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DOE OSTI2021

State predictive information bottleneck

We report the ability to make sense of the massive amounts of high-dimensional data generated from molecular dynamics simulations is heavily dependent on the knowledge of a low-dimensional manifold (parameterized by a reaction coordinate or RC) that typically distinguishes between relevant metastable states, and which captures the relevant slow dynamics of interest. Methods based on machine learning and artificial intelligence have been proposed over the years to deal with learning such low-dimensional manifolds, but they are often criticized for a disconnect from more traditional and physically interpretable approaches. To deal with such concerns, in this work we propose a deep learning based state predictive information bottleneck approach to learn the RC from high-dimensional molecular simulation trajectories. We demonstrate analytically and numerically how the RC learnt in this approach is connected to the committor in chemical physics and can be used to accurately identify transition states. A crucial hyperparameter in this approach is the time delay or how far into the future the algorithm should make predictions about. Through careful comparisons for benchmark systems, we demonstrate that this hyperparameter choice gives useful control over how coarse-grained we want the metastable state classification of the system to be. We thus believe that this work represents a step forward in systematic application of deep learning based ideas to molecular simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Deep kernel methods learn better: from cards to process optimization

Abstract The ability of deep learning methods to perform classification and regression tasks relies heavily on their capacity to uncover manifolds in high-dimensional data spaces and project them into low-dimensional representation spaces. In this study, we investigate the structure and character of the manifolds generated by classical variational autoencoder (VAE) approaches and deep kernel learning (DKL). In the former case, the structure of the latent space is determined by the properties of the input data alone, while in the latter, the latent manifold forms as a result of an active learning process that balances the data distribution and target functionalities. We show that DKL with active learning can produce a more compact and smooth latent space which is more conducive to optimization compared to previously reported methods, such as the VAE. We demonstrate this behavior using a simple cards dataset and extend it to the optimization of domain-generated trajectories in physical systems. Our findings suggest that latent manifolds constructed through active learning have a more beneficial structure for optimization problems, especially in feature-rich target-poor scenarios that are common in domain sciences, such as materials synthesis, energy storage, and molecular discovery. The Jupyter Notebooks that encapsulate the complete analysis accompany the article.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Full-field imaging learning machine (FILM)

A method of determining dynamic properties of a structure (linear or nonlinear) includes receiving spatio-temporal inputs, generating mode shapes and modal components corresponding to the spatio-temporal inputs using a trained deep complexity coding artificial neural network, and subsequently generating the dynamic properties by analyzing each modal component using a trained learning machine. A computing system for non-contact determination of dynamic properties of a structure includes a camera, a processor, and a memory including computer-executable instructions. When the instructions are executed, the system is caused to receive spatio-temporal image data, decompose the spatio-temporal image data into constituent manifold components using an autoencoder, and analyze the constituent manifold components using a trained learning machine to determine the dynamic properties.

Yang, Yongchao↗

DOE OSTI2025

cymyc: $\underline{C}$alabi-$\underline{Y}$au $\underline{M}$etrics, $\underline{Y}$ukawas, and $\underline{C}$urvature

We introduce cymyc, a high-performance Python library for numerical investigation of the geometry of a large class of string compactification manifolds and their associated moduli spaces. We develop a well-defined geometric ansatz to numerically model tensor fields of arbitrary degree on a large class of Calabi-Yau manifolds. cymyc includes a machine learning component which incorporates this ansatz to model tensor fields of interest on these spaces by finding an approximate solution to the system of partial differential equations they should satisfy.

