Traditional machine learning is generally treated as a black-box optimization problem and does not typically produce interpretable functions that connect inputs and outputs. However, the ability to discover such interpretable functions is desirable. In this work, we propose GINN-LP, an interpretable neural network to discover the form and coefficients of the underlying equation of a dataset, when the equation is assumed to take the form of a multivariate Laurent Polynomial. This is facilitated by a new type of interpretable neural network block, named the “power-term approximator block”, consisting of logarithmic and exponential activation functions. GINN-LP is end-to-end differentiable, making it possible to use backpropagation for training. We propose a neural network growth strategy that will enable finding the suitable number of terms in the Laurent polynomial that represents the data, along with sparsity regularization to promote the discovery of concise equations. To the best of our knowledge, this is the first model that can discover arbitrary multivariate Laurent polynomial terms without any prior information on the order. Our approach is first evaluated on a subset of data used in SRBench, a benchmark for symbolic regression. We first show that GINN-LP outperforms the state-of-the-art symbolic regression methods on datasets generated using 48 real-world equations in the form of multivariate Laurent polynomials. Next, we propose an ensemble method that combines our method with a high-performing symbolic regression method, enabling us to discover non-Laurent polynomial equations. We achieve state-of-the-art results in equation discovery, showing an absolute improvement of 7.1% over the best contender, by applying this ensemble method to 113 datasets within SRBench with known ground-truth equations.

In this study, we introduce a novel theoretical framework for detecting and decoding Terahertz (THz) frequency chip-scale wireless communication signals. By considering the quantum behavior of charge carriers exposed to intense time-periodic radiation, we employ Floquet engineering techniques for system analysis. Using a two-dimensional semiconductor quantum well (2DSQW) based voltage divider, we showcase the detection and decoding of frequency modulated signals at nanoscale dimensions. Exploring noise impact within the Floquet-2DSQW framework, we identify voltage shifts that compromise data demodulation in single signaling setups. To address this challenge, we suggest a dynamic dual-signaling Floquet-2DSQW architecture that adapts the reference voltage to prevalent noise effects in chip-scale environments. Through a numerical analysis configured for Gigabit per second (Gbps) data transmission in the THz carrier frequency range, we show that our dual-signaling approach surpasses conventional single signaling setups, significantly reducing the bit error rate across various signal-to-noise ratio (SNR) values. A comprehensive parametric study emphasizes the importance of correlated noise effects at two 2DSQW receivers for enhanced performance. Our findings offer valuable insights for advancing nanoscale wireless communication within or between chips in noisy conditions, with potential applications in high-speed, reliable data transfer.

This paper presents a novel numerical model that can be used for accurate performance prediction of time division multiplexed (TDM)-pumped fiber Raman amplifiers (FRAs). The modeling approach integrates the power analysis approach, commonly used for modeling such amplifiers, with field analysis, thereby allowing the study of the effects of not only stimulated Raman scattering, amplified spontaneous emission, and double Rayleigh backscattering, but also material dispersion and fiber nonlinearity.

Mining of text data from the Web has become a necessity in modern days due to the volumes of data available on the Web. While searching for information on the Web using search engines is popular, to analyze the content on large collections of Web pages, feature map techniques are still popular. One of the problems associated with processing large collections of text data from the Web using feature map techniques is the time taken to cluster them. This paper presents an algorithm based on a growing variant of the self organizing map called the HDGSOMr. This novel algorithm incorporates randomness into the self-organizing process to produce higher quality clusters within few epochs and utilizing smaller neighborhood sizes resulting in a significant reduction in overall processing time. Details of the HDGSOMr algorithm and results of processing large collections of text data proving the efficiency of the algorithm are also presented.