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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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Frontal Plane

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Dr. Rishabh Pathak

The frontal plane is an anatomical plane that divides the body into front and back halves, allowing for the analysis of movements that occur predominantly in the lateral direction. In human biomechanics, the frontal plane plays a significant role in studying various activities, including side-to-side movements, abduction, adduction, and frontal plane stability. Here is an overview of the frontal plane in human biomechanics along with an example of its application:


1.     Frontal Plane in Human Biomechanics:

§  Definition: The frontal plane is a vertical plane that divides the body into front (anterior) and back (posterior) halves. Movements in the frontal plane involve abduction (movement away from the midline) and adduction (movement toward the midline) around an anterior-posterior axis.

§  Role: The frontal plane is essential for analyzing movements such as side-to-side motions, frontal plane stability, hip abduction, hip adduction, and shoulder abduction in various activities.

§  Joint Movements: Frontal plane movements include abduction (raising the arm sideways), adduction (bringing the arm back to the body), lateral flexion of the spine, and other motions along the frontal axis.

2.     Example of Frontal Plane Analysis:

§  Hip Abduction/Adduction: When analyzing hip movements in the frontal plane in human biomechanics, the frontal plane is crucial for understanding the kinematics of hip abduction and adduction.

§  Joint Movements: In the frontal plane, hip abduction involves moving the leg away from the midline of the body, while hip adduction involves bringing the leg back toward the midline.

§  Kinematics: By studying the frontal plane kinematics of the hip joint, researchers can assess the range of motion, muscle activation patterns, and functional movements that involve hip abduction and adduction.

§  Biomechanical Parameters: Parameters such as hip abduction angle, hip adduction angle, and hip joint stability are commonly analyzed in the frontal plane to evaluate hip mechanics and functional performance.

3.     Clinical Applications:

§  Rehabilitation: In clinical settings, the frontal plane analysis of movements like hip abduction and adduction is used to assess hip joint function, muscle imbalances, and movement compensations in individuals recovering from hip injuries or undergoing rehabilitation.

§  Postural Control: Frontal plane stability and control are essential for maintaining balance, preventing falls, and optimizing functional movements in activities that require lateral stability and weight shifting.

4.     Research Studies:

§  Biomechanical Research: Researchers use frontal plane analysis to investigate the biomechanics of various activities, such as hip joint mechanics, lower limb alignment in gait, and the effects of frontal plane interventions on movement patterns.

§  Injury Prevention: Understanding frontal plane movements helps in identifying risk factors for hip injuries, knee valgus collapse, and other biomechanical issues that can be addressed through targeted interventions and training programs.

By incorporating frontal plane analysis in human biomechanics, researchers, clinicians, and practitioners can gain insights into lateral movements, joint stability, muscle activation patterns, and functional mechanics during a wide range of activities. The frontal plane serves as a critical reference for studying and interpreting human movement dynamics, providing valuable information for biomechanical assessments, injury prevention strategies, and rehabilitation protocols.

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