29,872 research outputs found
DMIS: Dynamic Mesh-based Importance Sampling for Training Physics-Informed Neural Networks
Modeling dynamics in the form of partial differential equations (PDEs) is an
effectual way to understand real-world physics processes. For complex physics
systems, analytical solutions are not available and numerical solutions are
widely-used. However, traditional numerical algorithms are computationally
expensive and challenging in handling multiphysics systems. Recently, using
neural networks to solve PDEs has made significant progress, called
physics-informed neural networks (PINNs). PINNs encode physical laws into
neural networks and learn the continuous solutions of PDEs. For the training of
PINNs, existing methods suffer from the problems of inefficiency and unstable
convergence, since the PDE residuals require calculating automatic
differentiation. In this paper, we propose Dynamic Mesh-based Importance
Sampling (DMIS) to tackle these problems. DMIS is a novel sampling scheme based
on importance sampling, which constructs a dynamic triangular mesh to estimate
sample weights efficiently. DMIS has broad applicability and can be easily
integrated into existing methods. The evaluation of DMIS on three widely-used
benchmarks shows that DMIS improves the convergence speed and accuracy in the
meantime. Especially in solving the highly nonlinear Schr\"odinger Equation,
compared with state-of-the-art methods, DMIS shows up to 46% smaller root mean
square error and five times faster convergence speed. Code are available at
https://github.com/MatrixBrain/DMIS.Comment: Accepted to AAAl-2
Machine Learning for Fluid Mechanics
The field of fluid mechanics is rapidly advancing, driven by unprecedented
volumes of data from field measurements, experiments and large-scale
simulations at multiple spatiotemporal scales. Machine learning offers a wealth
of techniques to extract information from data that could be translated into
knowledge about the underlying fluid mechanics. Moreover, machine learning
algorithms can augment domain knowledge and automate tasks related to flow
control and optimization. This article presents an overview of past history,
current developments, and emerging opportunities of machine learning for fluid
mechanics. It outlines fundamental machine learning methodologies and discusses
their uses for understanding, modeling, optimizing, and controlling fluid
flows. The strengths and limitations of these methods are addressed from the
perspective of scientific inquiry that considers data as an inherent part of
modeling, experimentation, and simulation. Machine learning provides a powerful
information processing framework that can enrich, and possibly even transform,
current lines of fluid mechanics research and industrial applications.Comment: To appear in the Annual Reviews of Fluid Mechanics, 202
Fast Neural Network Predictions from Constrained Aerodynamics Datasets
Incorporating computational fluid dynamics in the design process of jets,
spacecraft, or gas turbine engines is often challenged by the required
computational resources and simulation time, which depend on the chosen
physics-based computational models and grid resolutions. An ongoing problem in
the field is how to simulate these systems faster but with sufficient accuracy.
While many approaches involve simplified models of the underlying physics,
others are model-free and make predictions based only on existing simulation
data. We present a novel model-free approach in which we reformulate the
simulation problem to effectively increase the size of constrained pre-computed
datasets and introduce a novel neural network architecture (called a cluster
network) with an inductive bias well-suited to highly nonlinear computational
fluid dynamics solutions. Compared to the state-of-the-art in model-based
approximations, we show that our approach is nearly as accurate, an order of
magnitude faster, and easier to apply. Furthermore, we show that our method
outperforms other model-free approaches
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