IPC분류정보
국가/구분 |
United States(US) Patent
등록
|
국제특허분류(IPC7판) |
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출원번호 |
US-0372160
(2003-02-21)
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등록번호 |
US-7398162
(2008-07-08)
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발명자
/ 주소 |
- Downs,Oliver B.
- Attias,Hagai
- Burges,Christopher J. C.
- Rounthwaite,Robert L.
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출원인 / 주소 |
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대리인 / 주소 |
Amin, Turocy & Calvin, LLP
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인용정보 |
피인용 횟수 :
4 인용 특허 :
7 |
초록
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A model-based system and method for global optimization that utilizes quantum mechanics in order to approximate the global minimum of a given problem (e.g., mathematical function). A quantum mechanical particle with a sufficiently large mass has a ground state solution to the Schr��dinger Equation w
A model-based system and method for global optimization that utilizes quantum mechanics in order to approximate the global minimum of a given problem (e.g., mathematical function). A quantum mechanical particle with a sufficiently large mass has a ground state solution to the Schr��dinger Equation which is localized to the global minimum of the energy field, or potential, it experiences. A given function is modeled as a potential, and a quantum mechanical particle with a sufficiently large mass is placed in the potential. The ground state of the particle is determined, and the probability density function of the ground state of the particle is calculated. The peak of the probability density function is localized to the global minimum of the potential.
대표청구항
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What is claimed is: 1. A computer-implemented calculational system for finding a global optimization for a mathematical problem describing a specific problem comprising: an input component that receives the mathematical problem describing a specific problem, the problem being based, at least in par
What is claimed is: 1. A computer-implemented calculational system for finding a global optimization for a mathematical problem describing a specific problem comprising: an input component that receives the mathematical problem describing a specific problem, the problem being based, at least in part, upon a mathematical function; an optimization component that employs a quantum mechanical tunneling technique in connection with determining an optimal solution of the problem from among a plurality of solutions, the determination being based, at least in part, upon utilities associated with the respective solutions, the optimal solution corresponds to an approximation of a ground state solution of a quantum system, localized to the global minimum of a modeled energy potential of a particle in the quantum system; an output component that provides the optimal solution determined by the optimization component; and, an output device that outputs the optimal solution. 2. The system of claim 1, the optimization component utilizing the equation: where {circumflex over (V)}(x,t) is the energy potential experienced by the particle defined by space and time, ψ(x,t) is a wave function describing an energy of the particle defined by space and time; i is the imaginary number √{square root over (-1)}; is Planek's constant; m is a mass of the particle; and, ∇2 is the Laplacian operator 3. The system of claim 2, wherein the energy potential experienced by the particle includes multiple minima separated by barriers. 4. The system of claim 1, wherein the optimization component 120 utilizes the equation: description="In-line Formulae" end="lead"Ĥ(x)ψ(x)=Eψ(x) ,description="In-line Formulae" end="tail" where E is an energy of the particle. 5. The system of claim 1, the optimization component employs an approximation of energy potentials of the particle, the optimization component employing the approximation to calculate a probability density function of the ground state of the particle based, at least in part, upon the time-independent Schr��dinger Equation. 6. The system of claim 5, the optimization component determining the plurality of solutions through the use of an anisotropic harmonic oscillator. 7. The system of claim 1, wherein the mathematical function is one-dimensional. 8. The system of claim 1, wherein the mathematical function is N-dimensional, where N is an integer greater than one. 9. The system of claim 8, the optimization component employing an approximation of a ground state of a one-dimensional problem to find the optimal solution. 10. The system of claim 9, the optimization component employing an anisotropic harmonic oscillator approximation of the mathematical function at a local minimum based, at least in part, upon a computed Hessian. 11. A computer-implemented calculational method for finding a global optimization of a mathematical problem describing a specific problem comprising: receiving the mathematical problem describing a specific problem; employing a quantum mechanical tunneling technique in connection with determining an optimal solution of the problem from among a plurality of solutions, the optimal solution corresponding to an approximation of a ground state solution of a particle in a modeled quantum system; and, providing an output associated with the determined optimal solution to an output device. 12. A computer-implemented global optimization method comprising: receiving a one-dimensional function describing a specific problem; modeling the one-dimensional function as a potential of a quantum mechanical particle; employing the model to determine an optimal solution of the one-dimensional function, the optimal solution corresponds to an approximation of a ground state solution of the potential of the quantum mechanical particle; and, providing an output associated with the determined optimal solution to an output device. 