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Convolutional Neural Networks (CNNs) have recently led to incredible breakthroughs on a variety of pattern recognition problems. Banks of finite impulse response filters are learned on a hierarchy of layers, each contributing more abstract…
Kolmogorov-Arnold Networks (KANs) have gained attention as an alternative to traditional multilayer perceptrons (MLPs) for deep learning applications in computational physics, particularly for solving inverse problems with sparse data, as…
Physics Informed Neural Networks offer a mesh free framework for solving PDEs but are highly sensitive to loss weight selection. We propose two dimensional analysis based weighting schemes, one based on quantifiable terms, and another also…
The simulation of power system dynamics poses a computationally expensive task. Considering the growing uncertainty of generation and demand patterns, thousands of scenarios need to be continuously assessed to ensure the safety of power…
Binary neural networks (BNNs) have demonstrated their ability to solve complex tasks with comparable accuracy as full-precision deep neural networks (DNNs), while also reducing computational power and storage requirements and increasing the…
We introduce the notion of asymptotic integrability into the theory of nonlinear wave equations. It means that the Hamiltonian structure of equations describing propagation of high-frequency wave packets is preserved by hydrodynamic…
In this book chapter, we discuss recent advances in data-driven approaches for inverse problems. In particular, we focus on the \emph{paired autoencoder} framework, which has proven to be a powerful tool for solving inverse problems in…
As a typical application of deep learning, physics-informed neural network (PINN) {has been} successfully used to find numerical solutions of partial differential equations (PDEs), but how to improve the limited accuracy is still a great…
While physics-informed neural networks (PINNs) have become a popular deep learning framework for tackling forward and inverse problems governed by partial differential equations (PDEs), their performance is known to degrade when larger and…
Physics-informed neural networks (PINNs) face significant challenges in modeling multi-frequency wavefields in complex velocity models due to their slow convergence, difficulty in representing high-frequency details, and lack of…
Physics-informed neural networks (PINNs) [4, 10] are an approach for solving boundary value problems based on differential equations (PDEs). The key idea of PINNs is to use a neural network to approximate the solution to the PDE and to…
In this study, we present and validate the predictive capability of the Physics-Informed Neural Networks (PINNs) methodology for solving a variety of engineering and biological dynamical systems governed by ordinary differential equations…
As an emerging technology in deep learning, physics-informed neural networks (PINNs) have been widely used to solve various partial differential equations (PDEs) in engineering. However, PDEs based on practical considerations contain…
Graph neural networks (GNNs) have been successfully applied in many structured data domains, with applications ranging from molecular property prediction to the analysis of social networks. Motivated by the broad applicability of GNNs, we…
Variational Quantum Linear Solvers (VQLS) are a promising method for solving linear systems on near-term quantum devices. However, their performance is often limited by barren plateaus and inefficient parameter initialization, which…
We propose the Distance-informed Neural Process (DNP), a novel variant of Neural Processes that improves uncertainty estimation by combining global and distance-aware local latent structures. Standard Neural Processes (NPs) often rely on a…
Developing efficient methods for solving parametric partial differential equations is crucial for addressing inverse problems. This work introduces a Least-Squares-based Neural Network (LS-Net) method for solving linear parametric PDEs. It…
This paper proposes and studies two extensions of applying hp-variational physics-informed neural networks, more precisely the FastVPINNs framework, to convection-dominated convection-diffusion-reaction problems. First, a term in the spirit…
Deep neural networks (DNNs), particularly those using Rectified Linear Unit (ReLU) activation functions, have achieved remarkable success across diverse machine learning tasks, including image recognition, audio processing, and language…
This study introduces PV-RNN, a novel variational RNN inspired by the predictive-coding ideas. The model learns to extract the probabilistic structures hidden in fluctuating temporal patterns by dynamically changing the stochasticity of its…