Support Vector Machine Kernels as Quantum Propagators
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908742374653952 |
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| author | Kuo, Nan-Hong Wong, Renata |
| author_facet | Kuo, Nan-Hong Wong, Renata |
| contents | Selecting optimal kernels for regression in physical systems remains a challenge, often relying on trial-and-error with standard functions. In this work, we establish a mathematical correspondence between support vector machine kernels and quantum propagators, demonstrating that kernel efficacy is determined by its spectral alignment with the system's Green's function. Based on this isomorphism, we propose a unified, physics-informed framework for kernel selection and design. For systems with known propagator forms, we derive analytical selection rules that map standard kernels to physical operators. For complex systems where the Green's function is analytically intractable, we introduce a constructive numerical method using the Kernel Polynomial Method with Jackson smoothing to generate custom, physics-aligned kernels. Numerical experiments spanning electrical conductivity, electronic band structure, anharmonic oscillators, and photonic crystals demonstrate that this framework consistently performs well as long as there is an alignment with a Green's function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_11153 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Support Vector Machine Kernels as Quantum Propagators Kuo, Nan-Hong Wong, Renata Quantum Physics Statistical Mechanics Artificial Intelligence Machine Learning Mathematical Physics Selecting optimal kernels for regression in physical systems remains a challenge, often relying on trial-and-error with standard functions. In this work, we establish a mathematical correspondence between support vector machine kernels and quantum propagators, demonstrating that kernel efficacy is determined by its spectral alignment with the system's Green's function. Based on this isomorphism, we propose a unified, physics-informed framework for kernel selection and design. For systems with known propagator forms, we derive analytical selection rules that map standard kernels to physical operators. For complex systems where the Green's function is analytically intractable, we introduce a constructive numerical method using the Kernel Polynomial Method with Jackson smoothing to generate custom, physics-aligned kernels. Numerical experiments spanning electrical conductivity, electronic band structure, anharmonic oscillators, and photonic crystals demonstrate that this framework consistently performs well as long as there is an alignment with a Green's function. |
| title | Support Vector Machine Kernels as Quantum Propagators |
| topic | Quantum Physics Statistical Mechanics Artificial Intelligence Machine Learning Mathematical Physics |
| url | https://arxiv.org/abs/2502.11153 |