相关论文: Picard-KKT-hPINN: Enforcing Nonlinear Enthalpy Bal…

Surrogate modeling is used to replace computationally expensive simulations. Neural networks have been widely applied as surrogate models that enable efficient evaluations over complex physical systems. Despite this, neural networks are…

Traditional physics-informed neural networks (PINNs) do not guarantee strict constraint satisfaction. This is problematic in engineering systems where minor violations of governing laws can degrade the reliability and consistency of model…

Neural networks (NNs) accelerate simulations of quantum dissipative dynamics. Ensuring that these simulations adhere to fundamental physical laws is crucial, but has been largely ignored in the state-of-the-art NN approaches. We show that…

We propose an entropy-enhanced Generative Pre-Trained Physics-Informed Neural Network with a transform layer (EGPT-PINN) for solving parameterized nonlinear conservation laws. The EGPT-PINN extends the traditional physics-informed neural…

We propose Weak and Entropy PINNs (WE-PINNs) for the approximation of entropy solutions to nonlinear hyperbolic conservation laws. Standard physics-informed neural networks enforce governing equations in strong differential form, an…

Physics informed neural networks (PINNs) require regularity of solutions of the underlying PDE to guarantee accurate approximation. Consequently, they may fail at approximating discontinuous solutions of PDEs such as nonlinear hyperbolic…

Physics-informed Neural Network (PINN) faces significant challenges when approximating solutions to conservation laws, particularly in ensuring conservation and accurately resolving discontinuities. To address these limitations, we propose…

Physics-informed neural networks (PINNs) offer a unified framework for solving both forward and inverse problems of differential equations, yet their performance and physical consistency strongly depend on how governing laws are…

Real-time, physically-consistent predictions on low-power edge devices is critical for the next generation embodied AI systems, yet it remains a major challenge. Physics-Informed Neural Networks (PINNs) combine data-driven learning with…

Neural networks can emulate nonlinear physical systems with high accuracy, yet they may produce physically-inconsistent results when violating fundamental constraints. Here, we introduce a systematic way of enforcing nonlinear analytic…

We consider the approximation of entropy solutions of nonlinear hyperbolic conservation laws using neural networks. We provide explicit computations that highlight why classical PINNs will not work for discontinuous solutions to nonlinear…

Physics-Informed Neural Networks (PINNs) have emerged as an influential technology, merging the swift and automated capabilities of machine learning with the precision and dependability of simulations grounded in theoretical physics. PINNs…

This paper introduces a framework based on physics-informed neural networks (PINNs) for addressing key challenges in nonlinear lattices, including solution approximation, bifurcation diagram construction, and linear stability analysis. We…

Physics-informed neural networks (PINNs) incorporate physical laws into their training to efficiently solve partial differential equations (PDEs) with minimal data. However, PINNs fail to guarantee adherence to conservation laws, which are…

The prohibitive cost and low fidelity of experimental data in industry scale thermofluid systems limit the usefulness of pure data-driven machine learning methods. Physics-informed neural networks (PINN) strive to overcome this by embedding…

Recently, there has been growing interest in using physics-informed neural networks (PINNs) to solve differential equations. However, the preservation of structure, such as energy and stability, in a suitable manner has yet to be…

Physics-informed neural networks (PINNs) have emerged as a promising numerical method based on deep learning for modeling boundary value problems, showcasing promising results in various fields. In this work, we use PINNs to discretize…

Physics-Informed Neural Networks (PINNs) present a transformative approach for smart grid modeling by integrating physical laws directly into learning frameworks, addressing critical challenges of data scarcity and physical consistency in…

The Neural Tangent Kernel (NTK) viewpoint is widely employed to analyze the training dynamics of overparameterized Physics-Informed Neural Networks (PINNs). However, unlike the case of linear Partial Differential Equations (PDEs), we show…

Systems biology and systems neurophysiology in particular have recently emerged as powerful tools for a number of key applications in the biomedical sciences. Nevertheless, such models are often based on complex combinations of multiscale…