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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 are the type of research?

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Dr. Rishabh Pathak

Research can be classified into various types based on different criteria, including the purpose of the study, the nature of the research question, the methodology employed, and the scope of the investigation. Here are some common types of research:


1.     Basic Research: Also known as pure or fundamental research, basic research aims to expand knowledge and understanding of fundamental principles and concepts without any immediate practical application. It focuses on theoretical exploration and the advancement of scientific knowledge.


2.     Applied Research: Applied research is conducted to address specific practical problems, issues, or challenges and to generate solutions or interventions with direct relevance to real-world applications. It aims to solve practical problems and improve existing practices or processes.


3.     Quantitative Research: Quantitative research involves the collection and analysis of numerical data to quantify relationships, patterns, and trends. It relies on statistical methods and measures to draw conclusions and make generalizations based on numerical data.


4.     Qualitative Research: Qualitative research focuses on exploring and understanding complex phenomena, experiences, and perspectives through non-numerical data such as words, images, and observations. It emphasizes in-depth exploration, interpretation, and contextual understanding.


5.     Mixed-Methods Research: Mixed-methods research combines both quantitative and qualitative approaches within a single study to provide a comprehensive understanding of a research problem. It involves collecting, analyzing, and integrating both numerical and non-numerical data.


6.     Descriptive Research: Descriptive research aims to describe and portray the characteristics, features, and attributes of a particular individual, group, situation, or phenomenon. It provides a detailed account of the subject under study without manipulating variables.


7.     Exploratory Research: Exploratory research is conducted to explore a new topic, phenomenon, or problem, generate initial insights, and formulate research questions. It aims to gain familiarity with a subject and identify potential research avenues.


8.     Explanatory Research: Explanatory research seeks to explain the relationships between variables, identify causes and effects, and establish causal explanations for observed phenomena. It focuses on understanding the underlying mechanisms and processes.


9.     Experimental Research: Experimental research involves manipulating one or more variables to observe the effects on another variable while controlling for extraneous factors. It aims to establish cause-and-effect relationships through controlled experiments.


10.  Case Study Research: Case study research involves in-depth exploration and analysis of a specific case, individual, group, or organization to understand unique characteristics, contexts, and dynamics. It provides detailed insights into complex phenomena.


11.  Action Research: Action research is a participatory approach where researchers collaborate with stakeholders to identify and address practical problems, implement interventions, and generate actionable knowledge for improving practices or processes.


These are some of the common types of research that researchers may employ based on the nature of their research questions, objectives, and methodologies. Each type of research offers unique strengths and limitations, and researchers select the most appropriate type based on their research goals and requirements.

 

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