This paper presents a novel generative model to synthesize fluid simulations from a set of reduced parameters. A convolutional neural network is trained on a collection of discrete, parameterizable fluid simulation velocity fields. Due to the capability of deep learning architectures to learn representative features of the data, our generative model is able to accurately approximate the training data set, while providing plausible interpolated in-betweens. The proposed generative model is optimized for fluids by a novel loss function that guarantees divergence-free velocity fields at all times. In addition, we demonstrate that we can handle complex parameterizations in reduced spaces, and advance simulations in time by integrating in the latent space with a second network. Our method models a wide variety of fluid behaviors, thus enabling applications such as fast construction of simulations, interpolation of fluids with different parameters, time re-sampling, latent space simulations, and compression of fluid simulation data. Reconstructed velocity fields are generated up to 700x faster than re-simulating the data with the underlying CPU solver, while achieving compression rates of up to 1300x.
The true distribution parameterizations of commonly used image datasets are inaccessible. Rather than designing metrics for feature spaces with unknown characteristics, we propose to measure GAN performance by evaluating on explicitly parameterized, synthetic data distributions. As a case study, we examine the performance of 16 GAN variants on six multivariate distributions of varying dimensionalities and training set sizes. In this learning environment, we observe that: GANs exhibit similar performance trends across dimensionalities; learning depends on the underlying distribution and its com…
Convolutional neural networks were recently employed to fully reconstruct fluid simulation data from a set of reduced parameters. However, since (de-)convolutions traditionally trained with supervised L1-loss functions do not discriminate between low and high frequencies in the data, the error is not minimized efficiently for higher bands. This directly correlates with the quality of the perceived results, since missing high frequency details are easily noticeable. In this paper, we analyze the reconstruction quality of generative networks and present a frequency-aware loss function that is ab…
Stanford University（斯坦福大学）；Texas A & M University（德克萨斯农工大学）
The computational cost associated with simulating fluid flows can make it infeasible to run many simulations across multiple flow conditions. Building upon concepts from generative modeling, we introduce a new method for learning neural network models capable of performing efficient parameterized simulations of fluid flows. Evaluated on their ability to simulate both two-dimensional and three-dimensional fluid flows, trained models are shown to capture local and global properties of the flow fields at a wide array of flow conditions. Furthermore, flow simulations generated by the trained model…
The curse of dimensionality is a widely known issue in reinforcement learning (RL). In the tabular setting where the state space $\mathcal{S}$ and the action space $\mathcal{A}$ are both finite, to obtain a nearly optimal policy with sampling access to a generative model, the minimax optimal sample complexity scales linearly with $|\mathcal{S}|\times|\mathcal{A}|$, which can be prohibitively large when $\mathcal{S}$ or $\mathcal{A}$ is large. This paper considers a Markov decision process (MDP) that admits a set of state-action features, which can linearly express (or approximate) its probabil…
Leiden Institute of Advanced Computer Science（莱顿高级计算机科学研究所）；Bonn-Rhein-Sieg University of Applied Sciences（波恩-莱茵-锡格应用科学大学）；Queen Mary University of London（伦敦玛丽女王大学）；SensiLab, Monash University（莫纳什大学SensiLab）
We consider multi-solution optimization and generative models for the generation of diverse artifacts and the discovery of novel solutions. In cases where the domain's factors of variation are unknown or too complex to encode manually, generative models can provide a learned latent space to approximate these factors. When used as a search space, however, the range and diversity of possible outputs are limited to the expressivity and generative capabilities of the learned model. We compare the output diversity of a quality diversity evolutionary search performed in two different search spaces: …
UBTECH Sydney Artificial Intelligence Centre（优必选悉尼人工智能中心）；The University of Sydney（悉尼大学）；University of Technology Sydney（悉尼科技大学）
Parameterized quantum circuits (PQCs) have been broadly used as a hybrid quantum-classical machine learning scheme to accomplish generative tasks. However, whether PQCs have better expressive power than classical generative neural networks, such as restricted or deep Boltzmann machines, remains an open issue. In this paper, we prove that PQCs with a simple structure already outperform any classical neural network for generative tasks, unless the polynomial hierarchy collapses. Our proof builds on known results from tensor networks and quantum circuits (in particular, instantaneous quantum poly…
Parameterized Argumentation-based Reasoning Tasks for Benchmarking Generative Language Models
Bernoulli Institute of Mathematics, Computer Science and Artificial Intelligence, University of Groningen（伯努利数学、计算机科学和人工智能研究所，格罗宁根大学）；Department of Information and Computing Sciences, Utrecht University（信息与计算科学系，乌得勒支大学）
