Latent-space time evolution of non-intrusive reduced-order models using Gaussian process emulation
Argonne Leadership Computing Facility（阿贡领导力计算设施）；Argonne National Laboratory（阿贡国家实验室）；The Alan Turing Institute（艾伦·图灵研究所）；Imperial College London（帝国理工学院）
Romit Maulik, Themistoklis Botsas, Nesar Ramachandra, Lachlan Robert Mason, Indranil Pan
Non-intrusive reduced-order models (ROMs) have recently generated considerable interest for constructing computationally efficient counterparts of nonlinear dynamical systems emerging from various domain sciences. They provide a low-dimensional emulation framework for systems that may be intrinsically high-dimensional. This is accomplished by utilizing a construction algorithm that is purely data-driven. It is no surprise, therefore, that the algorithmic advances of machine learning have led to non-intrusive ROMs with greater accuracy and computational gains. However, in bypassing the utilization of an equation-based evolution, it is often seen that the interpretability of the ROM framework suffers. This becomes more problematic when black-box deep learning methods are used which are notorious for lacking robustness outside the physical regime of the observed data. In this article, we propose the use of a novel latent-space interpolation algorithm based on Gaussian process regression. Notably, this reduced-order evolution of the system is parameterized by control parameters to allow for interpolation in space. The use of this procedure also allows for a continuous interpretation of time which allows for temporal interpolation. The latter aspect provides information, with quantified uncertainty, about full-state evolution at a finer resolution than that utilized for training the ROMs. We assess the viability of this algorithm for an advection-dominated system given by the inviscid shallow water equations.
Lost in Latent Space: An Empirical Study of Latent Diffusion Models for Physics Emulation
Polymathic AI；Flatiron Institute；University of Liège（列日大学）；New York University（纽约大学）；Princeton University（普林斯顿大学）；Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM（巴黎-萨克莱大学、巴黎-cite大学、CEA、CNRS、AIM）
A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling
Cornell University（康奈尔大学）；ANSYS Inc.（ANSYS公司）；Korea Institute for Advanced Study（韩国高等研究院）；University of Arizona（亚利桑那大学）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；North Carolina State University（北卡罗来纳州立大学）；Pohang University of Science and Technology（浦项科技大学）；University of California, San Diego（加利福尼亚大学圣迭戈分校）
Wavelet Flow Matching for Multi-Scale Physics Emulation
Department of Earth and Environmental Engineering（地球与环境工程系）；Columbia University（哥伦比亚大学）；University of Edinburgh（爱丁堡大学）；Courant Institute of Mathematical Sciences（数学科学学院）；New York University（纽约大学）；Scripps Institution of Oceanography（斯克里普斯海洋研究所）；Halıcıoğlu Data Science Institute（哈利奇数据科学研究所）；University of California San Diego（加州大学圣地亚哥分校）；CUNY New York City College of Technology（纽约市立大学纽约技术学院）；Lamont-Doherty Earth Observatory（拉蒙特-多伊蒂地球观测站）
Reduced-order models (ROMs) are computationally inexpensive simplifications of high-fidelity complex ones. Such models can be found in computational fluid dynamics where they can be used to predict the characteristics of multiphase flows. In previous work, we presented a ROM analysis framework that coupled compression techniques, such as autoencoders (AE), with Gaussian process (GP) regression in the latent space. This pairing has significant advantages over the standard encoding-decoding routine, such as the ability to interpolate or extrapolate in the initial conditions' space, which can pro…
University College London（伦敦大学学院）；University of Exeter（埃克塞特大学）
Deep Gaussian processes (DGPs) provide a rich class of models that can better represent functions with varying regimes or sharp changes, compared to conventional GPs. In this work, we propose a novel inference method for DGPs for computer model emulation. By stochastically imputing the latent layers, our approach transforms a DGP into a linked GP: a novel emulator developed for systems of linked computer models. This transformation permits an efficient DGP training procedure that only involves optimizations of conventional GPs. In addition, predictions from DGP emulators can be made in a fast …
Flux inversion is the process by which sources and sinks of a gas are identified from observations of gas mole fraction. The inversion often involves running a Lagrangian particle dispersion model (LPDM) to generate sensitivities between observations and fluxes over a spatial domain of interest. The LPDM must be run backward in time for every gas measurement, and this can be computationally prohibitive. To address this problem, here we develop a novel spatio-temporal emulator for LPDM sensitivities that is built using a convolutional variational autoencoder (CVAE). With the encoder segment of …
End-to-End Historical Music Restoration in Latent Space
ETH Zurich（苏黎世联邦理工学院）；Sony Corporate Technology Center America, Inc.（索尼美国公司技术中心）；Sony Europe Ltd.（索尼欧洲有限公司）；Aalto University（阿尔托大学）；Sony Group Corporation（索尼集团公司）
