Shaowu Pan

Rensselaer Polytechnic Institute | RPI · Department of Mechanical, Aerospace and Nuclear Engineering

PyKoopman is a Python package for the data-driven approximation of the Koopman operator associated with a dynamical system. The Koopman operator is a principled linear embedding of nonlinear dynamics and facilitates the prediction, estimation, and control of strongly nonlinear dynamics using linear systems theory. In particular, PyKoopman provides...

Solving large sparse linear systems is a fundamental problem in many scientific and engineering domains, including computational fluid dynamics. In recent years, there has been a growing interest in using machine learning techniques to accelerate the convergence of iterative linear solvers. This work proposes a novel approach to precondition Krylov...

Coherent structures of hypersonic nonequilibrium non-reacting nitrogen flows over a 30/55-degree double wedge geometry using two-dimensional configurations, with unit Reynolds number increasing from 8.6 × 10 4 to 6.4 × 10 5 m −1 at a Mach number of approximately 7.1, are investigated using composite Koopman analysis inspired by Sayadi et al. [1] to...

Representation learning for high-dimensional, complex physical systems aims to identify a low-dimensional intrinsic latent space, which is crucial for reduced-order modeling and modal analysis. To overcome the well-known Kolmogorov barrier, deep autoencoders (AEs) have been introduced in recent years, but they often suffer from poor convergence beh...

We propose a novel learning framework for Koopman operator of nonlinear dynamical systems that is informed by the governing equation and guarantees long-time stability and robustness to noise. In contrast to existing frameworks where either ad-hoc observables or blackbox neural networks are used to construct observables in the extended dynamic mode...

Distributed acoustic sensing (DAS) presents challenges and opportunities for seismological research and data management. This study explores wavefield reconstruction using deep learning methods for data compression and wavefield separation. We test various architectures to treat DAS data as two‐dimensional arrays, such as the implicit neural repres...

The Koopman operator provides a linear perspective on non-linear dynamics by focusing on the evolution of observables in an invariant subspace. Observables of interest are typically linearly reconstructed from the Koopman eigenfunctions. Despite the broad use of Koopman operators over the past few years, there exist some misconceptions about the ap...

A large number of magnetohydrodynamic (MHD) equilibrium calculations are often required for uncertainty quantification, optimization, and real-time diagnostic information, making MHD equilibrium codes vital to the field of plasma physics. In this paper, we explore a method for solving the Grad–Shafranov equation by using physics-informed neural net...

The Koopman operator provides a linear perspective on non-linear dynamics by focusing on the evolution of observables in an invariant subspace. Observables of interest are typically linearly reconstructed from the Koopman eigenfunctions. Despite the broad use of Koopman operators over the past few years, there exist some misconceptions about the ap...

High-dimensional spatio-temporal dynamics can often be encoded in a low-dimensional subspace. Engineering applications for modeling, characterization, design, and control of such large-scale systems often rely on dimensionality reduction to make solutions computationally tractable in real time. Common existing paradigms for dimensionality reduction...

http://deepblue.lib.umich.edu/bitstream/2027.42/174074/1/42774_2022_Article_118.pdf

High-dimensional spatio-temporal dynamics can often be encoded in a low-dimensional subspace. Engineering applications for modeling, characterization, design, and control of such large-scale systems often rely on dimensionality reduction to make solutions computationally tractable in real-time. Common existing paradigms for dimensionality reduction...

Three-dimensional particle reconstruction with limited two-dimensional projections is an under-determined inverse problem that the exact solution is often difficult to be obtained. In general, approximate solutions can be obtained by iterative optimization methods. In the current work, a practical particle reconstruction method based on a convoluti...

Numerical solution of partial differential equations (PDEs) require expensive simulations, limiting their application in design optimization routines, model-based control, or solution of large-scale inverse problems. Existing Convolutional Neural Network-based frameworks for surrogate modeling require lossy pixelization and data-preprocessing, whic...

Non-linear dynamical systems are of significant interest to a wide range of science and engineering communities. This dissertation is focused on the advancement of theory and algorithms for operator-theoretic modeling and decomposition of non-linear dynamical systems, with a particular emphasis on the Koopman operator. The Koopman operator represen...

Recently developed physics-informed neural network (PINN) has achieved success in many science and engineering disciplines by encoding physics laws into the loss functions of the neural network, such that the network not only conforms to the measurements, initial and boundary conditions but also satisfies the governing equations. This work first in...

This work addresses fundamental issues related to the structure and conditioning of linear time-delayed models of non-linear dynamics on an attractor. While this approach has been well-studied in the asymptotic sense (e.g., for an infinite number of delays), the non-asymptotic setting is not well-understood. First, we show that the minimal time-del...

Koopman decomposition is a non-linear generalization of eigen decomposition, and is being increasingly utilized in the analysis of spatio-temporal dynamics. Well-known techniques such as the dynamic mode decomposition (DMD) and its variants provide approximations to the Koopman operator, and have been applied extensively in many fluid dynamic probl...

Numerical simulations on fluid dynamics problems primarily rely on spatially or/and temporally discretization of the governing equation using polynomials into a finite-dimensional algebraic system. Due to the multi-scale nature of the physics and sensitivity from meshing a complicated geometry, such a process can be computational prohibitive for mo...

