Potential Flow Generator With L 2 Optimal Transport Regularity for Generative Models
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Computer Science↗
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RockFlow: Fast Generation of Synthetic Source Rock Images Using Generative Flow Models
Image-based evaluation methods are a valuable tool for source rock characterization. The time and resources needed to obtain images has spurred development of machine-learning generative models to create synthetic images of pore structure and rock fabric from limited image data. While generative models have shown success, existing methods for generating 3D volumes from 2D training images are restricted to binary images and grayscale volume generation requires 3D training data. Shale characterization relies on 2D imaging techniques such as scanning electron microscopy (SEM), and grayscale values carry important information about porosity, kerogen content, and mineral composition of the shale. Here, we introduce RockFlow, a method based on generative flow models that creates grayscale volumes from 2D training data. We apply RockFlow to baseline binary micro-CT image volumes and compare performance to a previously proposed model. We also show the extension of our model to 2D grayscale data by generating grayscale image volumes from 2D SEM and dual modality nanoscale shale images. The results show that our method underestimates the porosity and surface area on the binary baseline datasets but is able to generate realistic grayscale image volumes for shales. With improved binary data preprocessing, we believe that our model is capable of generating synthetic porous media volumes for a very broad class of rocks from shale to carbonates to sandstone.
58 GEOSCIENCES↗
Learning turbulent flows with generative models for super resolution and sparse flow reconstruction
Neural operators are promising surrogates for dynamical systems but when trained with standard L 2 losses they tend to oversmooth fine-scale turbulent structures. Here, we show that combining operator learning with generative modeling overcomes this limitation. We consider three practical turbulent-flow challenges where conventional neural operators fail: spatio-temporal super-resolution, forecasting, and sparse flow reconstruction. For Schlieren jet super-resolution, an adversarially trained neural operator (adv-NO) reduces the energy-spectrum error by 15 × while preserving sharp gradients at neural operator-like inference cost. For 3D homogeneous isotropic turbulence, adv-NO trained on only 160 timesteps from a single trajectory forecasts accurately for five eddy-turnover times and offers 114 × wall-clock speed-up at inference than the baseline diffusion-based forecasters, enabling near-real-time rollouts. For reconstructing cylinder wake flows from highly sparse Particle Tracking Velocimetry-like inputs, a conditional generative model infers full 3D velocity and pressure fields with correct phase alignment and statistics. These advances enable accurate reconstruction and forecasting at low compute cost, bringing near-real-time analysis and control within reach in experimental and computational fluid mechanics.
Fluid dynamics↗
A Deep Gravity model for mobility flows generation
The movements of individuals within and among cities influence critical aspects of our society, such as well-being, the spreading of epidemics, and the quality of the environment. When information about mobility flows is not available for a particular region of interest, we must rely on mathematical models to generate them. In this work, we propose Deep Gravity, an effective model to generate flow probabilities that exploits many features (e.g., land use, road network, transport, food, health facilities) extracted from voluntary geographic data, and uses deep neural networks to discover non-linear relationships between those features and mobility flows. Our experiments, conducted on mobility flows in England, Italy, and New York State, show that Deep Gravity achieves a significant increase in performance, especially in densely populated regions of interest, with respect to the classic gravity model and models that do not use deep neural networks or geographic data. Deep Gravity has good generalization capability, generating realistic flows also for geographic areas for which there is no data availability for training. Finally, we show how flows generated by Deep Gravity may be explained in terms of the geographic features and highlight crucial differences among the three considered countries interpreting the model’s prediction with explainable AI techniques.
97 MATHEMATICS AND COMPUTING↗
MENT-Flow: maximum-entropy phase space tomography using normalizing flows
Generative models can be trained to reproduce low-dimensional projections of high-dimensional phase space distributions. Normalizing flows are generative models that parameterize invertible transformations, allowing exact probability density evaluation and sampling. Consequently, flows are unbiased entropy estimators and could be used to solve the high-dimensional maximum-entropy tomography (MENT) problem. In this work, we evaluate a flow-based MENT solver (MENT-Flow) against exact maximum-entropy solutions and Minerbo's iterative MENT algorithm in two dimensions.
