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...
A neuro-computational model of
subcortical growth integrates principles from neuroscience and computational
modeling to study the development of brain regions beneath the cerebral cortex,
known as the subcortex. Here are the key aspects of a neuro-computational model
of subcortical growth:
1. Biologically Realistic Representation: The model incorporates biologically
relevant features of subcortical development, such as the growth and elongation
of axons, the formation of neural circuits, and the influence of growth factors
on subcortical structures. By simulating these processes computationally,
researchers can study how subcortical regions develop and interact with the
cortex.
2.
Axonal Growth and Connectivity: The model accounts for the growth
of axons and the establishment of connections between subcortical regions and
cortical areas. By simulating axonal elongation and branching, researchers can
study how subcortical structures contribute to the overall connectivity and
function of the brain.
3. Mechanical Interactions: The model considers the mechanical
interactions between the subcortex and the overlying cortex, as well as the
effects of growth-induced deformations on subcortical structures. By
incorporating mechanical properties and growth-induced stresses, the model can
investigate how mechanical forces influence subcortical growth patterns.
4. Stretch-Induced Growth: The model includes mechanisms of stretch-induced
growth, where chronic stretching of axons in the subcortex leads to gradual
elongation and deformation. By simulating how axons respond to mechanical
stimuli, researchers can study the effects of stretch-induced growth on
subcortical morphology.
5. Computational Simulations: Neuro-computational models use
computational simulations, such as finite element analysis or agent-based
models, to study the dynamics of subcortical growth. These simulations allow
researchers to investigate how interactions between neurons, glial cells, and
mechanical forces shape the development of subcortical structures.
6. Sensitivity Analysis: The model can perform sensitivity analyses to assess
the impact of varying parameters, such as growth rates, mechanical properties,
and external stimuli, on subcortical growth. By systematically varying these
parameters in simulations, researchers can identify key factors influencing the
morphogenesis of subcortical regions.
7. Validation and Comparison: Neuro-computational models are
validated against experimental data, such as neuroimaging studies or
histological analyses, to ensure their biological accuracy. By comparing model
predictions with empirical observations, researchers can evaluate the model's
ability to capture the dynamics of subcortical growth.
8. Insights into Brain Development: By studying subcortical growth
processes computationally, researchers can gain insights into the mechanisms
underlying the development of brain structures below the cortex. These models
help elucidate how subcortical regions contribute to overall brain function and
connectivity, providing a deeper understanding of brain development.
In summary, a neuro-computational
model of subcortical growth offers a valuable framework for investigating the
complex processes involved in the development of brain regions beneath the
cerebral cortex. By combining neuroscience principles with computational
modeling techniques, researchers can explore the dynamics of subcortical
growth, connectivity formation, and mechanical interactions within the
developing brain.
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