Multi-fidelity modeling and calibration are data fusion tasks that ubiquitously arise in engineering design. In this paper, we introduce a novel approach based on latent-map Gaussian processes (LMGPs) that enables efficient and accurate data fusion. In our approach, we convert data fusion into a latent space learning problem where the relations among different data sources are automatically learned. This conversion endows our approach with attractive advantages such as increased accuracy, reduced costs, flexibility to jointly fuse any number of data sources, and ability to visualize correlatio…
CFD Correction of Open Tip Clearance Flow in a Compressor Cascade Using VAE Latent Space Adaptation
School of Aeronautics and Astronautics, Shanghai Jiao Tong University（上海交通大学航空航天学院）；Global Institute of Future Technology, Shanghai Jiao Tong University（上海交通大学未来技术学院）
In this paper, we propose a multi-speaker face-to-speech waveform generation model that also works for unseen speaker conditions. Using a generative adversarial network (GAN) with linguistic and speaker characteristic features as auxiliary conditions, our method directly converts face images into speech waveforms under an end-to-end training framework. The linguistic features are extracted from lip movements using a lip-reading model, and the speaker characteristic features are predicted from face images using cross-modal learning with a pre-trained acoustic model. Since these two features are…
Non-intrusive load monitoring (NILM) aims at separating a whole-home energy signal into its appliance components. Such method can be harnessed to provide various services to better manage and control energy consumption (optimal planning and saving). NILM has been traditionally approached from signal processing and electrical engineering perspectives. Recently, machine learning has started to play an important role in NILM. While most work has focused on supervised algorithms, unsupervised approaches can be more interesting and of practical use in real case scenarios. Specifically, they do not …
We study the performance of long short-term memory networks (LSTMs) and neural ordinary differential equations (NODEs) in learning latent-space representations of dynamical equations for an advection-dominated problem given by the viscous Burgers equation. Our formulation is devised in a non-intrusive manner with an equation-free evolution of dynamics in a reduced space with the latter being obtained through a proper orthogonal decomposition. In addition, we leverage the sequential nature of learning for both LSTMs and NODEs to demonstrate their capability for closure in systems which are not …
While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical interest is computationally infeasible or impractical. In complex systems, with limited physical insight on the coherent behavior of their constituents, the only available information is data obtained from simulations of the trajectories of huge numbers of degrees of freedom over microscopic time scales. This paper discusses a Bayesian approach to deriving prob…
This paper proposes a supervised machine learning framework for the non-intrusive model order reduction of unsteady fluid flows to provide accurate predictions of non-stationary state variables when the control parameter values vary. Our approach utilizes a training process from full-order scale direct numerical simulation data projected on proper orthogonal decomposition (POD) modes to achieve an artificial neural network (ANN) model with reduced memory requirements. This data-driven ANN framework allows for a nonlinear time evolution of the modal coefficients without performing a Galerkin pr…
U.S. Army Engineer Research and Development Center（美国陆军工程研究与发展中心）
Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. Here, we explore the use of Neural Ordinary Differential Equations, a recently introduced family of continuous-depth, differentiable networks (Chen et al 2018), as a way to propagate latent-space dynamics in reduced order models. We compare their behavior with two classical non-intrusive methods based on proper orthogonal decomposition and radial basis function interpolation as well as dynamic mode decomposition. The test problems we consider include incompressible …
Generative adversarial networks (GANs) have been recently applied as a novel emulation technique for large scale structure simulations. Recent results show that GANs can be used as a fast, efficient and computationally cheap emulator for producing novel weak lensing convergence maps as well as cosmic web data in 2-D and 3-D. However, like any algorithm, the GAN approach comes with a set of limitations, such as an unstable training procedure and the inherent randomness of the produced outputs. In this work we employ a number of techniques commonly used in the machine learning literature to addr…
This paper presents a new data-driven non-intrusive reduced-order model(NIROM) that outperforms the traditional Proper orthogonal decomposition (POD) based reducedorder model. This is achieved by using Auto-Encoder(AE) and attention-based deep learning methods. The novelty of the present work lies in that it uses Stacked AutoEncoder(SAE) network to project original high-dimensional dynamical systems onto a low dimensional nonlinear subspace and predict the fluid dynamics using an attentionbased deep learning method. A new model reduction neural network architecture for fluid flow problem is pr…
