Flow-based generative models synthesize data by integrating a learned velocity field from a reference distribution to the target data distribution. Prior work has focused on endpoint metrics (e.g., fidelity, likelihood, perceptual quality) while overlooking a deeper question: what do the sampling trajectories reveal? Motivated by classical mechanics, we introduce kinetic path energy (KPE), a simple yet powerful diagnostic that quantifies the total kinetic effort along each generation path of ODE-based samplers. Through comprehensive experiments on CIFAR-10 and ImageNet-256, we uncover two key phenomena: ({i}) higher KPE predicts stronger semantic quality, indicating that semantically richer samples require greater kinetic effort, and ({ii}) higher KPE inversely correlates with data density, with informative samples residing in sparse, low-density regions. Together, these findings reveal that semantically informative samples naturally reside on the sparse frontier of the data distribution, demanding greater generative effort. Our results suggest that trajectory-level analysis offers a physics-inspired and interpretable framework for understanding generation difficulty and sample characteristics.
Brown University（布朗大学）；Massachusetts Institute of Technology（麻省理工学院）；Pacific Northwest National Laboratory（西北太平洋国家实验室）
We propose a new method for inferring the governing stochastic ordinary differential equations (SODEs) by observing particle ensembles at discrete and sparse time instants, i.e., multiple "snapshots". Particle coordinates at a single time instant, possibly noisy or truncated, are recorded in each snapshot but are unpaired across the snapshots. By training a physics-informed generative model that generates "fake" sample paths, we aim to fit the observed particle ensemble distributions with a curve in the probability measure space, which is induced from the inferred particle dynamics. We employ …
Columbia University（哥伦比亚大学）；Data Science Institute, Columbia University（哥伦比亚大学数据科学研究所）
This paper proposes the TrafficFlowGAN, a physics-informed flow based generative adversarial network (GAN), for uncertainty quantification (UQ) of dynamical systems. TrafficFlowGAN adopts a normalizing flow model as the generator to explicitly estimate the data likelihood. This flow model is trained to maximize the data likelihood and to generate synthetic data that can fool a convolutional discriminator. We further regularize this training process using prior physics information, so-called physics-informed deep learning (PIDL). To the best of our knowledge, we are the first to propose an inte…
This paper extends the methodology to use physics-informed enhanced super-resolution generative adversarial networks (PIESRGANs) for LES subfilter modeling in turbulent flows with finite-rate chemistry and shows a successful application to a non-premixed temporal jet case. This is an important topic considering the need for more efficient and carbon-neutral energy devices to fight the climate change. Multiple a priori and a posteriori results are presented and discussed. As part of this, the impact of the underlying mesh on the prediction quality is emphasized, and a multi-mesh approach is dev…
Stanford University（斯坦福大学）；Center for Turbulence Research（湍流研究中心）
Generative Adversarial Networks (GANs) have been widely used for generating photo-realistic images. A variant of GANs called super-resolution GAN (SRGAN) has already been used successfully for image super-resolution where low resolution images can be upsampled to a $4\times$ larger image that is perceptually more realistic. However, when such generative models are used for data describing physical processes, there are additional known constraints that models must satisfy including governing equations and boundary conditions. In general, these constraints may not be obeyed by the generated data…
A Residual Guided strategy with Generative Adversarial Networks in training Physics-Informed Transformer Networks
College of Science, China Agricultural University（中国农业大学理学院）；College of Information and Electrical Engineering, China Agricultural University（中国农业大学信息与电气工程学院）；College of Water Resources and Civil Engineering, China Agricultural University（中国农业大学水利与土木工程学院）
Water Resources Research Center（水资源研究中心）；University of Hawai’i at Mānoa（夏威夷大学马诺阿分校）；Yeungnam University（岭南大学）；Sandia National Laboratories（桑迪亚国家实验室）
Stochastic network modeling is often limited by high computational costs to generate a large number of networks enough for meaningful statistical evaluation. In this study, Deep Convolutional Generative Adversarial Networks (DCGANs) were applied to quickly reproduce drainage networks from the already generated network samples without repetitive long modeling of the stochastic network model, Gibb's model. In particular, we developed a novel connectivity-informed method that converts the drainage network images to the directional information of flow on each node of the drainage network, and then…
