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Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...
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Phase Transitions: Sublimation and Deposition02:33

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Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and standard pressure, a piece of dry ice (solid CO2) sublimes, appearing to gradually disappear without ever forming any liquid. Snow and ice sublimate at temperatures below the melting point of water, a slow process that may be accelerated by winds and the reduced atmospheric pressures at high altitudes. When solid iodine is warmed, the solid sublimes...
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Phase Changes01:19

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Phase transitions play an important theoretical and practical role in the study of heat flow. In melting or fusion, a solid turns into a liquid; the opposite process is freezing. In evaporation, a liquid turns into a gas; the opposite process is condensation.
A substance melts or freezes at a temperature called its melting point and boils or condenses at its boiling point. These temperatures depend on pressure. High pressure favors the denser form of the substance, so typically, high pressure...
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Dynamic Equilibrium02:20

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A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...
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Generalization, Discrimination, and Extinction01:24

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Generalization, discrimination, and extinction are key concepts in operant conditioning that influence how behaviors are learned and maintained.
Generalization occurs when a behavior reinforced in one context is performed in similar situations. For instance, a student who studies diligently for calculus and receives excellent grades might apply the same study habits to psychology and history, expecting similar results. Generalization shows how learning in one setting can influence behavior in...
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Phase Diagram01:19

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The phase of a given substance depends on the pressure and temperature. Thus, plots of pressure versus temperature showing the phase in each region provide considerable insights into the thermal properties of substances. Such plots are known as phase diagrams. For instance, in the phase diagram for water (Figure 1), the solid curve boundaries between the phases indicate phase transitions (i.e., temperatures and pressures at which the phases coexist).
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Aprendizaje en PINNs: transición de fase, equilibrio de difusión y generalización

Sokratis J Anagnostopoulos1, Juan Diego Toscano2, Nikolaos Stergiopulos1

  • 1Laboratory of Hemodynamics and Cardiovascular Technology, EPFL, Lausanne, 1015, VD, Switzerland.

Neural networks : the official journal of the International Neural Network Society
|August 30, 2025
PubMed
Resumen
Este resumen es generado por máquina.

Identificamos una nueva fase de "equilibrio de difusión" en el entrenamiento de redes neuronales donde los gradientes se alinean, lo que lleva a una convergencia estable. Esta fase, cuando se combina con residuos homogéneos, mejora la generalización del modelo y acelera el aprendizaje.

Palabras clave:
GeneralizaciónEstocasticidad del gradienteTeoría del cuello de botella de la informaciónTransición de fase de los PINNHomogeneidad residual

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Área de la Ciencia:

  • Optimización del aprendizaje profundo
  • Dinámica de las redes neuronales
  • Teoría del aprendizaje automático

Sus antecedentes:

  • Comprender la dinámica de aprendizaje de la red neuronal es crucial para mejorar el rendimiento del modelo.
  • Las teorías existentes describen las fases de deriva y difusión en el entrenamiento.
  • El papel de la relación gradiente señal-ruido (SNR) en estas fases requiere más investigación.

Objetivo del estudio:

  • Investigar la dinámica de aprendizaje de las redes neuronales totalmente conectadas utilizando SNR de gradiente.
  • Identificar y caracterizar las nuevas fases de formación más allá de la deriva y la difusión.
  • Proponer métodos para mejorar la generalización y la convergencia basados en la dinámica observada.

Principales métodos:

  • Análisis de optimizadores de primer orden en objetivos no convexos.
  • Interpretación de las fases de formación a través de la lente de la teoría del cuello de botella de la información.
  • Examen de la relación señal-ruido del gradiente neural (SNR).
  • Desarrollo y ensayo de un esquema de reponderación por muestra.

Principales resultados:

  • Identificación de una novela
  • equilibrio de difusión
  • Fase (DE) caracterizada por gradientes neuronales ordenados y convergencia estable.
  • La fase DE se correlaciona con un aumento del SNR y residuos homogéneos, lo que conduce a una mejor generalización.
  • Un esquema de reponderación por muestra propuesto mejora la homogeneidad residual y la generalización.
  • Se observa una compresión inducida por la saturación de las activaciones durante la transición de fase DE.
  • Validación experimental en redes neuronales informadas por la física (PINNs) que muestran una convergencia y generalización más rápidas.

Conclusiones:

  • La fase DE identificada ofrece una nueva perspectiva sobre la formación de redes neuronales estables.
  • El logro de residuos homogéneos junto con gradientes ordenados en la fase DE es clave para la generalización superior.
  • Los hallazgos sugieren mejoras potenciales para las estrategias de optimización del aprendizaje profundo, particularmente para los métodos informados por la física.