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We introduce Neural Parameter Regression (NPR), a novel framework specifically developed for learning solution operators in Partial Differential Equations (PDEs). Tailored for operator learning, this approach surpasses traditional DeepONets…
In the previous article, we introduced a neural network framework based on symmetric differential equations. This novel framework exhibits complete symmetry, endowing it with perfect mathematical properties. While we have examined some of…
This work investigates model reduction techniques for nonlinear parameterized and time-dependent PDEs, specifically focusing on bifurcating phenomena in Computational Fluid Dynamics (CFD). We develop interpretable and non-intrusive Reduced…
Williams and Beer (2010) proposed a nonnegative mutual information decomposition, based on the construction of redundancy lattices, which allows separating the information that a set of variables contains about a target variable into…
We propose a private information retrieval (PIR) protocol for distributed storage systems with noncolluding nodes where data is stored using an arbitrary linear code. An expression for the PIR rate, i.e., the ratio of the amount of…
The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is…
In many scientific fields, the generation and evolution of data are governed by partial differential equations (PDEs) which are typically informed by established physical laws at the macroscopic level to describe general and predictable…
Semantic segmentation is a fundamental problem in computer vision. It is considered as a pixel-wise classification problem in practice, and most segmentation models use a pixel-wise loss as their optimization riterion. However, the…
Learning effective joint representations has been a central task in multi-modal sentiment analysis. Previous works addressing this task focus on exploring sophisticated fusion techniques to enhance performance. However, the inherent…
Understanding cognitive processes in major depressive disorder (MDD) often relies on behavioral tasks, which are typically analyzed separately, overlooking potential correlations and shared latent structure. To address this limitation, we…
Several data-driven approaches based on information theory have been proposed for analyzing high-order interactions involving three or more components of a network system. Most of these methods are defined only in the time domain and rely…
Partial differential equations (PDEs) are commonly employed to model complex industrial systems characterized by multivariable dependence. Existing physics-informed neural networks (PINNs) excel in solving PDEs in a homogeneous medium.…
Passive intermodulation (PIM) has emerged as a critical source of self-interference in modern MIMO-OFDM systems, especially under the stringent requirements of 5G and beyond. Conventional cancellation methods often rely on complex nonlinear…
Video Prediction is an interesting and challenging task of predicting future frames from a given set context frames that belong to a video sequence. Video prediction models have found prospective applications in Maneuver Planning, Health…
Proportional-integral-derivative (PID) control underlies more than $97\%$ of automated industrial processes. Controlling these processes effectively with respect to some specified set of performance goals requires finding an optimal set of…
The Dynamic-Mode Decomposition (DMD) is a well established data-driven method of finding temporally evolving linear-mode decompositions of nonlinear time series. Traditionally, this method presumes that all relevant dimensions are sampled…
Quantum reservoir computing (QRC) has emerged as a promising paradigm for harnessing near-term quantum devices to tackle temporal machine learning tasks. Yet identifying the mechanisms that underlie enhanced performance remains challenging,…
Learning solutions of partial differential equations (PDEs) with Physics-Informed Neural Networks (PINNs) is an attractive alternative approach to traditional solvers due to its flexibility and ease of incorporating observed data. Despite…
Highly accurate interval forecasting of electricity demand is fundamental to the success of reducing the risk when making power system planning and operational decisions by providing a range rather than point estimation. In this study, a…
This work addresses the development of a physics-informed neural network (PINN) with a loss term derived from a discretized time-dependent reduced-order system. In this work, first, the governing equations are discretized using a finite…