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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 Problems are studied by Biomechanics?

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Dr. Rishabh Pathak

Biomechanics addresses a wide range of problems related to the mechanical aspects of living organisms, particularly the human body. Some of the key problems studied by biomechanics include:


1.     Injury Prevention: Biomechanics researchers study the mechanisms of injury during physical activities such as sports, exercise, and daily movements. By analyzing the forces acting on the body and the resulting stresses on tissues and joints, biomechanists can identify risk factors for injuries and develop strategies to prevent them.

2.     Rehabilitation: Biomechanics plays a crucial role in designing rehabilitation programs for individuals recovering from injuries or surgeries. By understanding how forces and movements affect the body, biomechanists can develop targeted exercises and interventions to restore function and mobility.

3.     Performance Optimization: Biomechanics is used to analyze and optimize athletic performance in sports and physical activities. By studying movement patterns, muscle activation, and energy transfer, researchers can identify ways to enhance performance, improve technique, and reduce the risk of overuse injuries.

4.     Prosthetics and Orthotics: Biomechanics is essential in the design and development of prosthetic limbs, orthotic devices, and assistive technologies. By understanding how forces and movements interact with artificial limbs and devices, biomechanists can improve their functionality, comfort, and effectiveness for individuals with limb loss or mobility impairments.

5.     Ergonomics: Biomechanics is applied in ergonomics to optimize the design of workspaces, tools, and equipment to enhance human performance and prevent musculoskeletal disorders. By analyzing the biomechanical demands of various tasks, researchers can design ergonomic solutions that reduce strain and improve efficiency.

6.     Aging and Movement Disorders: Biomechanics research investigates the changes in movement patterns and biomechanical characteristics associated with aging and movement disorders such as Parkinson's disease, stroke, and cerebral palsy. By understanding these changes, researchers can develop interventions to improve mobility, balance, and quality of life for individuals with these conditions.

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


Overall, biomechanics addresses a diverse range of problems related to human movement, sports performance, injury prevention, rehabilitation, assistive technologies, ergonomics, and aging. By applying biomechanical principles and techniques, researchers and practitioners can advance our understanding of the mechanical aspects of the human body and develop innovative solutions to improve movement efficiency, health, and well-being.

 

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