Related papers: Helicity-conservative Physics-informed Neural Netw…
This paper introduces a Variational Multiscale Stabilization (VMS) formulation of the incompressible Navier--Stokes equations that utilizes the Finite Element Exterior Calculus (FEEC) framework. The FEEC framework preserves the geometric…
Physics-Informed Neural Networks (PINNs) often suffer from slow convergence, training instability, and reduced accuracy on challenging partial differential equations due to the anisotropic and rapidly varying geometry of their loss…
We show that the error achievable using physics-informed neural networks for solving systems of differential equations can be substantially reduced when these networks are trained using meta-learned optimization methods rather than to using…
Over the last few decades, existing Partial Differential Equation (PDE) solvers have demonstrated a tremendous success in solving complex, non-linear PDEs. Although accurate, these PDE solvers are computationally costly. With the advances…
We present hidden fluid mechanics (HFM), a physics informed deep learning framework capable of encoding an important class of physical laws governing fluid motions, namely the Navier-Stokes equations. In particular, we seek to leverage the…
We consider the numerical approximation of a sharp-interface model for two-phase flow, which is given by the incompressible Navier-Stokes equations in the bulk domain together with the classical interface conditions on the interface. We…
Modeling of conservative systems with neural networks is an area of active research. A popular approach is to use Hamiltonian neural networks (HNNs) which rely on the assumptions that a conservative system is described with Hamilton's…
Physics-informed neural networks solve partial differential equations by training neural networks. Since this method approximates infinite-dimensional PDE solutions with finite collocation points, minimizing discretization errors by…
In recent engineering applications using deep learning, physics-informed neural network (PINN) is a new development as it can exploit the underlying physics of engineering systems. The novelty of PINN lies in the use of partial differential…
In the work of Navier-Stokes (NSE) equation, derived a nonlinear parabolic equation for kinetic energy density, and identified an important property of this equation - the maximum principle. The latter shows the validity of the maximum…
We introduce a practical method to enforce partial differential equation (PDE) constraints for functions defined by neural networks (NNs), with a high degree of accuracy and up to a desired tolerance. We develop a differentiable…
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…
Recent works have shown that deep neural networks can be employed to solve partial differential equations, giving rise to the framework of physics informed neural networks. We introduce a generalization for these methods that manifests as a…
Physics-informed neural network (PINN) has been a prevalent framework for solving PDEs since proposed. By incorporating the physical information into the neural network through loss functions, it can predict solutions to PDEs in an…
Despite the immense success of neural networks in modeling system dynamics from data, they often remain physics-agnostic black boxes. In the particular case of physical systems, they might consequently make physically inconsistent…
Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…
Neural Networks (NN) has been used in many areas with great success. When a NN's structure (Model) is given, during the training steps, the parameters of the model are determined using an appropriate criterion and an optimization algorithm…
Approximating solutions to differential equations using neural networks has become increasingly popular and shows significant promise. In this paper, we propose a simplified framework for analyzing the potential of neural networks to…
We present a novel class of Physics-Informed Neural Networks that is formulated based on the principles of Evidential Deep Learning, where the model incorporates uncertainty quantification by learning parameters of a higher-order…
Finite element modeling is a well-established tool for structural analysis, yet modeling complex structures often requires extensive pre-processing, significant analysis effort, and considerable time. This study addresses this challenge by…