Neural Conjugate Flows: Physics-informed architectures with flow structure
We introduce Neural Conjugate Flows (NCF), a class of neural network architectures equipped with exact flow structure. By leveraging topological conjugation, we prove that these networks are not only naturally isomorphic to a continuous group, but are also universal approximators for flows of ordinary differential equation (ODEs). Furthermore, topological properties of these flows can be enforced by the architecture in an interpretable manner. We demonstrate in numerical experiments how this topological group structure leads to concrete computational gains over other physics informed neural networks in estimating and extrapolating latent dynamics of ODEs, while training up to five times faster than other flow-based architectures.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Physics-informed neural networks (PINNs) for fluid mechanics: A review
Despite the significant progress over the last 50 years in simulating flow problems using numerical discretization of the Navier-Stokes equations (NSE), we still cannot incorporate seamlessly noisy data into existing alg…
Geometry-Aware Physics-Informed PointNets for Modeling Flows Across Porous Structures
Predicting flows that occur both through and around porous bodies is challenging due to coupled physics across fluid and porous regions and the need to generalize across diverse geometries and boundary conditions. We add…
Physics-informed deep learning for incompressible laminar flows
Physics-informed deep learning has drawn tremendous interest in recent years to solve computational physics problems, whose basic concept is to embed physical laws to constrain/inform neural networks, with the need of le…
Deep LearningIndoor Airflow Imaging Using Physics-Informed Background-Oriented Schlieren Tomography
We develop a framework for non-invasive volumetric indoor airflow estimation from a single viewpoint using background-oriented schlieren (BOS) measurements and physics-informed reconstruction. Our framework utilizes a li…
Physics-informed neural networks for solving Reynolds-averaged Navier-Stokes equations
Physics-informed neural networks (PINNs) are successful machine-learning methods for the solution and identification of partial differential equations (PDEs). We employ PINNs for solving the Reynolds-averaged Navier-Stok…