Inference of response functions with the help of machine learning algorithms
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915109724487680 |
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| author | Kurkcuoglu, Doga Murat Roggero, Alessandro Perdue, Gabriel N. Gupta, Rajan |
| author_facet | Kurkcuoglu, Doga Murat Roggero, Alessandro Perdue, Gabriel N. Gupta, Rajan |
| contents | Response functions are a key quantity to describe the near-equilibrium dynamics of strongly-interacting many-body systems. Recent techniques that attempt to overcome the challenges of calculating these \emph{ab initio} have employed expansions in terms of orthogonal polynomials. We employ a neural network prediction algorithm to reconstruct a response function $S(ω)$ defined over a range in frequencies $ω$. We represent the calculated response function as a truncated Chebyshev series whose coefficients can be optimized to reduce the representation error. We compare the quality of response functions obtained using coefficients calculated using a neural network (NN) algorithm with those computed using the Gaussian Integral Transform (GIT) method. In the regime where only a small number of terms in the Chebyshev series are retained, we find that the NN scheme outperforms the GIT method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10583 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inference of response functions with the help of machine learning algorithms Kurkcuoglu, Doga Murat Roggero, Alessandro Perdue, Gabriel N. Gupta, Rajan Quantum Physics Response functions are a key quantity to describe the near-equilibrium dynamics of strongly-interacting many-body systems. Recent techniques that attempt to overcome the challenges of calculating these \emph{ab initio} have employed expansions in terms of orthogonal polynomials. We employ a neural network prediction algorithm to reconstruct a response function $S(ω)$ defined over a range in frequencies $ω$. We represent the calculated response function as a truncated Chebyshev series whose coefficients can be optimized to reduce the representation error. We compare the quality of response functions obtained using coefficients calculated using a neural network (NN) algorithm with those computed using the Gaussian Integral Transform (GIT) method. In the regime where only a small number of terms in the Chebyshev series are retained, we find that the NN scheme outperforms the GIT method. |
| title | Inference of response functions with the help of machine learning algorithms |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2501.10583 |