Hoover, Austin↗
Active learning for the design of polycrystalline textures using conditional normalizing flows
Generative modeling has opened new avenues for solving previously intractable materials design problems. However, these new opportunities are accompanied by a drastic increase in the required amount of training data. This is in stark juxtaposition to the high expense and difficulty in curating such large materials datasets. In this work, we propose a novel framework for integrating generative models within an active learning loop. Further, this enables the training of generative models with datasets significantly smaller than what has previously been demonstrated, providing a direct route for their application in data constrained environments. The functionality of this framework is then demonstrated by addressing the challenge of designing polycrystalline textures associated with target anisotropic mechanical properties. The developed protocol exhibited a cost reduction between 14 to 18 times over a randomly sampled experimental design.
36 MATERIALS SCIENCE↗
Reconstructing porous media using generative flow networks
One area of intense scientific interest for the study of sandstones, carbonates, and shale at the pore scale is the use of limited image and petrophysical data to generate multiple realizations of a rock’s pore structure. Such images aid efforts to quantify uncertainty in petrophysical properties, including porosity–permeability transforms. We develop and evaluate a deep learning-based method to synthesize porous media volumes using a so-called generative flow model trained on x-ray microscope images of rock texture and pore structure. These models are optimized on a log-likelihood objective and they synthesize large and realistic three-dimensional images. Further, we demonstrate the rapid generation of sandstone image volumes that display realism as gauged by quantitative comparison of topological features using Minkowski functionals of porosity, specific surface area, and the Euler–Poincaré characteristic (i.e., pore connectivity). We also evaluate the single-phase permeability using Navier–Stokes and lattice Boltzmann methods and show that transport properties of the generated samples match measured trends.
58 GEOSCIENCES↗
Applications of flow models to the generation of correlated lattice QCD ensembles
Machine-learned normalizing flows can be used in the context of lattice quantum field theory to generate statistically correlated ensembles of lattice gauge fields at different action parameters. This work demonstrates how these correlations can be exploited for variance reduction in the computation of observables. Three different proof-of-concept applications are demonstrated using a novel residual flow architecture: continuum limits of gauge theories, the mass dependence of QCD observables, and hadronic matrix elements based on the Feynman–Hellmann approach. In all three cases, it is shown that statistical uncertainties are significantly reduced when machine-learned flows are incorporated as compared with the same calculations performed with uncorrelated ensembles or direct reweighting. Published by the American Physical Society 2024
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Generative AI models for learning flow maps of stochastic dynamical systems in bounded domains
Simulating stochastic differential equations (SDEs) in bounded domains, presents significant computational challenges due to particle exit phenomena, which requires accurate modeling of interior stochastic dynamics and boundary interactions. Despite the success of machine learning-based methods in learning SDEs, existing learning methods are not applicable to SDEs in bounded domains because they cannot accurately capture the particle exit dynamics. We present a unified hybrid data-driven approach that combines a conditional diffusion model with an exit prediction neural network to capture both interior stochastic dynamics and boundary exit phenomena. Our ML model consists of two major components: a neural network that learns exit probabilities using binary cross-entropy loss with rigorous convergence guarantees, and a training-free diffusion model that generates state transitions for non-exiting particles using closed-form score functions. The two components are integrated through a probabilistic sampling algorithm that determines particle exit at each time step and generates appropriate state transitions. Here, the performance of the proposed approach is demonstrated via three test cases: a one-dimensional simplified problem for theoretical verification, a two-dimensional advection-diffusion problem in a bounded domain, and a three-dimensional problem of interest to magnetically confined fusion plasmas.