differential and algebraic geometry↗

DOE OSTI2023

Airfoil Computational Fluid Dynamics - 2k shapes, 25 AoA's, 3 Re numbers

This dataset contains aerodynamic quantities - including flow field values (momentum, energy, and vorticity) and summary values (coefficients of lift, drag, and momentum) - for 1,830 airfoil shapes computed using the HAM2D CFD (computational fluid dynamics) model. The airfoil shapes were designed using the separable shape tensor parameterization that encodes two-dimensional shapes as elements of the Grassmann manifold. This data-driven approach learns two independent spaces of parameter from a collection of sample airfoils. The first captures large-scale, linear perturbations, and the second defines small-scale, higher-order perturbations. For this dataset, we used the G2Aero database of over 19,000 airfoil shapes to learn a parameter space that captured a wide array of shape characteristics. We sampled airfoil designs over both parameter spaces to explore the full range of possible shape variations. The aerodynamic quantities for the generated airfoil were obtained using the HAM2D code, which is a finite-volume Reynolds-averaged Navier-Stokes (RANS) flow solver. We employ a fifth-order WENO scheme for spatial reconstruction with Roe's flux difference scheme for inviscid flux and second-order central differencing for viscous flux. A preconditioned GMRES method is applied for implicit integration. The Spalart-Allmaras 1-eq turbulence model is used for the turbulence closure, and the Medida-Baeder 2-eq transition model is applied to account for the effects of laminar turbulent transition. The airfoil grid is generated with a total of 400 points on the airfoil surface, the initial wall-normal spacing of y+ = 1, and an outer boundary located at 300 chord lengths away from the wall. The CFD simulations are performed at a freestream Mach number of 0.1, for or three different Reynolds' numbers (3M, 6M, and 9M), and for 25 angles of attack from -4 deg. to 20 deg. with 1 degree increments. Across all these various parameters, this dataset includes the results from over 250,000 CFD simulations. The simulations were performed using the Bridges-2 system at the Pittsburgh Supercomputing Center in February 2023 as part of the INTEGRATE project funded by the Advanced Research Projects Agency - Energy, in the U.S. Department of Energy. The data was collected, reformatted, and preprocessed for this OEDI submission in July 2023 under the Foundational AI for Wind Energy project funded by the U.S. Department of Energy Wind Energy Technologies Office. This dataset is intended to serve as a benchmark against which new artificial intelligence (AI) or machine learning (ML) tools may be tested. Baseline AI/ML methods for analyzing this dataset have been implemented, and a link to their repository containing those models has been provided. The .h5 data file structure can be found in the GitHub Repository resource under explore_airfoil_2k_data.ipynb.

2k↗

DOE OSTI2023

Airfoil Computational Fluid Dynamics - 9k shapes, 2 AoA's

This dataset contains aerodynamic quantities - including flow field values (momentum, energy, and vorticity) and summary values (coefficients of lift, drag, and momentum) - for 8,996 airfoil shapes, computed using the HAM2D CFD (computational fluid dynamics) model. The airfoil shapes were designed using the separable shape tensor parameterization that encodes two-dimensional shapes as elements of the Grassmann manifold. This data-driven approach learns two independent spaces of parameter from a collection of sample airfoils. The first captures large-scale, linear perturbations, and the second defines small-scale, higher-order perturbations. For this data, we used the G2Aero database of over 19,000 airfoil shapes to learn a parameter space that captured a wide array of shape characteristics. We fixed the linear deformations to be the mean over the database and sampled new shapes over a four-dimensional parameter space of higher-order perturbation. This sampling approaches allows for isolated analysis of non-linear airfoil shape deformations while holding other aspects (e.g., airfoil thickness) approximately constant. The aerodynamic quantities for the generated airfoil were obtained using the HAM2D code, which is a finite-volume Reynolds-averaged Navier-Stokes (RANS) flow solver. We employ a fifth-order WENO scheme for spatial reconstruction with Roe's flux difference scheme for inviscid flux and second-order central differencing for viscous flux. A preconditioned GMRES method is applied for implicit integration. The Spalart-Allmaras 1-eq turbulence model is used for the turbulence closure, and the Medida-Baeder 2-eq transition model is applied to account for the effects of laminar turbulent transition. The airfoil grid is generated with a total of 400 points on the airfoil surface, the initial wall-normal spacing of y+ = 1, and an outer boundary located at 300 chord lengths away from the wall. The CFD simulations are performed at a freestream Mach number of 0.1, Reynolds number of 9M, and at two angles of attack, 4 deg. and 12 deg. The simulations were performed using the Bridges-2 system at the Pittsburgh Supercomputing Center in February 2023 as part of the INTEGRATE project funded by the Advanced Research Projects Agency - Energy in the U.S. Department of Energy. The data was collected, reformatted, and preprocessed for this OEDI submission in July 2023 under the Foundational AI for Wind Energy project funded by the U.S. Department of Energy Wind Energy Technologies Office. This dataset is intended to serve as a benchmark against which new artificial intelligence (AI) or machine learning (ML) tools may be tested. Baseline AI/ML methods for analyzing this dataset have been implemented, and a link to their repository containing those models has been provided. The .h5 data file structure can be found in the GitHub Repository resource under explore_airfoil_9k_data.ipynb.

