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DOE OSTI2024

Adaptive Patching for High-resolution Image Segmentation with Transformers

Attention-based models are proliferating in the space of image analytics, including segmentation. The standard method of feeding images to transformer encoders is to divide the images into patches and then feed the patches to the model as a linear sequence of tokens. For high-resolution images, e.g. microscopic pathology images, the quadratic compute and memory cost prohibits the use of an attention-based model, if we are to use smaller patch sizes that are favorable in segmentation. The solution is to either use custom complex multi-resolution models or approximate attention schemes. We take inspiration from Adapative Mesh Refinement (AMR) methods in HPC by adaptively patching the images, as a pre-processing step, based on the image details to reduce the number of patches being fed to the model, by orders of magnitude. This method has a negligible overhead, and works seamlessly with any attention-based model, i.e. it is a pre-processing step that can be adopted by any attention-based model without friction. We demonstrate superior segmentation quality over SoTA segmentation models for realworld pathology datasets while gaining a geomean speedup of 6.9× for resolutions up to 64K2, on up to 2, 048 GPUs.

Zhang, Enzhi↗

DOE OSTI2015

Multifidelity importance sampling

Estimating statistics of model outputs with the Monte Carlo method usually requires a large number of model evaluations. This leads to long runtimes if the model is expensive to evaluate. Importance sampling is one method that can lead to a reduction in the number of model evaluations. Importance sampling uses a biasing distribution to sample the model more efficiently, but generating such a biasing distribution can be difficult and usually also requires model evaluations. A different strategy to speed up Monte Carlo sampling is to replace the computationally expensive high-fidelity model with a computationally cheap surrogate model; however, because the surrogate model outputs are only approximations of the high-fidelity model outputs, the estimate obtained using a surrogate model is in general biased with respect to the estimate obtained using the high-fidelity model. We introduce a multifidelity importance sampling (MFIS) method, which combines evaluations of both the high-fidelity and a surrogate model. It uses a surrogate model to facilitate the construction of the biasing distribution, but relies on a small number of evaluations of the high-fidelity model to derive an unbiased estimate of the statistics of interest. We prove that the MFIS estimate is unbiased even in the absence of accuracy guarantees on the surrogate model itself. The MFIS method can be used with any type of surrogate model, such as projection-based reduced-order models and data-fit models. Moreover, the MFIS method is applicable to black-box models, i.e., where only inputs and the corresponding outputs of the high-fidelity and the surrogate model are available but not the details of the models themselves. We demonstrate on nonlinear and time-dependent problems that our MFIS method achieves speedups of up to several orders of magnitude compared to Monte Carlo with importance sampling that uses the high-fidelity model only.

42 ENGINEERING↗

DOE OSTI2023

Context-aware learning of hierarchies of low-fidelity models for multi-fidelity uncertainty quantification

Multi-fidelity Monte Carlo methods leverage low-fidelity and surrogate models for variance reduction to make tractable uncertainty quantification even when numerically simulating the physical systems of interest with high-fidelity models is computationally expensive. This work proposes a context-aware multi-fidelity Monte Carlo method that optimally balances the costs of training low-fidelity models with the costs of Monte Carlo sampling. It generalizes the previously developed context-aware bi-fidelity Monte Carlo method to hierarchies of multiple models and to more general types of low-fidelity models. When training low-fidelity models, the proposed approach takes into account the context in which the learned low-fidelity models will be used, namely for variance reduction in Monte Carlo estimation, which allows it to find optimal trade-offs between training and sampling to minimize upper bounds of the mean-squared errors of the estimators for given computational budgets. This is in stark contrast to traditional surrogate modeling and model reduction techniques that construct low-fidelity models with the primary goal of approximating well the high-fidelity model outputs and typically ignore the context in which the learned models will be used in upstream tasks. Further, the proposed context-aware multi-fidelity Monte Carlo method applies to hierarchies of a wide range of types of low-fidelity models such as sparse-grid and deep-network models. Numerical experiments with the gyrokinetic simulation code Gene show speedups of up to two orders of magnitude compared to standard estimators when quantifying uncertainties in small-scale fluctuations in confined plasma in fusion reactors. This corresponds to a runtime reduction from 72 days to four hours on one node of the Lonestar6 supercomputer at the Texas Advanced Computing Center.