Bounded domains↗
Generative machine learning for detector response modeling with a conditional normalizing flow
In this paper, we explore the potential of generative machine learning models as an alternative to the computationally expensive Monte Carlo (MC) simulations commonly used by the Large Hadron Collider (LHC) experiments. Our objective is to develop a generative model capable of efficiently simulating detector responses for specific particle observables, focusing on the correlations between detector responses of different particles in the same event and accommodating asymmetric detector responses. Here, we present a conditional normalizing flow model ($\mathcal{CNF}$) based on a chain of Masked Autoregressive Flows, which effectively incorporates conditional variables and models high-dimensional density distributions. We assess the performance of the $\mathcal{CNF}$ model using a simulated sample of Higgs boson decaying to diphoton events at the LHC. We create reconstruction-level observables using a smearing technique. We show that conditional normalizing flows can accurately model complex detector responses and their correlation. This method can potentially reduce the computational burden associated with generating large numbers of simulated events while ensuring that the generated events meet the requirements for data analyses. We make our code available at https://github.com/allixu/normalizing_flow_for_detector_response
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Flow-based likelihoods for non-Gaussian inference
We investigate the use of data-driven likelihoods to bypass a key assumption made in many scientific analyses, which is that the true likelihood of the data is Gaussian. In particular, we suggest using the optimization targets of flow-based generative models, a class of models that can capture complex distributions by transforming a simple base distribution through layers of nonlinearities. We call these flow-based likelihoods (FBL). We analyze the accuracy and precision of the reconstructed likelihoods on mock Gaussian data, and show that simply gauging the quality of samples drawn from the trained model is not a sufficient indicator that the true likelihood has been learned. We nevertheless demonstrate that the likelihood can be reconstructed to a precision equal to that of sampling error due to a finite sample size. We then apply FBLs to mock weak lensing convergence power spectra, a cosmological observable that is significantly non-Gaussian (NG). We find that the FBL captures the NG signatures in the data extremely well, while other commonly used data-driven likelihoods, such as Gaussian mixture models and independent component analysis, fail to do so. This suggests that works that have found small posterior shifts in NG data with data-driven likelihoods such as these could be underestimating the impact of non-Gaussianity in parameter constraints. By introducing a suite of tests that can capture different levels of NG in the data, we show that the success or failure of traditional data-driven likelihoods can be tied back to the structure of the NG in the data. Here, unlike other methods, the flexibility of the FBL makes it successful at tackling different types of NG simultaneously. Because of this, and consequently their likely applicability across datasets and domains, we encourage their use for inference when sufficient mock data are available for training.
79 ASTRONOMY AND ASTROPHYSICS↗
Nonadiabatic Force Matching for Alchemical Free-Energy Estimation
We propose a method to compute free-energy differences from nonadiabatic alchemical transformations by using flow-based generative models. The method, nonadiabatic force matching, hinges on estimating the dissipation along an alchemical switching process in terms of a nonadiabatic force field that can be learned through stochastic flow matching. The learned field can be used in conjunction with short-time trajectory data to evaluate upper and lower bounds on the alchemical free energy that variationally converge to the exact value if the field is optimal. Applying the method to evaluate the alchemical free energy of atomistic models shows that it can substantially reduce the simulation cost of a free-energy estimate at a negligible loss of accuracy when compared with thermodynamic integration.