Generative Adversarial Networks have been shown to be powerful in generating content. To this end, they have been studied intensively in the last few years. Nonetheless, training these networks requires solving a saddle point problem that is difficult to solve and slowly converging. Motivated from techniques in the registration of point clouds and by the fluid flow formulation of mass transport, we investigate a new formulation that is based on strict minimization, without the need for the maximization. The formulation views the problem as a matching problem rather than an adversarial one and …
FluidFlow: a flow-matching generative model for fluid dynamics surrogates on unstructured meshes
ETSIAE-UPM-School of Aeronautics, Universidad Politécnica de Madrid（马德里理工大学航空学院）；Institute for Cross-Disciplinary Physics and Complex Systems (IFISC, CSIC-UIB)（跨学科物理与复杂系统研究所（IFISC，CSIC-UIB））；Center for Computational Simulation, Universidad Politécnica de Madrid（马德里理工大学计算模拟中心）
CERN（欧洲核子研究中心）；EPFL（洛桑联邦理工学院）；Cambridge Quantum Computing Ltd（剑桥量子计算公司）；University of Cambridge（剑桥大学）；University of Oviedo（奥维耶多大学）；University of Strathclyde（斯特拉斯克莱德大学）；University College London（伦敦大学学院）
Generative models, and Generative Adversarial Networks (GAN) in particular, are being studied as possible alternatives to Monte Carlo simulations. It has been proposed that, in certain circumstances, simulation using GANs can be sped-up by using quantum GANs (qGANs). We present a new design of qGAN, the dual-Parameterized Quantum Circuit(PQC) GAN, which consists of a classical discriminator and two quantum generators which take the form of PQCs. The first PQC learns a probability distribution over N-pixel images, while the second generates normalized pixel intensities of an individual image fo…
A Synergistic Framework Leveraging Autoencoders and Generative Adversarial Networks for the Synthesis of Computational Fluid Dynamics Results in Aerofoil Aerodynamics
Multimodal learning is a framework for building models that make predictions based on different types of modalities. Important challenges in multimodal learning are the inference of shared representations from arbitrary modalities and cross-modal generation via these representations; however, achieving this requires taking the heterogeneous nature of multimodal data into account. In recent years, deep generative models, i.e., generative models in which distributions are parameterized by deep neural networks, have attracted much attention, especially variational autoencoders, which are suitable…
We introduce a new category of multivariate conditional generative models and demonstrate its performance and versatility in probabilistic time series forecasting and simulation. Specifically, the output of quantile regression networks is expanded from a set of fixed quantiles to the whole Quantile Function by a univariate mapping from a latent uniform distribution to the target distribution. Then the multivariate case is solved by learning such quantile functions for each dimension's marginal distribution, followed by estimating a conditional Copula to associate these latent uniform random va…
Parameterized Physics-informed Neural Networks for Parameterized PDEs
Yonsei University（延世大学）；Arizona State University（亚利桑那州立大学）；LG CNS；Texas A&M University-Commerce（德州农工大学Commerce分校）；Oregon State University（俄勒冈州立大学）；KAIST（韩国科学技术院）
Technical University of Denmark（丹麦技术大学）；University of Copenhagen（哥本哈根大学）
Deep generative models parameterized by neural networks have recently achieved state-of-the-art performance in unsupervised and semi-supervised learning. We extend deep generative models with auxiliary variables which improves the variational approximation. The auxiliary variables leave the generative model unchanged but make the variational distribution more expressive. Inspired by the structure of the auxiliary variable we also propose a model with two stochastic layers and skip connections. Our findings suggest that more expressive and properly specified deep generative models converge fast…
In computational fluid dynamics, there is an inevitable trade off between accuracy and computational cost. In this work, a novel multi-fidelity deep generative model is introduced for the surrogate modeling of high-fidelity turbulent flow fields given the solution of a computationally inexpensive but inaccurate low-fidelity solver. The resulting surrogate is able to generate physically accurate turbulent realizations at a computational cost magnitudes lower than that of a high-fidelity simulation. The deep generative model developed is a conditional invertible neural network, built with normal…
We present doubly stochastic gradient MCMC, a simple and generic method for (approximate) Bayesian inference of deep generative models (DGMs) in a collapsed continuous parameter space. At each MCMC sampling step, the algorithm randomly draws a mini-batch of data samples to estimate the gradient of log-posterior and further estimates the intractable expectation over hidden variables via a neural adaptive importance sampler, where the proposal distribution is parameterized by a deep neural network and learnt jointly. We demonstrate the effectiveness on learning various DGMs in a wide range of ta…
We present Ordinary Differential Equation Variational Auto-Encoder (ODE$^2$VAE), a latent second order ODE model for high-dimensional sequential data. Leveraging the advances in deep generative models, ODE$^2$VAE can simultaneously learn the embedding of high dimensional trajectories and infer arbitrarily complex continuous-time latent dynamics. Our model explicitly decomposes the latent space into momentum and position components and solves a second order ODE system, which is in contrast to recurrent neural network (RNN) based time series models and recently proposed black-box ODE techniques.…
CSEM（瑞士电子与微技术中心）；University of Maryland（马里兰大学）；ETHZ（苏黎世联邦理工学院）