Entropy-Informed Weighting Channel Normalizing Flow for Deep Generative Models
School of Mathematics, South China University of Technology, Guangzhou, China（华南理工大学数学学院）；Shenzhen International Graduate School, Tsinghua University, Shenzhen, China（清华大学深圳国际研究生院）；School of Electronic and Information Engineering, South China University of Technology, Guangzhou, China（华南理工大学电子信息学院）；Department of Electrical Engineering, Columbia University, New York, NY USA（哥伦比亚大学电气工程系）
Harbin Institute of Technology（哈尔滨工业大学）；Peking University（北京大学）
Seismic full waveform inversion (FWI) is a powerful geophysical imaging technique that produces high-resolution subsurface models by iteratively minimizing the misfit between the simulated and observed seismograms. Unfortunately, conventional FWI with least-squares function suffers from many drawbacks such as the local-minima problem and computation of explicit gradient. It is particularly challenging with the contaminated measurements or poor starting models. Recent works relying on partial differential equations and neural networks show promising performance for two-dimensional FWI. Inspired…
Generative VS non-Generative Models in Engineering Shape Optimization
University of Strathclyde（斯特拉斯克莱德大学）；Nazarbayev University（纳扎尔巴耶夫大学）；BAR Technologies（BAR科技公司）；Foundation for Research & Technology Hellas (FORTH)（希腊研究与技术基金会）
Mobility datasets are fundamental for evaluating algorithms pertaining to geographic information systems and facilitating experimental reproducibility. But privacy implications restrict sharing such datasets, as even aggregated location-data is vulnerable to membership inference attacks. Current synthetic mobility dataset generators attempt to superficially match a priori modeled mobility characteristics which do not accurately reflect the real-world characteristics. Modeling human mobility to generate synthetic yet semantically and statistically realistic trajectories is therefore crucial for…
GenAI-FDIA: Physics-Informed Generative Models for False Data Injection Attacks
School of Computing, Engineering and Digital Technologies, Teesside University, UK（Teesside大学计算与工程数字技术学院，英国）；Smartifier Ltd, Stockton-on-Tees, UK（Smartifier有限公司，英国Stockton-on-Tees）
Jülich Supercomputing Centre, Forschungszentrum Jülich GmbH（于利希研究中心于利希超级计算中心）；RWTH Aachen University（亚琛工业大学）
Models for finite-rate-chemistry in underresolved flows still pose one of the main challenges for predictive simulations of complex configurations. The problem gets even more challenging if turbulence is involved. This work advances the recently developed PIESRGAN modeling approach to turbulent premixed combustion. For that, the physical information processed by the network and considered in the loss function are adjusted, the training process is smoothed, and especially effects from density changes are considered. The resulting model provides good results for a priori and a posteriori tests o…
FunDiff: Diffusion Models over Function Spaces for Physics-Informed Generative Modeling
Institute for Foundations of Data Science, Yale University（数据科学基础研究所，耶鲁大学）；Department of Statistics and Data Science, Yale University（统计与数据科学系，耶鲁大学）；Laboratoire Navier, École nationale des ponts et chaussées, Institut Polytechnique de Paris, University Gustave Eiffel, CNRS UMR 8205（纳维实验室，巴黎理工学院，格斯塔夫·埃菲尔大学，CNRS UMR 8205）；Department of Chemical and Environmental Engineering, Yale University（化学与环境工程系，耶鲁大学）
NASA Langley Research Center（美国国家航空航天局兰利研究中心）；University of Puerto Rico (Mayagüez)（波多黎各大学（马亚圭斯））
While standard generative adversarial networks (GANs) rely solely on training data to learn unknown probability distributions, physics-informed GANs (PI-GANs) encode physical laws in the form of stochastic partial differential equations (PDEs) using auto differentiation. By relating observed data to unobserved quantities of interest through PDEs, PI-GANs allow for the estimation of underlying probability distributions without their direct measurement (i.e. inverse problems). The scalable nature of GANs allows high-dimensional, spatially-dependent probability distributions (i.e., random fields)…
