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Quantum many-body systems are of great interest for many research areas, including physics, biology and chemistry. However, their simulation is extremely challenging, due to the exponential growth of the Hilbert space with the system size,…

The utilization of Deep Neural Networks (DNNs) in physical science and engineering applications has gained traction due to their capacity to learn intricate functions. While large datasets are crucial for training DNN models in fields like…

Solving inverse problems in dynamical systems governed by high-dimensional coupled ordinary differential equations (ODEs) is a ubiquitous challenge in scientific machine learning. In many real-world applications, researchers seek to uncover…

Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving Partial Differential Equations (PDEs) by incorporating physical constraints into deep learning models. However, standard PINNs often require a large…

Modeling viscoelastic behavior is crucial in engineering and biomechanics, where materials undergo time-dependent deformations, including stress relaxation, creep buckling and biological tissue development. Traditional numerical methods,…

Recently developed physics-informed neural network (PINN) has achieved success in many science and engineering disciplines by encoding physics laws into the loss functions of the neural network, such that the network not only conforms to…

We propose a physics-informed neural network (PINN) model to efficiently predict the self-energy of Anderson impurity models (AIMs) based on the Lehmann representation. As an example, we apply the PINN model to a single-orbital AIM (SAIM)…

The importance and cost of time-domain simulations when studying power systems have exponentially increased in the last decades. With the growing share of renewable energy sources, the slow and predictable responses from large turbines are…

We show that the physics-informed neural networks (PINNs), in combination with some recently developed discontinuity capturing neural networks, can be applied to solve optimal control problems subject to partial differential equations…

The conservation of cultural heritage increasingly relies on integrating technological innovation with domain expertise to ensure effective monitoring and predictive maintenance. This paper presents a novel framework to support the…

This work focuses on understanding the minimum eradication time for the controlled Susceptible-Infectious-Recovered (SIR) model in the time-homogeneous setting, where the infection and recovery rates are constant. The eradication time is…

Physics-informed neural networks (PINNs) have gained significant attention as a surrogate modeling strategy for partial differential equations (PDEs), particularly in regimes where labeled data are scarce and physical constraints can be…

Physics-Informed Neural Networks (PINNs) solve partial differential equations using deep learning. However, conventional PINNs perform pointwise predictions that neglect dependencies within a domain, which may result in suboptimal…

Physics-informed neural networks (PINNs) have been proven as a promising way for solving various partial differential equations, especially high-dimensional ones and those with irregular boundaries. However, their capabilities in real…

Physics-informed neural networks (PINNs) have recently emerged as a promising way to compute the solutions of partial differential equations (PDEs) using deep neural networks. However, despite their significant success in various fields, it…

Physics-informed neural networks (PINNs) offer a promising avenue for tackling both forward and inverse problems in partial differential equations (PDEs) by incorporating deep learning with fundamental physics principles. Despite their…

Physics-informed neural networks (PINNs) provide a mesh-free framework for solving PDE-constrained inverse problems, but their extension to Bayesian inversion still faces a fundamental difficulty: prior distributions are typically defined…

This paper presents adaptive weighted Euler-Lagrange theorem combined physics-informed neural networks (AW-EL-PINNs) for solving Euler-Lagrange systems in optimal control problems. The framework systematically converts optimal control…

Accurately and efficiently solving nonlinear differential equations is crucial for modeling dynamic behavior across science and engineering. Physics-Informed Neural Networks (PINNs) have emerged as a powerful solution that embeds physical…

Extremum Seeking (ES) is an effective real-time optimization method for PDE systems in cascade with nonlinear quadratic maps. To address PDEs in the feedback loop, a boundary control law and a re-design of the additive probing signal are…