9k↗

DOE OSTI2024

Boosting Barlow Twins Reduced Order Modeling for Machine Learning‐Based Surrogate Models in Multiphase Flow Problems

Abstract We present an innovative approach called boosting Barlow Twins reduced order modeling (BBT‐ROM) to enhance the reliability of machine learning surrogate models for multiphase flow problems. BBT‐ROM builds upon Barlow Twins reduced order modeling that leverages self‐supervised learning to effectively handle linear and nonlinear manifolds by constructing well‐structured latent spaces of input parameters and output quantities. To address the challenge of high contrast data in multiphase flow problems due to injection wells and faults, we employ a boosting algorithm within BBT‐ROM. This algorithm sequentially trains a set of weak models (i.e., inaccurate models), improving prediction accuracy through ensemble learning. To evaluate the performance of BBT‐ROM, we conduct three three‐dimensional multiphase flow problems, including waterflooding and geologic carbon storage (GCS), with varying numbers of input parameter cases and model domain features. The results demonstrate that BBT‐ROM excels at predicting non‐wetting phase saturation (e.g., oil or saturation) and fluid pressure, with average relative errors ranging from 0.5% to 3%. Importantly, BBT‐ROM showcases robustness when faced with limited input parameter space during GCS testing.

58 GEOSCIENCES↗

DOE OSTI2020

Machine Learning Calabi–Yau Metrics

We apply machine learning to the problem of finding numerical Calabi–Yau metrics. Building on Donaldson's algorithm for calculating balanced metrics on Kähler manifolds, we combine conventional curve fitting and machine-learning techniques to numerically approximate Ricci-flat metrics. We show that machine learning is able to predict the Calabi–Yau metric and quantities associated with it, such as its determinant, having seen only a small sample of training data. Using this in conjunction with a straightforward curve fitting routine, we demonstrate that it is possible to find highly accurate numerical metrics much more quickly than by using Donaldson's algorithm alone, with our new machine-learning algorithm decreasing the time required by between one and two orders of magnitude.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems

Constructing surrogate models for uncertainty quantification (UQ) on complex partial differential equations (PDEs) having inherently high-dimensional O(10 n ), n ≥ 2, stochastic inputs (e.g., forcing terms, boundary conditions, initial conditions) poses tremendous challenges. The “curse of dimensionality” can be addressed with suitable unsupervised learning techniques used as a pre-processing tool to encode inputs onto lower-dimensional subspaces while retaining its structural information and meaningful properties. In this work, we review and investigate thirteen dimension reduction methods including linear and nonlinear, spectral, blind source separation, convex and non-convex methods and utilize the resulting embeddings to construct a mapping to quantities of interest via polynomial chaos expansions (PCE). Here, we refer to the general proposed approach as manifold PCE (m-PCE), where manifold corresponds to the latent space resulting from any of the studied dimension reduction methods. To investigate the capabilities and limitations of these methods we conduct numerical tests for three physics-based systems (treated as black-boxes) having high-dimensional stochastic inputs of varying complexity modeled as both Gaussian and non-Gaussian random fields to investigate the effect of the intrinsic dimensionality of input data. We demonstrate both the advantages and limitations of the unsupervised learning methods and we conclude that a suitable m-PCE model provides a cost-effective approach compared to alternative algorithms proposed in the literature, including recently proposed expensive deep neural network-based surrogates and can be readily applied for high-dimensional UQ in stochastic PDEs.

42 ENGINEERING↗

DOE OSTI2024

Subcellular Feature-Based Classification of α and β Cells Using Soft X-ray Tomography

The dysfunction of α and β cells in pancreatic islets can lead to diabetes. Many questions remain on the subcellular organization of islet cells during the progression of disease. Existing three-dimensional cellular mapping approaches face challenges such as time-intensive sample sectioning and subjective cellular identification. To address these challenges, we have developed a subcellular feature-based classification approach, which allows us to identify α and β cells and quantify their subcellular structural characteristics using soft X-ray tomography (SXT). We observed significant differences in whole-cell morphological and organelle statistics between the two cell types. Additionally, we characterize subtle biophysical differences between individual insulin and glucagon vesicles by analyzing vesicle size and molecular density distributions, which were not previously possible using other methods. These sub-vesicular parameters enable us to predict cell types systematically using supervised machine learning. We also visualize distinct vesicle and cell subtypes using Uniform Manifold Approximation and Projection (UMAP) embeddings, which provides us with an innovative approach to explore structural heterogeneity in islet cells. This methodology presents an innovative approach for tracking biologically meaningful heterogeneity in cells that can be applied to any cellular system.

