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Generative Adversarial Networks (GANs) have made significant progress in enhancing the quality of image synthesis. Recent methods frequently leverage pretrained networks to calculate perceptual losses or utilize pretrained feature spaces.…
While Hamiltonian mechanics provides a powerful inductive bias for neural networks modeling dynamical systems, Hamiltonian Neural Networks and their variants often fail to capture complex temporal dynamics spanning multiple timescales. This…
We propose a physics-augmented neural network (PANN) framework for finite strain incompressible viscoelasticity within the generalized standard materials theory. The formulation is based on the multiplicative decomposition of the…
In this paper, a proximal augmented Lagrangian homotopy (PAL-Hom) method for solving convex quadratic programming problems is proposed. This method takes the proximal augmented Lagrangian method as the outer iteration. To solve the proximal…
Classical methods of solving spatiotemporal dynamical systems include statistical approaches such as autoregressive integrated moving average, which assume linear and stationary relationships between systems' previous outputs. Development…
Existing deep learning-based approaches for histopathology image analysis require large annotated training sets to achieve good performance; but annotating histopathology images is slow and resource-intensive. Conditional generative…
Artificial Intelligence and Machine learning have been widely used in various fields of mathematical computing, physical modeling, computational science, communication science, and stochastic analysis. Approaches based on Deep Artificial…
Graph Neural Networks (GNNs) excel at relational reasoning but face two persistent challenges: the lack of interpretable attribution for heterogeneous node types, and the computational overhead of message passing over large, noisy graphs.…
Solving partial differential equations (PDEs) using neural networks has become a central focus in scientific machine learning. Training neural networks for singularly perturbed problems is particularly challenging due to certain parameters…
Artificial and biological neural networks (ANNs and BNNs) can encode inputs in the form of combinations of individual neurons' activities. These combinatorial neural codes present a computational challenge for direct and efficient analysis…
We propose a new semi-analytic physics informed neural network (PINN) to solve singularly perturbed boundary value problems. The PINN is a scientific machine learning framework that offers a promising perspective for finding numerical…
Non-autonomous differential equations are crucial for modeling systems influenced by external signals, yet fitting these models to data becomes particularly challenging when the signals change abruptly. To address this problem, we propose a…
One of the most common and universal problems in science is to investigate a function. The prediction can be made by an Artificial Neural Network (ANN) or a mathematical model. Both approaches have their advantages and disadvantages.…
The manuscript addresses the problem of finding all solutions of power flow equations or other similar nonlinear system of algebraic equations. This problem arises naturally in a number of power systems contexts, most importantly in the…
While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving…
Generative deep learning methods built upon Convolutional Neural Networks (CNNs) provide a great tool for predicting non-linear structure in cosmology. In this work we predict high resolution dark matter halos from large scale, low…
We present PFNN, a penalty-free neural network method, to efficiently solve a class of second-order boundary-value problems on complex geometries. To reduce the smoothness requirement, the original problem is reformulated to a weak form so…
Hearing aids (HAs) are widely used to provide personalized speech enhancement (PSE) services, improving the quality of life for individuals with hearing loss. However, HA performance significantly declines in noisy environments as it treats…
Systems of polynomial equations arise frequently in computer vision, especially in multiview geometry problems. Traditional methods for solving these systems typically aim to eliminate variables to reach a univariate polynomial, e.g., a…
Hypergraph representation learning has garnered increasing attention across various domains due to its capability to model high-order relationships. Traditional methods often rely on hypergraph neural networks (HNNs) employing message…