Inference of response functions with the help of machine learning algorithms

• URL: http://arxiv.org/abs/2501.10583v1
• Date: Fri, 17 Jan 2025 22:21:41 GMT
• Title: Inference of response functions with the help of machine learning algorithms
• Authors: Doga Murat Kurkcuoglu, Alessandro Roggero, Gabriel N. Perdue, Rajan Gupta,
• Abstract summary: We employ a neural network prediction algorithm to reconstruct a response function $S(omega)$ defined over a range in $omega$. 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.
• Score: 42.12937192948916
• License:
• Abstract: 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 $S(\omega)$ defined over a range in frequencies $\omega$. 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.

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