42 ENGINEERING↗

DOE OSTI2025

A hybrid surrogate modeling framework for the Digital Twin of a Fluoride-salt-cooled High-temperature Reactor (FHR)

While nuclear energy is a non-greenhouse-gas emitting energy source, expensive operational costs due to the high-level of safety requirements decreases their competitiveness in the sustainable energy market. Advanced reactor concepts paired with Digital Twins aim to increase the commercialization gains of nuclear energy by reducing operational costs, increasing reactor reliability and enhancing power generation. To support Digital Twin tasks such as real-time autonomous control, proactive maintenance monitoring or optimizing power demand operations, a fast and accurate virtual representation of the Nuclear Power Plant (NPP) is required. The computational cost of high-fidelity, physics-based models are unsuitable for real-time analysis or scalability. Here, in this work, a hybrid surrogate modeling framework is developed fora Fluoride-salt-cooled High-temperature Reactor (FHR) that leverages physics-inspired models for key reactor components and uses data-driven methods for rapid system state space prediction. The Xenon reactivity feedback model is integrated to inform the surrogate model about the reactor core and the homologous pump theory model is the basis for representing pump degradation. Using a detailed, two dimensional thermal hydraulics model to generate data on the FHR, we train a network of Vectorized Autoregressive Moving-Average with eXogenous input (VARMAX) models to predict the remaining state values. The result is a surrogate model that provides a detailed reactor state representation of 41 system states and a pump degradation analysis. The framework is applied to Load Follows profiles, yielding high accuracy and a speedup that is more than 4000x faster compared to the higher- fidelity thermal hydraulics model, enabling real-time operational intelligence and applications in long horizon predictions. While the surrogate model framework is demonstrated for the particular case of FHR, the hybrid physical/data-driven modeling approach including the network of surrogates and the underlying modularity has the potential to be applied to other physical asset systems.

Digital Twins↗

DOE OSTI2016

Inference of reaction rate parameters based on summary statistics from experiments

Here, we present the results of an application of Bayesian inference and maximum entropy methods for the estimation of the joint probability density for the Arrhenius rate para meters of the rate coefficient of the H 2 /O 2 -mechanism chain branching reaction H + O 2 → OH + O. Available published data is in the form of summary statistics in terms of nominal values and error bars of the rate coefficient of this reaction at a number of temperature values obtained from shock-tube experiments. Our approach relies on generating data, in this case OH concentration profiles, consistent with the given summary statistics, using Approximate Bayesian Computation methods and a Markov Chain Monte Carlo procedure. The approach permits the forward propagation of parametric uncertainty through the computational model in a manner that is consistent with the published statistics. A consensus joint posterior on the parameters is obtained by pooling the posterior parameter densities given each consistent data set. To expedite this process, we construct efficient surrogates for the OH concentration using a combination of Pad'e and polynomial approximants. These surrogate models adequately represent forward model observables and their dependence on input parameters and are computationally efficient to allow their use in the Bayesian inference procedure. We also utilize Gauss-Hermite quadrature with Gaussian proposal probability density functions for moment computation resulting in orders of magnitude speedup in data likelihood evaluation. Despite the strong non-linearity in the model, the consistent data sets all res ult in nearly Gaussian conditional parameter probability density functions. The technique also accounts for nuisance parameters in the form of Arrhenius parameters of other rate coefficients with prescribed uncertainty. The resulting pooled parameter probability density function is propagated through stoichiometric hydrogen-air auto-ignition computations to illustrate the need to account for correlation among the Arrhenius rate parameters of one reaction and across rate parameters of different reactions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Weak-Form Latent Space Dynamics Identification

This software showcases the enhanced capabilities of the Latent Space Dynamics Identification (LaSDI) algorithm through the application of the weak form, resulting in WLaSDI. WLaSDI first compresses the data, then projects it onto test functions, and subsequently learns the local latent space models. Notably, WLaSDI demonstrates significantly improved robustness to noise. Using weak-form equation learning techniques, WLaSDI achieves local latent space modeling. Compared to the standard sparse identification of nonlinear dynamics (SINDy) used in LaSDI, the variance reduction of the weak form ensures robust and precise latent space recovery, enabling fast, robust, and accurate simulations. We demonstrate the efficacy of WLaSDI against LaSDI using several common benchmark examples, including viscid and inviscid Burgers', radial advection, and heat conduction. For instance, in 1D inviscid Burgers' simulations with up to 100% Gaussian white noise, WLaSDI maintains relative errors consistently below 6%, whereas LaSDI errors can exceed 10,000%. Similarly, in radial advection simulations, WLaSDI keeps relative errors below 16%, compared to potential errors of up to 10,000% with LaSDI. Additionally, WLaSDI achieves significant speedups, such as a 140X speedup in 1D Burgers' simulations compared to the corresponding full order model.