Generative Adversarial Networks (GANs) represent a promising class of generative networks that combine neural networks with game theory. From generating realistic images and videos to assisting musical creation, GANs are transforming many fields of arts and sciences. However, their application to healthcare has not been fully realized, more specifically in generating electronic health records (EHR) data. In this paper, we propose a framework for exploring the value of GANs in the context of continuous laboratory time series data. We devise an unsupervised evaluation method that measures the pr…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
We propose a new class of physics-informed neural networks, called physics-informed Variational Autoencoder (PI-VAE), to solve stochastic differential equations (SDEs) or inverse problems involving SDEs. In these problems the governing equations are known but only a limited number of measurements of system parameters are available. PI-VAE consists of a variational autoencoder (VAE), which generates samples of system variables and parameters. This generative model is integrated with the governing equations. In this integration, the derivatives of VAE outputs are readily calculated using automat…
University of Colorado Boulder（科罗拉多大学博尔德分校）；The Charles Stark Draper Laboratory, Inc.（查尔斯·斯塔克·德雷珀实验室公司）
For autonomous agents to act as trustworthy partners to human users, they must be able to reliably communicate their competency for the tasks they are asked to perform. Towards this objective, we develop probabilistic world models based on deep generative modelling that allow for the simulation of agent trajectories and accurate calculation of tasking outcome probabilities. By combining the strengths of conditional variational autoencoders with recurrent neural networks, the deep generative world model can probabilistically forecast trajectories over long horizons to task completion. We show h…
Predicting the Stock movement attracts much attention from both industry and academia. Despite such significant efforts, the results remain unsatisfactory due to the inherently complicated nature of the stock market driven by factors including supply and demand, the state of the economy, the political climate, and even irrational human behavior. Recently, Generative Adversarial Networks (GAN) have been extended for time series data; however, robust methods are primarily for synthetic series generation, which fall short for appropriate stock prediction. This is because existing GANs for stock a…
Weighted Flow Matching and Physics-Informed Nonlinear Filtering for Parameter Estimation in Digital Twins
Department of Applied Mathematics, University of California, Santa Cruz, CA 95064, USA（应用数学系，加州大学圣克鲁兹分校）；Department of Electrical and Computer Engineering, University of California, Santa Cruz, CA 95064, USA（电气与计算机工程系，加州大学圣克鲁兹分校）
Turbulence is still one of the main challenges for accurately predicting reactive flows. Therefore, the development of new turbulence closures which can be applied to combustion problems is essential. Data-driven modeling has become very popular in many fields over the last years as large, often extensively labeled, datasets became available and training of large neural networks became possible on GPUs speeding up the learning process tremendously. However, the successful application of deep neural networks in fluid dynamics, for example for subgrid modeling in the context of large-eddy simula…
The accurate prediction of small scales in underresolved flows is still one of the main challenges in predictive simulations of complex configurations. Over the last few years, data-driven modeling has become popular in many fields as large, often extensively labeled datasets are now available and training of large neural networks has become possible on graphics processing units (GPUs) that speed up the learning process tremendously. In fact, the successful application of deep neural networks in fluid dynamics, such as for underresolved reactive flows, is still challenging. This work advances …
Zhejiang University（浙江大学）；Brown University（布朗大学）；South Dakota School of Mines and Technology（南达科他矿业理工学院）；Pacific Northwest National Laboratory（太平洋西北国家实验室）
A fundamental problem in geostatistical modeling is to infer the heterogeneous geological field based on limited measurements and some prior spatial statistics. Semantic inpainting, a technique for image processing using deep generative models, has been recently applied for this purpose, demonstrating its effectiveness in dealing with complex spatial patterns. However, the original semantic inpainting framework incorporates only information from direct measurements, while in geostatistics indirect measurements are often plentiful. To overcome this limitation, here we propose a physics-informed…
