Zobrazeno 1 - 10
of 40
pro vyhledávání: '"Zeinhofer, Marius"'
Autor:
Sun, Jingtong, Berner, Julius, Richter, Lorenz, Zeinhofer, Marius, Müller, Johannes, Azizzadenesheli, Kamyar, Anandkumar, Anima
The task of sampling from a probability density can be approached as transporting a tractable density function to the target, known as dynamical measure transport. In this work, we tackle it through a principled unified framework using deterministic
Externí odkaz:
http://arxiv.org/abs/2407.07873
Physics-informed neural networks (PINNs) are infamous for being hard to train. Recently, second-order methods based on natural gradient and Gauss-Newton methods have shown promising performance, improving the accuracy achieved by first-order methods
Externí odkaz:
http://arxiv.org/abs/2405.15603
We propose Gauss-Newton's method in function space for the solution of the Navier-Stokes equations in the physics-informed neural network (PINN) framework. Upon discretization, this yields a natural gradient method that provably mimics the function s
Externí odkaz:
http://arxiv.org/abs/2402.10680
Autor:
Müller, Johannes, Zeinhofer, Marius
Publikováno v:
Proceedings of the 41 st International Conference on Machine Learning, Vienna, Austria. PMLR 235, 2024
Scientific machine learning (SciML) is a relatively new field that aims to solve problems from different fields of natural sciences using machine learning tools. It is well-documented that the optimizers commonly used in other areas of machine learni
Externí odkaz:
http://arxiv.org/abs/2402.07318
The recently introduced Physics-Informed Neural Networks (PINNs) have popularized least squares formulations of both forward and inverse problems involving partial differential equations (PDEs) in strong form. We employ both Isogeometric Analysis and
Externí odkaz:
http://arxiv.org/abs/2312.03496
We prove a priori and a posteriori error estimates for physics-informed neural networks (PINNs) for linear PDEs. We analyze elliptic equations in primal and mixed form, elasticity, parabolic, hyperbolic and Stokes equations; and a PDE constrained opt
Externí odkaz:
http://arxiv.org/abs/2311.00529
Starting from full-dimensional models of solute transport, we derive and analyze multi-dimensional models of time-dependent convection, diffusion, and exchange in and around pulsating vascular and perivascular networks. These models are widely applic
Externí odkaz:
http://arxiv.org/abs/2303.17999
Autor:
Müller, Johannes, Zeinhofer, Marius
We propose energy natural gradient descent, a natural gradient method with respect to a Hessian-induced Riemannian metric as an optimization algorithm for physics-informed neural networks (PINNs) and the deep Ritz method. As a main motivation we show
Externí odkaz:
http://arxiv.org/abs/2302.13163
Autor:
Kaltenbach, Alex, Zeinhofer, Marius
We establish error estimates for the approximation of parametric $p$-Dirichlet problems deploying the Deep Ritz Method. Parametric dependencies include, e.g., varying geometries and exponents $p\in (1,\infty)$. Combining the derived error estimates w
Externí odkaz:
http://arxiv.org/abs/2207.01894
Mesh degeneration is a bottleneck for fluid-structure interaction (FSI) simulations and for shape optimization via the method of mappings. In both cases, an appropriate mesh motion technique is required. The choice is typically based on heuristics, e
Externí odkaz:
http://arxiv.org/abs/2206.02217