13. The method of claim 12, further comprising utilizing a gradient method to determine a location of a global minimum of the potential. 14. The method of claim 12, further comprising at least one of the following acts: determining a ground state of the particle; or, calculating the probability density function of the ground state of the particle. 15. The method of claim 14, determining a ground state of the particle is determined by at least one of the following acts: creating an approximation of the potential; employing the approximation of the potential to calculate a probability density function of the ground state of the particle based, at least in part, upon the time-independent Schr��dinger Equation. 16. The method of claim 15, wherein creating an approximation of the potential is based, at least in part, upon a harmonic oscillator. 17. The method of claim 15, creating an approximation of the potential further comprising at least one of the following acts: creating an approximation of the potential at a local minimum; determining a perturbation of the approximation of the potential at a local minimum; or adding the approximation of the potential at the local minimum to the perturbation of the approximation at the local minimum. 18. The method of claim 17, wherein basis functions of the approximation to the potential at the local minimum are used to create the approximation of the ground state of a system. 19. The method of claim 18, wherein the basis functions used to create the approximation of the potential at the local minimum are limited to basis functions having a predetermined energy level. 20. The method of claim 17, wherein the approximation used is a harmonic oscillator. 21. A computer-implemented method for global optimization of a mathematical function describing a specific problem comprising: receiving a multi-dimensional function describing a specific problem; modeling the multi-dimensional function as a potential of a quantum mechanical particle; employing the model to determine an optimal solution of the multi-dimensional function, the optimal solution corresponds to an approximation of a ground state solution of the potential of the quantum mechanical particle; and, providing an output associated with the determined optimal solution to an output device. 22. The method of claim 21, further comprising utilizing a gradient method to determine a location of a global minimum of the potential. 23. The method of claim 21, further comprising at least one of the following acts: determining a ground state of the particle; or, calculating a probability density function of the ground state of the particle. 24. The method of claim 23, determining a ground state of the particle by at least one of the following acts: creating an approximation of the potential; employing the approximation of the potential to calculate a probability density function of the ground state of the particle based, at least in part, upon the time-independent Schr��dinger Equation. 25. The method of claim 24, wherein creating an approximation of the potential is based, at least in part, upon a harmonic oscillator. 26. The method of claim 24, creating an approximation of the potential further comprising at least one of the following acts: creating a Hessian matrix of a local minimum of the potential; factorizing harmonic oscillator wave functions by changing the coordinates of the potential to an eigenbasis of the Hessian matrix at the local minimum of the potential; computing matrix elements of the local harmonic oscillator wave functions under a fall Hamiltonian of the system; evaluating the matrix elements of the local harmonic oscillator wave functions in terms of one dimensional ladder operators; performing eigen-decomposition of the matrix in order to create approximate eigenstate wave functions for a fall system of the multi-dimensional function; or summing the harmonic oscillator basis functions with coefficients being the eigenvectors of the matrix. 27. The method of claim 26, wherein the basis functions used to approximate the local minimum of the function are limited to those having a pre-determined energy level. 28. A computer readable medium storing computer executable components of a global optimization system comprising: an input component that receives a problem, the problem being based, at least in part, upon a mathematical function describing a specific problem; an optimization component that employs a quantum mechanical tunneling technique in connection with determining an optimal solution of the problem from among a plurality of solutions, the determination being based, at least in part, upon utilities associated with the respective solutions, the optimal solution corresponds to an approximation of a ground state solution of a quantum system, localized to the global minimum of a modeled energy potential of a particle in the quantum system; and, an output component that provides the optimal solution determined by the optimization component to an output device. 29. A computer-implemented global optimization system comprising: means for inputting a problem, the problem being based, at least in part, upon a mathematical function describing a specific problem; means for providing an optimal solution of the problem from among a plurality of solutions based, at least in part, upon a quantum mechanical tunneling technique, the determination being based, at least in part, upon utilities associated with the respective solutions, the optimal solution corresponds to an approximation of a ground state solution of a quantum system, localized to the global minimum of a modeled energy potential of a particle in the quantum system; and, means for outputting the optimal solution.
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