Choi, Youngsoo↗

DOE OSTI2024

Accelerating structural dynamics simulations with localised phenomena through matrix compression and projection‐based model order reduction

In this work, a novel approach is introduced for accelerating the solution of structural dynamics problems in the presence of localised phenomena, such as cracks. For this category of problems, conventional projection-based Model Order Reduction (MOR) methods are either limited with respect to the range of system configurations that can be represented or require frequent solutions of the Full Order Model (FOM) to update the low-dimensional spaces, in which solutions are represented. In the proposed approach, low-dimensional spaces, constructed for the healthy structure, are enriched with appropriately selected columns of the flexibility matrix of the system. It can be shown that these spaces contain the solution to the original problem for the static case, while their dimension is much smaller. In order to allow their online construction for arbitrary localised features, the full flexibility matrix of the system should be available. To this end, a hierarchical representation is used for the matrices involved, allowing to compute the flexibility matrix efficiently and with reduced memory requirements. The resulting method offers significant speedups, without sacrificing the flexibility and accuracy of the full order model. The performance and limitations of the approach are studied through a series of examples in structural dynamics.

fracture mechanics↗

NASA NTRS1991

High-performance multiprocessor architecture for a 3-D lattice gas model

The lattice gas method has recently emerged as a promising discrete particle simulation method in areas such as fluid dynamics. We present a very high-performance scalable multiprocessor architecture, called ALGE, proposed for the simulation of a realistic 3-D lattice gas model, Henon's 24-bit FCHC isometric model. Each of these VLSI processors is as powerful as a CRAY-2 for this application. ALGE is scalable in the sense that it achieves linear speedup for both fixed and increasing problem sizes with more processors. The core computation of a lattice gas model consists of many repetitions of two alternating phases: particle collision and propagation. Functional decomposition by symmetry group and virtual move are the respective keys to efficient implementation of collision and propagation.

Lee, F.↗

DOE OSTI2020

Koopman-Based Approach to Nonintrusive Reduced Order Modeling: Application to Aerodynamic Shape Optimization and Uncertainty Propagation

A methodology for nonintrusive projection-based nonlinear model reduction originally presented by Renganathan et al. is further extended here toward parametric systems with a focus on application to aerospace design. Specifically, the method is extended to address static systems with parametric geometry (that deforms the mesh) in addition to parametric freestream boundary conditions. The main idea is to first perform a transformation on the governing equations such that it is lifted to a higher-dimensional but linear underdetermined system. This enables one to extract the system matrices easily as compared to that of the original nonlinear system. The underdetermined system is closed with a set of model-dependent nonlinear constraints upon which the model reduction is finally performed. The methodology is validated on the subsonic and transonic inviscid flows past the NACA0012 and the RAE2822 airfoils with parametrized shapes. The utility of the approach is further demonstrated by applying it to two common problems in aerospace design, namely, derivative-free global optimization and parametric uncertainty quantification with Monte Carlo sampling. Overall, the methodology is shown to achieve accuracy up to 5% and computational speedup of two to three orders of magnitude relative to the full order model. Comparison against another nonintrusive model reduction method revealed that the proposed approach is more robust, accurate, and retains the consistency between the state variables.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Addressing quantum’s “fine print” with efficient state preparation and information extraction for quantum algorithms and geologic fracture networks

Abstract Quantum algorithms provide an exponential speedup for solving certain classes of linear systems, including those that model geologic fracture flow. However, this revolutionary gain in efficiency does not come without difficulty. Quantum algorithms require that problems satisfy not only algorithm-specific constraints, but also application-specific ones. Otherwise, the quantum advantage carefully attained through algorithmic ingenuity can be entirely negated. Previous work addressing quantum algorithms for geologic fracture flow has illustrated core algorithmic approaches while incrementally removing assumptions. This work addresses two further requirements for solving geologic fracture flow systems with quantum algorithms: efficient system state preparation and efficient information extraction. Our approach to addressing each is consistent with an overall exponential speed-up.

