormalities and design interventions to improve walking efficiency and reduce injury risk.

6.  Sports Biomechanics: Sports biomechanics applies biomechanical principles to analyze athletic performance, technique, and injury prevention in sports. By studying the biomechanics of sports movements such as throwing, jumping, and kicking, researchers can optimize training programs and enhance athletic performance.


Overall, biomechanics plays a crucial role in understanding the mechanical principles underlying human movement, sports performance, rehabilitation, and ergonomics. By applying biomechanical principles and techniques, researchers and practitioners can improve movement efficiency, prevent injuries, and enhance overall human performance and well-being.

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