Related papers: Physics-Modeled Neural Networks
We propose a new approach for large-scale high-dynamic range computational imaging. Deep Neural Networks (DNNs) trained end-to-end can solve linear inverse imaging problems almost instantaneously. While unfolded architectures provide…
PDEs arise ubiquitously in science and engineering, where solutions depend on parameters (physical properties, boundary conditions, geometry). Traditional numerical methods require re-solving the PDE for each parameter, making parameter…
This paper proposes a new mean-field framework for over-parameterized deep neural networks (DNNs), which can be used to analyze neural network training. In this framework, a DNN is represented by probability measures and functions over its…
Physics-informed neural networks (PINNs) represent a new paradigm for solving partial differential equations (PDEs) by integrating physical laws into the learning process of neural networks. However, ensuring that such frameworks fully…
We use physics-informed neural networks for solving the shallow-water equations for tsunami modeling. Physics-informed neural networks are an optimization based approach for solving differential equations that is completely meshless. This…
Deep operator networks (DeepONets) represent a powerful class of data-driven methods for operator learning, demonstrating strong approximation capabilities for a wide range of linear and nonlinear operators. They have shown promising…
Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…
We develop a deep neural network (DNN) that accounts for the phase behaviors of polymer-containing liquid mixtures. The key component in the DNN consists of a theory-embedded layer that captures the characteristic features of the phase…
We propose extrinsic and intrinsic deep neural network architectures as general frameworks for deep learning on manifolds. Specifically, extrinsic deep neural networks (eDNNs) preserve geometric features on manifolds by utilizing an…
Physics-Informed Neural Networks (PINNs) and Neural Ordinary Differential Equations (NODEs) represent two distinct machine learning frameworks for modeling nonlinear neuronal dynamics. This study systematically evaluates their performance…
Graph neural network (GNN) is a promising approach to learning and predicting physical phenomena described in boundary value problems, such as partial differential equations (PDEs) with boundary conditions. However, existing models…
Pseudo-Hamiltonian neural networks (PHNN) were recently introduced for learning dynamical systems that can be modelled by ordinary differential equations. In this paper, we extend the method to partial differential equations. The resulting…
The success of the current wave of artificial intelligence can be partly attributed to deep neural networks, which have proven to be very effective in learning complex patterns from large datasets with minimal human intervention. However,…
Identifying accurate dynamic models is required for the simulation and control of various technical systems. In many important real-world applications, however, the two main modeling approaches often fail to meet requirements: first…
Neural operators, which aim to approximate mappings between infinite-dimensional function spaces, have been widely applied in the simulation and prediction of physical systems. However, the limited representational capacity of network…
Physics-informed neural networks (PINNs) are revolutionizing science and engineering practice by bringing together the power of deep learning to bear on scientific computation. In forward modeling problems, PINNs are meshless partial…
The article discusses the development of various methods and techniques for initializing and training neural networks with a single hidden layer, as well as training a separable physics-informed neural network consisting of neural networks…
To improve predictive models for STEM applications, supplemental physics-based features computed from input parameters are introduced into single and multiple layers of a deep neural network (DNN). While many studies focus on informing DNNs…
Physics-Informed Neural Networks (PINNs) are machine learning tools that approximate the solution of general partial differential equations (PDEs) by adding them in some form as terms of the loss/cost function of a Neural Network. Most…
For its robust predictive power (compared to pure physics-based models) and sample-efficient training (compared to pure deep learning models), physics-informed deep learning (PIDL), a paradigm hybridizing physics-based models and deep…