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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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Why we must have to study the Biomechanics?

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Dr. Rishabh Pathak

Studying biomechanics is essential for several reasons, as it provides valuable insights into the mechanical aspects of living organisms, particularly the human body. Here are some key reasons why studying biomechanics is important:


1.     Understanding Human Movement: Biomechanics helps us understand how the musculoskeletal system functions during various activities such as walking, running, jumping, and sports movements. By analyzing the forces, torques, and motions involved in human movement, researchers can gain insights into optimal performance, injury prevention, and rehabilitation strategies.

2.     Injury Prevention and Rehabilitation: By studying biomechanics, researchers can identify risk factors for injuries, assess movement patterns that contribute to overuse injuries, and develop effective rehabilitation programs. Understanding the biomechanical mechanisms of injury can help in designing interventions to prevent injuries and promote safe movement practices.

3.     Enhancing Athletic Performance: Biomechanics plays a crucial role in optimizing athletic performance by analyzing movement patterns, muscle activation, and energy transfer during sports activities. By applying biomechanical principles, coaches and athletes can improve technique, efficiency, and power generation in sports performance.

4.     Designing Prosthetics and Orthotics: Biomechanics is essential in the design and development of prosthetic limbs, orthotic devices, and assistive technologies for individuals with limb loss or mobility impairments. By understanding the biomechanics of human movement, researchers can improve the functionality, comfort, and effectiveness of these devices.

5.     Ergonomics and Workplace Design: Biomechanics is applied in ergonomics to optimize the design of workspaces, tools, and equipment to reduce the risk of musculoskeletal disorders and enhance human performance. By studying the biomechanical demands of various tasks, researchers can design ergonomic solutions that promote comfort, safety, and efficiency in the workplace.

6.     Advancing Healthcare and Rehabilitation: Biomechanics research contributes to advancements in healthcare by providing insights into movement disorders, gait abnormalities, and rehabilitation strategies. By studying the biomechanics of aging, injury, and disease, researchers can develop interventions to improve mobility, balance, and quality of life for individuals with movement impairments.

7.     Biomechanical Modeling and Simulation: Biomechanics involves creating mathematical models and simulations to predict and analyze the mechanical behavior of biological systems. These models help researchers understand complex movements, assess the impact of interventions, and optimize performance in various applications.


Overall, studying biomechanics is crucial for advancing our understanding of human movement, optimizing performance, preventing injuries, designing assistive technologies, improving workplace ergonomics, and enhancing healthcare and rehabilitation practices. By applying biomechanical principles and techniques, researchers and practitioners can make significant contributions to various fields and improve the well-being and quality of life of individuals.

 

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