Ising Model Creation for Composite Material Formulation Constraints
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Solution Overview
Problem
Existing Ising models face challenges in effectively expressing and enforcing constraint conditions on formulations, particularly in optimizing the composition of composite materials with specific characteristics and constraints.
Innovation Solution
An information processing device and system are developed to assist in creating Ising models that can handle constraint conditions by formulating them into specific mathematical expressions. This system includes input reception for objective functions and constraint conditions, data creation for Ising models, and optimization using annealing type machines.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If constraint conditions are imposed on formulation to ensure satisfaction of mix number and amount conditions, then the reliability of optimization results is improved, but the device complexity increases due to the need for additional constraint terms and mathematical formulations
Solution Approach 1:
The patent introduces auxiliary variables as intermediary elements that mediate between the original formulation variables and the constraint conditions. These auxiliary variables serve as a bridge to enforce constraints without directly modifying the primary optimization variables, thereby maintaining model structure while ensuring constraint satisfaction through penalty terms in the objective function.
2Manufacturing precision
If comprehensive constraint conditions are added to handle mix number and amount specifications, then the manufacturing precision of formulation optimization is improved, but the ease of operation deteriorates due to increased difficulty in formulating and solving the Ising model
Solution Approach 1:
The patent segments the constraint conditions into distinct components: mix number constraints and amount constraints. Each constraint type is handled separately with dedicated auxiliary variables and penalty terms. This segmentation allows the complex formulation process to be broken down into manageable steps, improving ease of operation while maintaining manufacturing precision.
3Reliability
If penalty functions are used to enforce constraint conditions in the Ising model, then the reliability of constraint satisfaction is improved, but the loss of information increases due to the transformation of continuous constraints into discrete Ising-type expressions
Solution Approach 1:
The patent changes the parameter representation by introducing auxiliary variables that transform continuous constraint conditions into discrete Ising-compatible expressions. The penalty function parameters are carefully designed to maintain the essential characteristics of the original constraints while adapting them to the discrete nature of the Ising model, thereby minimizing information loss during the transformation process.
Data Source
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AI summary
An information processing device for assisting creation of an Ising model, includes an input reception unit for receiving an input of an objective function that formulates characteristics of a composite material according to a formulation and a condition of constraint on the formulation, and a data creation unit for creating the Ising model for causing an annealing type optimization machine to solve an optimal solution of the formulation that satisfies a constraint condition expression and optimizes the characteristics, wherein the condition of constraint on the formulation includes a condition related to a mix number of substances included in a substance group and to be mixed in the composite material, for each substance group composing the composite material, and a condition related to an amount of substance to be mixed in the composite material, for each substance included in the substance group, and the constraint condition expression is formulated so as not to be calculated as the optimal solution of the formulation in a case where at least one of the condition regarding the mix number and the condition related to the amount of substance is not satisfied.