Learning probabilistic models that can estimate the density of a given set of samples, and generate samples from that density, is one of the fundamental challenges in unsupervised machine learning. We introduce a new generative model based on denoising density estimators (DDEs), which are scalar functions parameterized by neural networks, that are efficiently trained to represent kernel density estimators of the data. Leveraging DDEs, our main contribution is a novel technique to obtain generative models by minimizing the KL-divergence directly. We prove that our algorithm for obtaining genera…
Princeton University（普林斯顿大学）；Peking University（北京大学）；Beijing Institute of Big Data Research（北京大数据研究院）；Chinese Academy of Sciences（中国科学院）
We present a deep generative model, named Monge-Ampère flow, which builds on continuous-time gradient flow arising from the Monge-Ampère equation in optimal transport theory. The generative map from the latent space to the data space follows a dynamical system, where a learnable potential function guides a compressible fluid to flow towards the target density distribution. Training of the model amounts to solving an optimal control problem. The Monge-Ampère flow has tractable likelihoods and supports efficient sampling and inference. One can easily impose symmetry constraints in the generative…
State University of New York at Buffalo（纽约州立大学布法罗分校）
Learning with kernels is an important concept in machine learning. Standard approaches for kernel methods often use predefined kernels that require careful selection of hyperparameters. To mitigate this burden, we propose in this paper a framework to construct and learn a data-dependent kernel based on random features and implicit spectral distributions that are parameterized by deep neural networks. The constructed network (called KernelNet) can be applied to deep generative modeling in various scenarios, including two popular learning paradigms in deep generative models, MMD-GAN and implicit…
Criteo AI Lab（Criteo人工智能实验室）；IRIT（图卢兹计算机科学研究所）；Université de Toulouse（图卢兹大学）；CNRS（法国国家科学研究中心）
Binary data matrices can represent many types of data such as social networks, votes, or gene expression. In some cases, the analysis of binary matrices can be tackled with nonnegative matrix factorization (NMF), where the observed data matrix is approximated by the product of two smaller nonnegative matrices. In this context, probabilistic NMF assumes a generative model where the data is usually Bernoulli-distributed. Often, a link function is used to map the factorization to the $[0,1]$ range, ensuring a valid Bernoulli mean parameter. However, link functions have the potential disadvantage …
Generative Quasi-Continuum Modeling of Confined Fluids at the Nanoscale
Oden Institute for Computational Engineering and Sciences（奥登计算工程与科学研究所）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Walker Department of Mechanical Engineering（沃克机械工程系）；Department of Mechanical Science and Engineering（机械科学与工程系）；University of Illinois at Urbana–Champaign（伊利诺伊大学厄巴纳-香槟分校）
Autoencoders and generative neural network models have recently gained popularity in fluid mechanics due to their spontaneity and low processing time instead of high fidelity CFD simulations. Auto encoders are used as model order reduction tools in applications of fluid mechanics by compressing input high-dimensional data using an encoder to map the input space into a lower-dimensional latent space. Whereas, generative models such as Variational Auto-encoders (VAEs) and Generative Adversarial Networks (GANs) are proving to be effective in generating solutions to chaotic models with high 'rando…
This paper studies probability distributions of penultimate activations of classification networks. We show that, when a classification network is trained with the cross-entropy loss, its final classification layer forms a Generative-Discriminative pair with a generative classifier based on a specific distribution of penultimate activations. More importantly, the distribution is parameterized by the weights of the final fully-connected layer, and can be considered as a generative model that synthesizes the penultimate activations without feeding input data. We empirically demonstrate that this…
We propose a novel method to up-sample volumetric functions with generative neural networks using several orthogonal passes. Our method decomposes generative problems on Cartesian field functions into multiple smaller sub-problems that can be learned more efficiently. Specifically, we utilize two separate generative adversarial networks: the first one up-scales slices which are parallel to the XY-plane, whereas the second one refines the whole volume along the Z-axis working on slices in the YZ-plane. In this way, we obtain full coverage for the 3D target function and can leverage spatio-tempo…
Warsaw University of Technology（华沙理工大学）；Vrije Universiteit Amsterdam（阿姆斯特丹自由大学）
Diffusion-based Deep Generative Models (DDGMs) offer state-of-the-art performance in generative modeling. Their main strength comes from their unique setup in which a model (the backward diffusion process) is trained to reverse the forward diffusion process, which gradually adds noise to the input signal. Although DDGMs are well studied, it is still unclear how the small amount of noise is transformed during the backward diffusion process. Here, we focus on analyzing this problem to gain more insight into the behavior of DDGMs and their denoising and generative capabilities. We observe a fluid…
