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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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The 3D biventricular electromechanical model in account for the interaction between the heart and the circulatory system.

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Dr. Rishabh Pathak


    The 3D biventricular electromechanical model described in the PDF file incorporates a detailed representation of the interaction between the heart and the circulatory system. This model couples the electromechanical behavior of the heart with a 0D closed-loop (lumped parameters) hemodynamical model of the entire cardiovascular system, including blood flow dynamics. By integrating these two components, the model can simulate the complex interplay between cardiac mechanics and circulatory dynamics.Specifically, the electromechanical aspect of the model accounts for processes such as cardiac electrophysiology, active contraction of cardiomyocytes, tissue mechanics, and blood circulation within the heart chambers. These core models capture the molecular, cellular, tissue, and organ-level processes involved in the heart's pumping function. The coupling between these electromechanical components and the closed-loop hemodynamical model is achieved through suitable interface conditions, such as volume conservation constraints.

     By considering the holistic interaction between the heart's electromechanical activity and the circulatory system's hemodynamics, the 3D biventricular electromechanical model provides a comprehensive framework for studying cardiac function in a physiological context. This integrated approach allows researchers to investigate how changes in cardiac mechanics affect blood flow dynamics and vice versa, providing valuable insights into the complex behavior of the cardiovascular system.

 

Piersanti, R., Regazzoni, F., Salvador, M., Corno, A. F., Dede', L., Vergara, C., & Quarteroni, A. (2021). 3D-0D closed-loop model for the simulation of cardiac biventricular electromechanics. *arXiv preprint arXiv:2108.01907*.

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