Related papers: Physically constrained neural networks to solve th…

Physics-informed neural networks (PINNs) have proven to be a promising method for the rapid solving of partial differential equations (PDEs) in both forward and inverse problems. However, due to the smoothness assumption of functions…

Deep learning methods have gained considerable interest in the numerical solution of various partial differential equations (PDEs). One particular focus is physics-informed neural networks (PINN), which integrate physical principles into…

In this work, we study physics-informed neural networks (PINNs) constrained by partial differential equations (PDEs) and their application in approximating PDEs with two characteristic scales. From a continuous perspective, our formulation…

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 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…

This paper deals with the following important research question. Traditionally, the neural network employs non-linear activation functions concatenated with linear operators to approximate a given physical phenomenon. They "fill the space"…

We introduce conditional PINNs (physics informed neural networks) for estimating the solution of classes of eigenvalue problems. The concept of PINNs is expanded to learn not only the solution of one particular differential equation but the…

This article introduces Perception-Informed Neural Networks (PrINNs), a framework designed to incorporate perception-based information into neural networks, addressing both systems with known and unknown physics laws or differential…

Recent work in scientific machine learning has developed so-called physics-informed neural network (PINN) models. The typical approach is to incorporate physical domain knowledge as soft constraints on an empirical loss function and use…

The use of deep learning methods in scientific computing represents a potential paradigm shift in engineering problem solving. One of the most prominent developments is Physics-Informed Neural Networks (PINNs), in which neural networks are…

Physics informed neural networks (PINNs) have emerged as a powerful tool to provide robust and accurate approximations of solutions to partial differential equations (PDEs). However, PINNs face serious difficulties and challenges when…

Physics-Informed Neural Networks (PINNs) offer a promising approach to solving differential equations and, more generally, to applying deep learning to problems in the physical sciences. We adopt a recently developed transfer learning…

Physics-informed neural networks (PINNs) impose known physical laws into the learning of deep neural networks, making sure they respect the physics of the process while decreasing the demand of labeled data. For systems represented by…

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…

Physics-informed neural networks (PINNs) provide a powerful framework for learning governing equations of dynamical systems from data. Biologically-informed neural networks (BINNs) are a variant of PINNs that preserve the known differential…

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…

Physics-informed neural networks (PINNs) have gained significant prominence as a powerful tool in the field of scientific computing and simulations. Their ability to seamlessly integrate physical principles into deep learning architectures…

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…

The accurate modelling of structural dynamics is crucial across numerous engineering applications, such as Structural Health Monitoring (SHM), seismic analysis, and vibration control. Often, these models originate from physics-based…

Physics-Informed Neural Networks (PINNs) recast PDE solving as an optimisation problem in function space by minimising a residual-based objective, yet many applications require additional derivative-based relations that are just as…