Related papers: Hyperbolic mean curvature flow computed by physics…
Addressing high-dimensional partial differential equations to derive effective actions within the functional renormalization group is formidable, especially when considering various field configurations, including inhomogeneous states, even…
We discuss nonlinear model predictive control (NMPC) for multi-body dynamics via physics-informed machine learning methods. Physics-informed neural networks (PINNs) are a promising tool to approximate (partial) differential equations. PINNs…
Form-finding of unilateral membrane structures is commonly addressed by solving equilibrium equations with Finite Element Methods (FEMs). This paper investigates Physics-Informed Neural Networks (PINNs) as an alternative, where the…
Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…
Physics-informed neural networks (PINNs) have shown remarkable prospects in solving partial differential equations (PDEs) involving fluid mechanics. However, the method has so far succeeded only in inviscid flows and incompressible viscous…
We extend the physics-informed neural network (PINN) method to learn viscosity models of two non-Newtonian systems (polymer melts and suspensions of particles) using only velocity measurements. The PINN-inferred viscosity models agree with…
We study diffusion-controlled growth of a spherical droplet with a moving boundary using a physics-informed neural network (PINN) formulation. The governing diffusion equation is coupled to the interfacial mass balance, with the droplet…
Computational Fluid Dynamics (CFD) simulations are used for many air flow simulations including road vehicle aerodynamics. Numerical diffusion occurs when local flow direction is not aligned with the mesh lines and when there is a non-zero…
The Earth's main geomagnetic field arises from the constant motion of the fluid outer core. By assuming that the field changes are advection-dominated, the fluid motion at the core surface can be related to the secular variation of the…
Solving partial differential equations (PDE) is an indispensable part of many branches of science as many processes can be modelled in terms of PDEs. However, recent numerical solvers require manual discretization of the underlying equation…
Emerging technologies like hypersonic aircraft, space exploration vehicles, and batteries avail fluid circulation in embedded microvasculatures for efficient thermal regulation. Modeling is vital during these engineered systems' design and…
We harness the physics-informed neural network (PINN) approach to extend the utility of phenomenological models for particle migration in shear flow. Specifically, we propose to constrain the neural network training via a model for the…
Parametric finite elements lead to very efficient numerical methods for surface evolution equations. We introduce several computational techniques for curvature driven evolution equations based on a weak formulation for the mean curvature.…
Accurate solutions to inverse supersonic compressible flow problems are often required for designing specialized aerospace vehicles. In particular, we consider the problem where we have data available for density gradients from Schlieren…
Data-driven modeling of spatiotemporal physical processes with general deep learning methods is a highly challenging task. It is further exacerbated by the limited availability of data, leading to poor generalizations in standard neural…
In this paper we investigate the one-dimensional hyperbolic mean curvature flow for closed plane curves. We show that there exists a class of initial velocities such that the solution of the corresponding initial value problem exists only…
Physics-informed neural networks (PINNs) are a simple surrogate-modelling paradigm for partial differential equations, but their standard strong-form residual formulation is ill suited to the shallow water equations (SWE). It cannot enforce…
Many types of physics-informed neural network models have been proposed in recent years as approaches for learning solutions to differential equations. When a particular task requires solving a differential equation at multiple…
We introduce a novel methodology that leverages the strength of Physics-Informed Neural Networks (PINNs) to address the counterdiabatic (CD) protocol in the optimization of quantum circuits comprised of systems with $N_{Q}$ qubits. The…
Mesh generation is essential for accurate and efficient computational fluid dynamics simulations. To resolve critical features in the flow, adaptive mesh refinement (AMR) is routinely employed in certain regions of the computational domain,…