58 GEOSCIENCES↗

DOE OSTI2023

hIPPYlib-MUQ: A Bayesian Inference Software Framework for Integration of Data with Complex Predictive Models under Uncertainty

Bayesian inference provides a systematic framework for integration of data with mathematical models to quantify the uncertainty in the solution of the inverse problem. However, the solution of Bayesian inverse problems governed by complex forward models described by partial differential equations (PDEs) remains prohibitive with black-box Markov chain Monte Carlo (MCMC) methods. We present hIPPYlib-MUQ, an extensible and scalable software framework that contains implementations of state-of-the art algorithms aimed to overcome the challenges of high-dimensional, PDE-constrained Bayesian inverse problems. These algorithms accelerate MCMC sampling by exploiting the geometry and intrinsic low-dimensionality of parameter space via derivative information and low rank approximation. The software integrates two complementary open-source software packages, hIPPYlib and MUQ. hIPPYlib solves PDE-constrained inverse problems using automatically-generated adjoint-based derivatives, but it lacks full Bayesian capabilities. MUQ provides a spectrum of powerful Bayesian inversion models and algorithms, but expects forward models to come equipped with gradients and Hessians to permit large-scale solution. By combining these two complementary libraries, we created a robust, scalable, and efficient software framework that realizes the benefits of each and allows us to tackle complex large-scale Bayesian inverse problems across a broad spectrum of scientific and engineering disciplines. To illustrate the capabilities of hIPPYlib-MUQ, we present a comparison of a number of MCMC methods available in the integrated software on several high-dimensional Bayesian inverse problems. These include problems characterized by both linear and nonlinear PDEs, various noise models, and different parameter dimensions. The results demonstrate that large (~ 50×) speedups over conventional black box and gradient-based MCMC algorithms can be obtained by exploiting Hessian information (from the log-posterior), underscoring the power of the integrated hIPPYlib-MUQ framework.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1987

Time-partitioning simulation models for calculation on parallel computers

A technique allowing time-staggered solution of partial differential equations is presented in this report. Using this technique, called time-partitioning, simulation execution speedup is proportional to the number of processors used because all processors operate simultaneously, with each updating of the solution grid at a different time point. The technique is limited by neither the number of processors available nor by the dimension of the solution grid. Time-partitioning was used to obtain the flow pattern through a cascade of airfoils, modeled by the Euler partial differential equations. An execution speedup factor of 1.77 was achieved using a two processor Cray X-MP/24 computer.

Milner, Edward J.↗

NASA NTRS1987

Time-partitioning simulation models for calculation of parallel computers

Milner, Edward J.↗

DOE OSTI2020

LA17-V-InverseRadTransportProblem-PD2Kb. Final Project Report

In the inverse radiation transport problem, a radiation signal emanating from an unknown object is used to reconstruct geometric and material parameters of the object , e.g., the mass of special nuclear material (SNM), the isotopic composition of the SNM (e.g., the enrichment of 235U), the thickness of shielding, etc. The inverse radiation transport problem is one of the most fundamental and important in the emergency response mission, and has been addressed in previous NA-22 and NA-42/84 investments by using derivative-free optimization methods. Our project was aimed at (i) consolidating previous work by applying polynomial chaos expansion (PCE) for reducing significantly the number of forward model simulations required by derivative-free optimization methods; (ii) developing a general-purpose framework and stand-alone software for solving the inverse radiation transport problem by applying a new “predictive modeling” methodology (predictive modeling of coupled multi-physics systems, PM_CMPS) which enables the fusing of experimental and computational information; and (iii) developing several benchmarks (for unscattered gamma rays) for demonstrating the quantification of non-Gaussian features (e.g., skewness and kurtosis, which characterize asymmetries and long tails) of response distributions by deterministically and efficiently propagating parameter uncertainties (covariances and higher-order moments, where available) using high-order sensitivities computed by the recently developed comprehensive adjoint sensitivity analysis methodology (C-ASAM). With regard to (i), application of PCE, the most significant accomplishment of this project was an implementation of PCE into INVERSE that significantly reduced computation time for the DiffeRential Evolution Adaptive Metropolis (DREAM) and Differential Evolution (DE) methods. For inverse transport problems with measurements of neutron leakage, neutron multiplication, and neutron-induced gamma-rays, the solution times for the DREAM and DE methods were reduced by factors of 30-300, reducing run times from hours to minutes while maintaining the same accuracy as the standard (non-PCE) DREAM and DE. Speedups were further improved by exploring sparse grid quadrature sets using the Toolkit for Adaptive Stochastic Modeling and Non-Intrusive ApproximatioN (Tasmanian) toolset. An initial exploration of sparse grids indicated that further speedups factors of 5-10 are obtainable. The implementation of PCE in INVERSE is not in a form that users can easily access. With regard to (ii), solving the inverse problem using a predictive modeling paradigm, the most significant accomplishment of this project were the derivation and implementation of adjoint-based second derivatives in neutron and photon transport theory. There are two codes that compute these derivatives. SENSPG computes them for uncollided gamma rays and SENSMG computes them for neutron leakage. SENSMG is open-source code available on github. Other significant accomplishments included a stand-alone code, MULTI-PRED, that implements the predictive modeling paradigm, along with a detailed manual. The code was implemented in the existing INVERSE code for inverse problems, but a head-to-head comparison of inverse methods was not achieved. We also derived and implemented the capability to compute sensitivities for multiplicity measurements into the SENSMG code, and this capability was used in a data assimilation application, but it was not used for solving inverse problems. With regard to (iii), developing benchmarks to demonstrate the importance of high-order sensitivity and uncertainty analysis, the most significant accomplishment of this project were two test problems that showed how important second-order sensitivities are.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2025

