Learning to extrapolate using continued fractions: Predicting the critical temperature of superconductor materials

• URL: http://arxiv.org/abs/2012.03774v3
• Date: Mon, 10 Jul 2023 06:38:22 GMT
• Title: Learning to extrapolate using continued fractions: Predicting the critical temperature of superconductor materials
• Authors: Pablo Moscato, Mohammad Nazmul Haque, Kevin Huang, Julia Sloan, Jon C. de Oliveira
• Abstract summary: In the field of Artificial Intelligence (AI) and Machine Learning (ML), the approximation of unknown target functions $y=f(mathbfx)$ is a common objective. We refer to $S$ as the training set and aim to identify a low-complexity mathematical model that can effectively approximate this target function for new instances $mathbfx$.
• Score: 5.905364646955811
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In the field of Artificial Intelligence (AI) and Machine Learning (ML), the approximation of unknown target functions $y=f(\mathbf{x})$ using limited instances $S={(\mathbf{x^{(i)}},y^{(i)})}$, where $\mathbf{x^{(i)}} \in D$ and $D$ represents the domain of interest, is a common objective. We refer to $S$ as the training set and aim to identify a low-complexity mathematical model that can effectively approximate this target function for new instances $\mathbf{x}$. Consequently, the model's generalization ability is evaluated on a separate set $T=\{\mathbf{x^{(j)}}\} \subset D$, where $T \neq S$, frequently with $T \cap S = \emptyset$, to assess its performance beyond the training set. However, certain applications require accurate approximation not only within the original domain $D$ but also in an extended domain $D'$ that encompasses $D$. This becomes particularly relevant in scenarios involving the design of new structures, where minimizing errors in approximations is crucial. For example, when developing new materials through data-driven approaches, the AI/ML system can provide valuable insights to guide the design process by serving as a surrogate function. Consequently, the learned model can be employed to facilitate the design of new laboratory experiments. In this paper, we propose a method for multivariate regression based on iterative fitting of a continued fraction, incorporating additive spline models. We compare the performance of our method with established techniques, including AdaBoost, Kernel Ridge, Linear Regression, Lasso Lars, Linear Support Vector Regression, Multi-Layer Perceptrons, Random Forests, Stochastic Gradient Descent, and XGBoost. To evaluate these methods, we focus on an important problem in the field: predicting the critical temperature of superconductors based on physical-chemical characteristics.

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