Computational chemistry↗
Optimizing flow condensation models for next-generation refrigerants in axial micro-fin aluminum tubes
To support the transition to next-generation refrigerants, accurate modelling of heat transfer and pressure drop is essential for designing efficient heat exchangers. Current models, largely based on traditional refrigerants and unexpanded micro-fin tubes, may not reliably predict performance for new refrigerants and expanded micro-fin geometries. This study evaluates four condensation models using experimental data for six A2L refrigerants: R-32, R-454B, R-454C, R-455A, R-1234yf, and R-1234ze(E). For heat transfer models, the Han and Lee (2005) model initially yields the best accuracy (mean absolute Deviation, MAD = 22.1%). To further improve predictions, a correction factor reduces the Cavallini et al. (2009) model’s MAD from 68.2% to 15.4%, while optimization of the Kedzierski and Goncalves (1997) model achieves a MAD of 13.1%. For pressure drop, the Cavallini et al. (1997) model proves most accurate (MAD = 6.4%), with the simpler Haraguchi et al. (1993) model also effective (MAD = 9.4%). Keywords: Flow condensation models, heat transfer coefficient, frictional pressure drop, next-generation refrigerants, aluminum micro-fin tubes
Hu, Yifeng [ORNL] (ORCID:0000000242875185)↗
Terrain-Influenced Winds and Fire-Fire Interactions in Wildland Fire Simulations [Dissertation]
Ensemble-based approaches to prescribed fire planning cannot be supported by computational fluid dynamics based models like FIRETEC and the Wildland-Urban Interface Fire Dynamics Simulator (WFDS) because they are too computationally expensive and cannot leverage large eddy simulation approaches like CAWFE and WRF-SFIRE because they have too coarse of resolution. QUIC-Fire was developed to fill this gap but it cannot currently address complex terrain, that is typical for instance in the Western United States. This dissertation describes a variety of improvements made to QUIC-Fire and its various incorporated algorithms in an effort to make it a viable tool in simulating wildland and prescribed fires on terrain. The modifications made to QUIC-Fire are described in three chapters. The first chapter describes the extension of the diagnostic wind model QUIC-URB, the wind engine of QUIC-Fire, to a terrain-following coordinate system. The terraininfluenced winds it generates are analyzed and compared. In particular, this chapter presents the mathematical derivation of the wind solver leading to a linear system of equations that are solved through the successive over-relaxation method. The model is validated against a standard test used in previous works (the Askervein Hill) and against a new dataset from measurements in the Socorro Mountains, New Mexico. The terrain-following implementation captures the correct phenomenology for the isolated Askervein Hill, with a wind speed up at the top of the hill. The model agrees well with measurements on the upwind side of the peak, but overestimates speed-up on the downwind side of the hill. This is due to the inability of the model to generate flow separation and wake-eddy dynamics. On a common laptop, the divergence-free wind field is obtained in 6 s, making the solver appealing for coupled fire-atmosphere simulations. The Socorro Mountain is highly complex, with many cliff faces, peaks, and valleys. Although the model captures the magnitude and direction of inlet and outlet areas of the domain, it performs rather poorly in the valley region and in the regions near the steep cliffs. Hence, the model shows good agreement with data in areas of open sloped terrain but lacks in areas where flow separation and thermally driven effects may be present (neither effect is addressed in this work). In the second chapter the implementation of the terrain-following version of QUIC-URB into QUIC-Fire, and the necessary changes needed to include terrain are described. No changes to the underlying fire spread algorithm are made other than what is required to correctly account for the inclusion of terrain. Previously published FIRETEC results that use five different topographies that share the same centerline profile are compared to simulation results from the modified QUIC-Fire that use the same topographies and fuels. QUIC-Fire results show overall similar behaviors in terms of how the topographies affect fire shapes and trends in spread rates. Due to the terrain-following version of QUIC-URB being unable to generate flow separations at the crest of hills, fire spread rates in these regions across all topographies are over-predicted when compared to FIRETEC. Lateral fire growth shows similar trends with FIRETEC between topographies but does not capture the increase in spread due to a diagonal interface between grassland and forested fuel region of the domain. These results suggest that there are three algorithms within QUIC-Fire that could use improvement: how flame tilt angle is accounted for, the incorporation of non-local drag effects, and the inclusion of the wake-eddy parameterizations that are used in QUIC-URB. Lastly, the third chapter describes a modification to the initial guess used for the calculation of the QUIC-URB mass-conserved wind solution during fire simulations. The modification is aimed at improving fire-fire interactions in QUIC-Fire simulations. The modification consists of using the solution from the previous timestep as the starting point for the calculation of the solution for the next timestep. Fire-fire interactions is greatly improved by the change but a new source of error is introduced. Due to how plumes are modelled in QUIC-Fire the new solution contains errors where gaps in the plume structure are present. However, these errors are mostly limited to the upper atmosphere, where they do not affect fire behavior at the surface, and their magnitude isn’t significant enough to discount the amount of new fire phenomenology now captured in QUIC-Fire with the change.