With the wide use of deep neural networks (DNN), model interpretability has become a critical concern, since explainable decisions are preferred in high-stake scenarios. Current interpretation techniques mainly focus on the feature attribution perspective, which are limited in indicating why and how particular explanations are related to the prediction. To this end, an intriguing class of explanations, named counterfactuals, has been developed to further explore the "what-if" circumstances for interpretation, and enables the reasoning capability on black-box models. However, generating counter…
SIGMA-PPG: Statistical-prior Informed Generative Masking Architecture for PPG Foundation Model
Department of Electronics, Information and Bioengineering, Politecnico di Milano（电子工程与信息生物工程系，米兰理工大学）；State Key Laboratory of Industrial Control Technology, Zhejiang University（工业控制技术国家重点实验室，浙江大学）；Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences（深圳先进技术研究院，中国科学院）；Nell Hodgson Woodruff School of Nursing, Emory University（埃默里大学护理学院）
Physics-informed generative AI for semiconductor manufacturing: Enforcing hard physical constraints in generative models by construction
School of Electrical and Computer Engineering, University of Oklahoma（俄克拉荷马大学电气与计算机工程学院）；Center for Quantum Research and Technology, University of Oklahoma（俄克拉荷马大学量子研究与技术中心）；Intelligent Neuromorphic and Quantum Understanding for Innovative Research and Engineering (INQUIRE) Laboratory（创新研究与工程智能神经形态与量子理解实验室）；Material Science and Engineering Program, University of Oklahoma, Norman, OK 73019 USA（俄克拉荷马大学材料科学与工程项目，Norman, OK 73019 USA）
We consider the application of deep generative models in propagating uncertainty through complex physical systems. Specifically, we put forth an implicit variational inference formulation that constrains the generative model output to satisfy given physical laws expressed by partial differential equations. Such physics-informed constraints provide a regularization mechanism for effectively training deep probabilistic models for modeling physical systems in which the cost of data acquisition is high and training data-sets are typically small. This provides a scalable framework for characterizin…
Dalian University of Technology（大连理工大学）；Harbin Institute of Technology（哈尔滨工业大学）；JD Explore Academy（京东探索研究院）
Physics-informed neural networks (PINNs) provide a deep learning framework for numerically solving partial differential equations (PDEs), and have been widely used in a variety of PDE problems. However, there still remain some challenges in the application of PINNs: 1) the mechanism of PINNs is unsuitable (at least cannot be directly applied) to exploiting a small size of (usually very few) extra informative samples to refine the networks; and 2) the efficiency of training PINNs often becomes low for some complicated PDEs. In this paper, we propose the generative adversarial physics-informed n…
Physics-Informed Generative Solver: Bridging Data-Driven Priors and Conservation Laws for Stable Spatiotemporal Field Reconstruction
School of Advanced Manufacturing Engineering, Nanjing University（南京大学先进制造工程学院）；National Laboratory of Solid State Microstructures, Nanjing University（南京大学固态微结构国家实验室）；Suzhou Acoustics Industry Technology Research Institute Co., Ltd.（苏州声学工业技术研究所有限公司）；School of Mechanical and Electric Engineering, Soochow University（苏州大学机械与电子工程学院）；Shishan Laboratory, Nanjing University（仙山实验室）
East China Regional Air Traffic Management Bureau, CAAC（中国民用航空局华东地区空中交通管理局）；Shanghai Em-Data Technology Co. Ltd.（上海亿数数据科技有限公司）
The troposphere is one of the atmospheric layers where most weather phenomena occur. Temperature variations in the troposphere, especially at 500 hPa, a typical level of the middle troposphere, are significant indicators of future weather changes. Numerical weather prediction is effective for temperature prediction, but its computational complexity hinders a timely response. This paper proposes a novel temperature prediction approach in framework ofphysics-informed deep learning. The new model, called PGnet, builds upon a generative neural network with a mask matrix. The mask is designed to di…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Microsoft Research Cambridge（微软研究院剑桥实验室）
Computer vision is hard because of a large variability in lighting, shape, and texture; in addition the image signal is non-additive due to occlusion. Generative models promised to account for this variability by accurately modelling the image formation process as a function of latent variables with prior beliefs. Bayesian posterior inference could then, in principle, explain the observation. While intuitively appealing, generative models for computer vision have largely failed to deliver on that promise due to the difficulty of posterior inference. As a result the community has favoured effic…