3D cell mapping↗

DOE OSTI2022

Geometric prior of multi-resolution yielding manifolds and the local closest point projection for nearly non-smooth plasticity

Elastoplasticity models often introduce a scalar-valued yield function to implicitly represent the boundary between elastic and plastic material states. Here this paper introduces a new alternative where the yield envelope is represented by a manifold of which the topology and the geometry are learned from a set of data points in a parametric space (e.g. principal stress space, π-plane). Here, deep geometric learning enables us to reconstruct a highly complex yield envelope by breaking it down into multiple coordinate charts. The global atlas that consists of these coordinate charts in return allows us to represent the yield surface via multiple overlapping patches, each with a specific local parametrization. This setup provides several advantages over the classical implicit function representation approach. For instance, the availability of coordinate charts enables us to introduce an alternative stress integration algorithm where the trial stress may project directly on a local patch and hence circumvent the issues related to non-smoothness and the lack of convexity of yield surfaces. Meanwhile, the local parametric approach also enables us to predict hardening/softening locally in the parametric space, even without complete knowledge of the yield surface. Comparisons between the classical yield function approach on the non-smooth plasticity and anisotropic cam-clay plasticity model are provided to demonstrate the capacity of the models for highly precise yield surface and the feasibility of the implementation of the learned model in the local stress integration algorithm.

42 ENGINEERING↗

DOE OSTI2021

Variational Autoencoders for Learning Nonlinear Dynamics of Physical Systems

We develop data-driven methods for incorporating physical information for priors to learn parsimonious representations of nonlinear systems arising from parameterized PDEs and mechanics. Our approach is based on Variational Autoencoders (VAEs) for learning nonlinear state space models from observations. We develop ways to incorporate geometric and topological priors through general manifold latent space representations. We investigate the performance of our methods for learning low dimensional representations for the nonlinear Burgers equation and constrained mechanical systems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Data-Driven Modeling and Correction of Vehicle Dynamics

We develop a data-driven framework for learning and correcting nonautonomous vehicle dynamics. Physics-based vehicle models are often simplified for tractability and therefore exhibit inherent model-form uncertainty, motivating the need for data-driven correction. Moreover, nonautonomous dynamics are governed by time-dependent control inputs, which pose challenges in learning predictive models directly from temporal snapshot data. To address these, we reformulate the vehicle dynamics via a local parameterization of the time-dependent inputs, yielding a modified system composed ofa sequence of local parametric dynamical systems. Here, we approximate these parametric systems using two complementary approaches. First, we employ the dimension reduction and interpolation in parameter space (DRIPS) methodology to construct efficient linear surrogate models, equipped with lifted observable spaces and manifold-based operator interpolation. This enables data-efficient learning of vehicle models whose dynamics admit accurate linear representations in the lifted spaces. Second, for more strongly nonlinear systems, we employ flow map learning (FML), a deep neural network (DNN) approach that approximates the parametric evolution map without requiring special treatment of nonlinearities. We further extend FML with a transfer-learning-based model correction procedure, enabling the correction of misspecified prior models using only a sparse set of high-fidelity or experimental measurements, without assuming a prescribed form for the correction term. Through a suite of numerical experiments on unicycle, simplified bicycle, and slip-based bicycle models, we demonstrate that DRIPS offers robust and highly data-efficient learning of nonautonomous vehicle dynamics, while FML provides expressive nonlinear modeling and effective correction of model-form errors under severe data scarcity.

data-driven modeling↗

DOE OSTI2025

Persistent Classification: Understanding Adversarial Attacks by Studying Decision Boundary Dynamics