58 GEOSCIENCES↗
QUIC-URB and QUIC-fire extension to complex terrain: Development of a terrain-following coordinate system
Ensemble-based approaches to prescribed fire planning cannot be supported by CFD-based models like FIRETEC and WFDS because they are too computationally expensive and cannot leverage LES approaches like CAWFE and WRF-SFIRE because too coarse of resolution. QUIC-Fire was developed to fill this gap but it cannot currently address complex terrain, typical for instance of the Western United States. In this paper, we describe the extension of the diagnostic wind model QUIC-URB, the wind engine of QUIC-Fire, to a terrain-following coordinate system. In particular, the paper presents the mathematical derivation of the wind solver leading to a linear system of equations that are solved through the successive over-relaxation method. The model is validated against a standard test used in previous works (the Askervein Hill) and against a new dataset from measurements in the Socorro Mountains, New Mexico. The terrain-following implementation captured the correct phenomenology for the isolated Askervein Hill, with a wind speed up at the top of the hill. We report the model agreed well with measurements on the upwind side of the peak, but overestimated speed-up on the downwind side of the hill. This is due to the inability of the model to generate flow separation and wake-eddy dynamics. On a common laptop, the divergence-free wind field was obtained in 6 s, making the solver appealing for coupled fire–atmosphere simulations. The Socorro Mountain was highly complex, with many cliff faces, peaks, and valleys. Although the model captures the magnitude and direction of inlet and outlet areas of the domain, it performs rather poorly in the valley region and in the regions near the steep cliffs. Hence, the model shows good agreement with data in areas of open sloped terrain but lacks in areas where flow separation and thermally driven effects may be present (neither effect was addressed in this work). Results highlight that future work should focus on the implementation of parameterizations of wake-eddies, similar to QUIC-URB’s building parameterizations, and on thermodynamic-driven flow.
54 ENVIRONMENTAL SCIENCES↗
A Pseudoreversible Normalizing Flow for Stochastic Dynamical Systems with Various Initial Distributions
Here, we present a pseudoreversible normalizing flow method for efficiently generating samples of the state of a stochastic differential equation (SDE) with various initial distributions. The primary objective is to construct an accurate and efficient sampler that can be used as a surrogate model for computationally expensive numerical integration of SDEs, such as those employed in particle simulation. After training, the normalizing flow model can directly generate samples of the SDE’s final state without simulating trajectories. The existing normalizing flow model for SDEs depends on the initial distribution, meaning the model needs to be retrained when the initial distribution changes. The main novelty of our normalizing flow model is that it can learn the conditional distribution of the state, i.e., the distribution of the final state conditional on any initial state, such that the model only needs to be trained once and the trained model can be used to handle various initial distributions. This feature can provide a significant computational saving in studies of how the final state varies with the initial distribution. Additionally, we propose to use a pseudoreversible network architecture to define the normalizing flow model, which has sufficient expressive power and training efficiency for a variety of SDEs in science and engineering, e.g., in particle physics. We provide a rigorous convergence analysis of the pseudoreversible normalizing flow model to the target probability density function in the Kullback–Leibler divergence metric. Numerical experiments are provided to demonstrate the effectiveness of the proposed normalizing flow model.
97 MATHEMATICS AND COMPUTING↗
Memory embedded non-intrusive reduced order modeling of non-ergodic flows
Generating a digital twin of any complex system requires modeling and computational approaches that are efficient, accurate, and modular. Traditional reduced order modeling techniques are targeted at only the first two, but the novel nonintrusive approach we present in this study is an attempt at taking all three into account effectively compared to their traditional counterparts. Based on dimensionality reduction using proper orthogonal decomposition (POD), we introduce a long short-term memory neural network architecture together with a principal interval decomposition (PID) framework as an enabler to account for localized modal deformation. As an effective partitioning tool for breaking the Kolmogorov barrier, our PID framework, therefore, can be considered a key element in the accurate reduced order modeling of convective flows. Our applications for convection-dominated systems governed by Burgers, Navier-Stokes, and Boussinesq equations demonstrate that the proposed approach yields significantly more accurate predictions than the POD-Galerkin method and could be a key enabler toward near real-time predictions of unsteady flows.
42 ENGINEERING↗