Generative design has been growing across the design community as a viable method for design space exploration. Thermal design is more complex than mechanical or aerodynamic design because of the additional convection-diffusion equation and its pertinent boundary interaction. We present a generative thermal design using cooperative multi-agent deep reinforcement learning and continuous geometric representation of the fluid and solid domain. The proposed framework consists of a pre-trained neural network surrogate model as an environment to predict heat transfer and pressure drop of the generat…
The calibration of a reservoir model with observed transient data of fluid pressures and rates is a key task in obtaining a predictive model of the flow and transport behaviour of the earth's subsurface. The model calibration task, commonly referred to as "history matching", can be formalised as an ill-posed inverse problem where we aim to find the underlying spatial distribution of petrophysical properties that explain the observed dynamic data. We use a generative adversarial network pretrained on geostatistical object-based models to represent the distribution of rock properties for a synth…
Missing values widely exist in many real-world datasets, which hinders the performing of advanced data analytics. Properly filling these missing values is crucial but challenging, especially when the missing rate is high. Many approaches have been proposed for missing value imputation (MVI), but they are mostly heuristics-based, lacking a principled foundation and do not perform satisfactorily in practice. In this paper, we propose a probabilistic framework based on deep generative models for MVI. Under this framework, imputing the missing entries amounts to seeking a fixed-point solution betw…
Institute of Artificial Intelligence（人工智能研究所）；University of Groningen（格罗宁根大学）
Generative adversarial networks (GANs) have demonstrated to be successful at generating realistic real-world images. In this paper we compare various GAN techniques, both supervised and unsupervised. The effects on training stability of different objective functions are compared. We add an encoder to the network, making it possible to encode images to the latent space of the GAN. The generator, discriminator and encoder are parameterized by deep convolutional neural networks. For the discriminator network we experimented with using the novel Capsule Network, a state-of-the-art technique for de…
Forecasting on sparse multivariate time series (MTS) aims to model the predictors of future values of time series given their incomplete past, which is important for many emerging applications. However, most existing methods process MTS's individually, and do not leverage the dynamic distributions underlying the MTS's, leading to sub-optimal results when the sparsity is high. To address this challenge, we propose a novel generative model, which tracks the transition of latent clusters, instead of isolated feature representations, to achieve robust modeling. It is characterized by a newly desig…
Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔研究所）；DIKU, University of Copenhagen（哥本哈根大学计算机科学系）
We propose a novel denoising diffusion generative model for predicting nonlinear fluid fields named FluidDiff. By performing a diffusion process, the model is able to learn a complex representation of the high-dimensional dynamic system, and then Langevin sampling is used to generate predictions for the flow state under specified initial conditions. The model is trained with finite, discrete fluid simulation data. We demonstrate that our model has the capacity to model the distribution of simulated training data and that it gives accurate predictions on the test data. Without encoded prior kno…
Carbon capture and storage (CCS) can aid decarbonization of the atmosphere to limit further global temperature increases. A framework utilizing unsupervised learning is used to generate a range of subsurface geologic volumes to investigate potential sites for long-term storage of carbon dioxide. Generative adversarial networks are used to create geologic volumes, with a further neural network used to sample the posterior distribution of a trained Generator conditional to sparsely sampled physical measurements. These generative models are further conditioned to historic dynamic fluid flow data …
This work presents a novel semi-supervised learning approach for data-driven modeling of asset failures when health status is only partially known in historical data. We combine a generative model parameterized by deep neural networks with non-linear embedding technique. It allows us to build prognostic models with the limited amount of health status information for the precise prediction of future asset reliability. The proposed method is evaluated on a publicly available dataset for remaining useful life (RUL) estimation, which shows significant improvement even when a fraction of the data w…
Bayesian generative models can flag performance loss, bias, and out-of-distribution image content
Instituto Universitario de Investigación en Tecnología Centrada en el Ser Humano, Universitat Politècnica de València（瓦伦西亚理工大学人类中心技术研究大学学院）；Technical University of Denmark（丹麦技术大学）
Simulating fluid flows in different virtual scenarios is of key importance in engineering applications. However, high-fidelity, full-order models relying, e.g., on the finite element method, are unaffordable whenever fluid flows must be simulated in almost real-time. Reduced order models (ROMs) relying, e.g., on proper orthogonal decomposition (POD) provide reliable approximations to parameter-dependent fluid dynamics problems in rapid times. However, they might require expensive hyper-reduction strategies for handling parameterized nonlinear terms, and enriched reduced spaces (or Petrov-Galer…
