Restricted Boltzmann Machine Parameter Extraction
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Solution Overview
Problem
Current methods for modeling complex interacting systems, such as those in biology and physics, rely on simplified models and crude approximations to determine parameter values, leading to inaccurate representations of the systems being modeled.
Innovation Solution
The use of restricted Boltzmann machines (RBM) trained with a maximum entropy principle to determine parameters of parametrized physical models, such as the Ising or Bose-Hubbard models, allowing for more accurate prediction of system properties and behavior.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If simplified physical models with crude approximations are used to model complex systems, then the modeling process becomes computationally simpler, but the accuracy of parameter determination and system representation deteriorates
Solution Approach 1:
The patent introduces Restricted Boltzmann Machines (RBMs) as an intermediary computational framework that bridges simplified physical models and complex system reality. The RBM learns the underlying probability distribution of training data from complex systems, enabling accurate parameter determination for simplified physical models without requiring direct complex computations on the original systems.
Solution Approach 2:
The patent transforms the parameter determination problem by changing from direct physical model fitting to learning parameters through RBM training on data. This parameter transformation approach allows the system to capture complex system behavior through learned parameters while maintaining the computational simplicity of the underlying physical models.
2Use of energy by moving object
If traditional crude approximation methods are used to determine model parameters, then the computational resources required are reduced, but the accuracy of system representation deteriorates
Solution Approach 1:
The RBM serves as a computational intermediary that processes training data to extract accurate parameter values. This intermediary approach avoids the need for extensive computational resources while maintaining high accuracy, as the RBM learns the essential patterns from data rather than performing exhaustive simulations.
Solution Approach 2:
The patent replaces traditional mechanical/computational methods of parameter determination (such as direct simulation or iterative fitting) with a machine learning-based RBM approach. This substitution enables more efficient computation while achieving superior parameter accuracy through the RBM's ability to learn from training data.
Data Source
AI summary
This specification describes machine-learning systems and methods for modelling physical and/or biological systems that apply the principle of maximum entropy to restricted Boltzmann machines. According to a first aspect of this specification, there is described a method for modelling a complex system using machine learning. The method includes: obtaining training data representing the complex system; determining one or more parameters of a parametrised physical model representing the complex system using the training data; and predicting one or more properties of the complex system and/or behaviour of the complex system from the parametrised physical model. Determining parameters of the parametrised physical model representing the complex system using the training data includes: mapping the parametrised physical model to a restricted Boltzmann machine; training the restricted Boltzmann machine on the training data representing the complex system using a maximum entropy principle; and extracting the one or more parameters of the parametrised physical model from the trained restricted Boltzmann machine.