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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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Qualitative Problems in Biomechanics

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Dr. Rishabh Pathak


Qualitative problems in biomechanics involve analyzing and understanding movement patterns, forces, and interactions within the human body without relying solely on numerical data or measurements. These qualitative approaches complement quantitative biomechanical analyses and provide valuable insights into movement mechanics. Some common qualitative problems in biomechanics include:


1.     Movement Analysis: Qualitatively analyzing movement patterns, such as gait, running mechanics, or sports techniques, to identify key components, phases, and coordination strategies. Observational techniques, video analysis, and expert judgment are often used to assess movement quality and efficiency.

2.  Joint Kinematics: Qualitatively assessing joint motions and alignments during activities to understand joint stability, range of motion, and coordination. Observing joint angles, movement smoothness, and joint center trajectories can provide insights into joint function and potential issues.

3.     Muscle Activation Patterns: Qualitatively examining muscle activation patterns during movements to understand muscle recruitment strategies, timing, and coordination. Observing muscle firing sequences, synergistic muscle actions, and muscle recruitment patterns can help assess movement efficiency and performance.

4.     Balance and Stability: Qualitatively evaluating balance and stability during static and dynamic tasks to assess postural control, weight distribution, and compensatory movements. Observing body sway, alignment adjustments, and control strategies can provide insights into balance mechanisms.

5.   Technique Assessment: Qualitatively analyzing movement techniques in sports and activities to evaluate skill execution, body positioning, and movement efficiency. Assessing factors such as timing, coordination, fluidity, and precision can help identify areas for improvement and performance optimization.

6.  Biomechanical Feedback: Providing qualitative feedback to individuals based on movement observations to enhance performance, correct movement errors, and prevent injuries. Using verbal cues, visual demonstrations, and tactile feedback can help individuals improve movement quality and motor skills.

7.   Functional Movement Screening: Qualitatively assessing functional movements and tasks to identify movement dysfunctions, asymmetries, and compensations. Conducting movement screenings can help detect movement limitations, imbalances, and risk factors for injuries.

8.   Skill Acquisition: Qualitatively studying the process of skill acquisition and motor learning to understand how individuals develop proficiency in complex movements. Observing movement progression, error correction strategies, and feedback mechanisms can inform teaching and coaching practices.


By addressing these qualitative problems in biomechanics, researchers, coaches, clinicians, and practitioners can gain a deeper understanding of movement mechanics, enhance performance outcomes, optimize rehabilitation strategies, and promote movement efficiency and quality. Integrating qualitative analyses with quantitative biomechanical assessments can provide a comprehensive perspective on human movement and contribute to advancements in sports science, rehabilitation, ergonomics, and healthcare.

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