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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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How do I develop an interest in research?

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Dr. Rishabh Pathak

Developing an interest in research can be a rewarding and intellectually stimulating journey. Here are some tips to help you cultivate a passion for research:


1.   Explore Different Fields: Start by exploring various fields of study and research areas that align with your interests, curiosities, and career goals. Consider attending seminars, workshops, and conferences to learn about cutting-edge research topics and trends.

2.  Engage with Research Literature: Read research papers, articles, and publications in your field of interest to familiarize yourself with current research findings, methodologies, and debates. This can inspire new ideas and spark your curiosity to delve deeper into specific topics.

3.  Seek Mentorship: Connect with experienced researchers, professors, or professionals in your field who can serve as mentors and provide guidance on how to get involved in research. Their insights, advice, and support can help you navigate the research landscape effectively.

4.  Participate in Research Projects: Look for opportunities to participate in research projects, internships, or research assistant positions at universities, research institutions, or industry organizations. Hands-on experience in conducting research can enhance your skills, knowledge, and passion for the research process.

5.  Attend Workshops and Training Programs: Enroll in workshops, training programs, or courses on research methodology, data analysis, and academic writing to develop essential research skills and enhance your understanding of research practices.

6.  Form a Research Group or Study Circle: Collaborate with peers, colleagues, or classmates who share your interest in research to form a research group or study circle. Engaging in discussions, sharing ideas, and working together on research projects can foster a sense of community and motivation.

7.  Stay Curious and Ask Questions: Cultivate a curious mindset by asking questions, seeking answers, and exploring new avenues of inquiry. Curiosity is a driving force behind research, and embracing a spirit of inquiry can fuel your passion for uncovering knowledge and solving problems.

8.   Set Goals and Stay Motivated: Define clear research goals, set milestones, and track your progress to stay motivated and focused on your research journey. Celebrate achievements, learn from challenges, and maintain a positive attitude towards research endeavors.

9.  Embrace Challenges and Learn from Failures: Research involves facing challenges, setbacks, and uncertainties. Embrace these obstacles as opportunities for growth, learning, and resilience. Reflect on failures, adapt your approach, and persevere in pursuit of your research interests.


By following these tips and actively engaging in the research process, you can develop a strong interest in research, deepen your understanding of your field of study, and contribute meaningfully to the advancement of knowledge and innovation.

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