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...
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 p...