Three-dimensional particle reconstruction with limited two-dimensional projects is an underdetermined inverse problem that the exact solution is often difficulty to be obtained. In general, approximate solutions can be obtained by optimization methods. In the current work, a practical particle reconstruction method based on convolutional neural net...

An approximation model based on convolutional neural networks (CNNs) is proposed for flow field predictions. The CNN is used to predict the velocity and pressure field in unseen flow conditions and geometries given the pixelated shape of the object. In particular, we consider Reynolds Averaged Navier–Stokes (RANS) flow solutions over airfoil shapes...

The Koopman operator has emerged as a powerful tool for the analysis of nonlinear dynamical systems as it provides coordinate transformations which can globally linearize the dynamics. Recent deep learning approaches such as Linearly-Recurrent Autoencoder Networks (LRAN) show great promise for discovering the Koopman operator for a general nonlinea...

Numerical simulations on fluid dynamics problems primarily rely on spatially or/and temporally discretization of the governing equation into the finite-dimensional algebraic system solved by computers. Due to complicated nature of the physics and geometry, such process can be computational prohibitive for most real-time applications and many-query...

An approximation model based on convolutional neural networks (CNNs) is proposed for flow field predictions. The CNN is used to predict the velocity and pressure field in unseen flow conditions and geometries given the pixelated shape of the object. In particular, we consider Reynolds Averaged Navier-Stokes (RANS) flow solutions over airfoil shapes...

It is known that for a non-linear dynamical system, periodic and quasi-periodic attractors can be reconstructed in a discrete sense using time-delay embedding. Following this argument, it has been shown that even chaotic non-linear systems can be represented as a linear system with intermittent forcing. Although it is known that linear models such...

This work addresses fundamental issues related to the structure and conditioning of linear time-delayed models of non-linear dynamics on an attractor. While this approach has been well-studied in the asymptotic sense (e.g. for infinite number of delays), the non-asymptotic setting is not well-understood. First, we show that the minimal time-delays...

We study the use of feedforward neural networks (FNN) to develop models of nonlinear dynamical systems from data. Emphasis is placed on predictions at long times, with limited data availability. Inspired by global stability analysis, and the observation of strong correlation between the local error and the maximal singular value of the Jacobian of...

We study the use of feedforward neural networks (FNN) to develop models of nonlinear dynamical systems from data. Emphasis is placed on predictions at long times, with limited data availability. Inspired by global stability analysis, and the observation of the strong correlation between the local error and the maximum singular value of the Jacobian...

Derivation of reduced order representations of dynamical systems requires the modeling of the truncated dynamics on the retained dynamics. In its most general form, this so-called closure model has to account for memory effects. In this work, we present a framework of operator inference to extract the governing dynamics of closure from data in a co...

Derivation of reduced order representations of dynamical systems requires the modeling of the truncated dynamics on the retained dynamics. In its most general form, this so-called closure model has to account for memory effects. In this work, we present a framework of operator inference to extract the governing dynamics of closure from data in a co...

While Stokes’ hypothesis of neglecting bulk viscous effects is exact for monatomic gases and unlikely to strongly affect the dynamics of fluids whose bulk-to-shear viscosity ratio is small and/or of weakly compressible turbulence, it is unclear to what extent this assumption holds for compressible, turbulent flows of gases whose bulk viscosity is o...

A data-driven framework is applied to enhance Reynolds-averaged Navier-Stokes (RANS) predictions of flows involving shock-boundary layer interactions. The methodology involves solving inverse problems to infer spatial discrepancies in the Spalart Allmaras (SA) model and projecting these discrepancies to locally non-dimensional flow features using m...

While several innovative ideas for turbulence modeling have been proposed over the past three decades, it can be argued that the improvement of modeling accuracy in complex flows has not been consistent or significant. Our view is that experimental and high-fidelity data, combined with, and informed by knowledge of the physical processes could be a...

Exhaust and muffler aeroacoustics predictions using Lattice Boltzmann Method have been performed and published for several designs at the SAE Noise and Vibration Conference (NVC) in 2015. While the predictions showed excellent accuracy and an innovative methodology for the aeroacoustics design of mufflers was presented, the results were obtained wi...

espite growing interests in compressible turbulence, the effect of bulk viscosity has been long ignored. For certain gases, the bulk viscosity may be 1000 times greater than the shear viscosity and thus modify energy transfer and dissipation mechanisms. In this study, we use direct numerical simulations to investigate the role of bulk viscosity on...

Influences of heat release by the hydrogen combustion in supersonic turbulent boundary layers are numerically studied using Reynolds-averaged Navier–Stokes equations. The adopted Reynolds-averaged Navier–Stokes methodology is first validated by comparing the numerical results with the existing experimental data. Studies on the effects of the flame...

Continuum based CFD model is extended with slip wall approximation and rarefaction effect on viscosity, in an attempt to predict the pumping flow characteristics in low pressure plasma etch chambers. The flow regime inside the chamber ranges from slip wall (Kn ∼ 0.01), and up to free molecular (Kn = 10). Momentum accommodation coefficient and param...

This paper presents a study of rarefaction effect on hypersonic flow over a sharp leading edge. Both continuum approach and kinetic method: a widely spread commercial Computational Fluid Dynamics-Navior-Stokes-Fourier (CFD-NSF) software - Fluent together with a direct simulation Monte Carlo (DSMC) code developed by the authors are employed for simu...