ABSTRACT There are a number of hypotheses underlying the existence of adversarial examples for classification problems. These include the high‐dimensionality of the data, the high codimension in the ambient space of the data manifolds of interest, and that the structure of machine learning models may encourage classifiers to develop decision boundaries close to data points. This article proposes a new framework for studying adversarial examples that does not depend directly on the distance to the decision boundary. Similarly to the smoothed classifier literature, we define a (natural or adversarial) data point to be ( γ , σ)‐stable if the probability of the same classification is at least for points sampled in a Gaussian neighborhood of the point with a given standard deviation . We focus on studying the differences between persistence metrics along interpolants of natural and adversarial points. We show that adversarial examples have significantly lower persistence than natural examples for large neural networks in the context of the MNIST and ImageNet datasets. We connect this lack of persistence with decision boundary geometry by measuring angles of interpolants with respect to decision boundaries. Finally, we connect this approach with robustness by developing a manifold alignment gradient metric and demonstrating the increase in robustness that can be achieved when training with the addition of this metric.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Conflict Detection in Open RAN with Recurrent Neural Networks Using Geometric Manifolds

Allowing third-party applications on Radio Access Network (RAN) Intelligent Controllers (RICs) within the OpenRAN (O-RAN) framework introduces conflicting interactions that are often difficult to detect in advance. These conflicts, occurring between third-party applications in the Near RealTime RIC (Near-RT RIC), known as xApps, can lead to performance degradation and instability in O-RAN if not identified early. Existing conflict detection and mitigation solutions in the literature assume that the conflicts are known beforehand, which is not always accurate due to the complex and often hidden relationships between control parameters and Key Performance Indicators (KPIs). In this paper, we propose a novel Recurrent Neural Network (RNN) to detect both known and unknown conflicts in O-RAN xApps as specified in the O-RAN standards. We model the xApps, control parameters, and KPIs with nodes and edges to create graph structures and use the hidden nonEuclidean geometric properties of the Riemannian manifold to train the RNN model. The performance of this proposed model is validated using evaluation metrics and compared with benchmarks. Results demonstrate that the proposed RNN model, leveraging Riemannian geometric properties, can achieve 100% of the F1-score provided by an optimal solution in just 20 iterations.

5G↗

DOE OSTI2025

Conflict Detection in Open RAN with Recurrent Neural Networks Using Geometric Manifolds

5G↗

DOE OSTI2026

Local reduced-order modeling for electrostatic plasmas by physics-informed solution manifold decomposition

Despite advancements in high-performance computing and modern numerical algorithms, computational cost remains prohibitive for multi-query kinetic plasma simulations. Here, in this work, we develop data-driven reduced-order models (ROMs) for collisionless electrostatic plasma dynamics, based on the kinetic Vlasov-Poisson equation. Our ROM approach projects the equation onto a linear subspace defined by the proper orthogonal decomposition (POD) modes. We introduce an efficient tensorial method to update the nonlinear term using a precomputed third-order tensor. We capture multiscale behavior with a minimal number of POD modes by decomposing the solution manifold into multiple time windows and creating temporally local ROMs. We consider two strategies for decomposition: one based on the physical time and the other based on the electric field energy. Applied to the 1D1V Vlasov–Poisson simulations, that is, prescribed E-field, Landau damping, and two-stream instability, we demonstrate that our ROMs accurately capture the total energy of the system both for parametric and time extrapolation cases. The temporally local ROMs are more efficient and accurate than the single ROM. In addition, in the two-stream instability case, we show that the energy-windowing reduced-order model (EW-ROM) is more efficient and accurate than the time-windowing reduced-order model (TW-ROM). With the tensorial approach, EW-ROM solves the equation approximately 90 times faster than Eulerian simulations while maintaining a maximum relative error of 7.5% for the training data and 11% for the testing data.

Electrostatic plasmas↗

DOE OSTI2022

LaSDI: Parametric Latent Space Dynamics Identification

Enabling fast and accurate physical simulations with data has become an important area of computational physics to aid in inverse problems, design-optimization, uncertainty quantification, and other various decision-making applications. This paper presents a data-driven framework for parametric latent space dynamics identification procedure that enables fast and accurate simulations. The parametric model is achieved by building a set of local latent space model and designing an interaction among them. An individual local latent space dynamics model achieves accurate solution in a trust region. By letting the set of trust region to cover the whole parameter space, our model shows an increase in accuracy with an increase in training data. Herein we introduce two different types of interaction mechanisms, i.e., point-wise and region-based approach. Both linear and nonlinear data compression techniques are used. We illustrate the framework of Latent Space Dynamics Identification (LaSDI) enable a fast and accurate solution process on various partial differential equations, i.e., Burgers’ equations, radial advection problem, and nonlinear heat conduction problem, achieving 0 (100)x speed-up and 0 (1)% relative error with respect to the corresponding full order models.

97 MATHEMATICS AND COMPUTING↗