Development of a River Dynamical Core for E3SM to simulate compound flooding on Exascale-class heterogeneous supercomputers

Flooding events pose significant risk to human life, property, and infrastructure. Physically-consistent quantification of altered flood risks in global models requires hyper-resolution (~1 km) or fine flood simulations using two-dimensional (2D) physics schemes, both of which are unavailable in the current generation Earth System Models. Here, in this work, we have developed the River Dynamical Core (RDycore), which is an open-source, 2D shallow water equation (SWE) library for the U.S. Department of Energy's Energy Exascale Earth System Model (E3SM). RDycore uses PETSc and libCEED libraries that allows it to run efficiently on CPUs and GPUs, as well as select a time-integration algorithm at runtime without requiring any code modifications. RDycore achieves spatial error convergence rates for problems with analytical and manufactured solutions similar to those reported previously in the literature, or consistent with the implemented first-order spatial discretization scheme. RDycore's accuracy in predicting flooding for a well-studied dam break problem is comparable to existing SWE models. For a problem with 471 million grid cells, RDycore achieves a speedup of 6.6x and 7.6x on GPUs compared to CPUs when using 320 compute nodes on DOE's Perlmutter and Frontier supercomputers, respectively. The one-way coupling of the RDycore library within E3SM is demonstrated by performing multiple 5-day flooding simulations during Hurricane Harvey driven by five precipitation datasets. The E3SM--RDycore simulations at 30 m spatial resolution accurately simulate maximum water height during the hurricane when benchmarked against a previously published study and achieve a speedup of 15x (Perlmutter) and 21x (Frontier) on GPUs relative to CPUs. The work presented here is the foundational step in providing hardware and algorithmic portability framework for simulating kilometer-scale river dynamics within E3SM.

Flood Simulation↗

DOE OSTI2024

Two-Step Hyperparameter Optimization Method: Accelerating Hyperparameter Search by Using a Fraction of a Training Dataset

Abstract Hyperparameter optimization (HPO) is an important step in machine learning (ML) model development, but common practices are archaic—primarily relying on manual or grid searches. This is partly because adopting advanced HPO algorithms introduces added complexity to the workflow, leading to longer computation times. This poses a notable challenge to ML applications, as suboptimal hyperparameter selections curtail the potential of ML model performance, ultimately obstructing the full exploitation of ML techniques. In this article, we present a two-step HPO method as a strategic solution to curbing computational demands and wait times, gleaned from practical experiences in applied ML parameterization work. The initial phase involves a preliminary evaluation of hyperparameters on a small subset of the training dataset, followed by a reevaluation of the top-performing candidate models postretraining with the entire training dataset. This two-step HPO method is universally applicable across HPO search algorithms, and we argue it has attractive efficiency gains. As a case study, we present our recent application of the two-step HPO method to the development of neural network emulators for aerosol activation. Although our primary use case is a data-rich limit with many millions of samples, we also find that using up to 0.0025% of the data—a few thousand samples—in the initial step is sufficient to find optimal hyperparameter configurations from much more extensive sampling, achieving up to 135× speedup. The benefits of this method materialize through an assessment of hyperparameters and model performance, revealing the minimal model complexity required to achieve the best performance. The assortment of top-performing models harvested from the HPO process allows us to choose a high-performing model with a low inference cost for efficient use in global climate models (GCMs).

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Non-intrusive reduced-order modeling for dynamical systems with spatially localized features

This work presents a non-intrusive reduced-order modeling framework for dynamical systems with spatially localized features characterized by slow singular value decay. The proposed approach builds upon two existing methodologies for reduced and full-order non-intrusive modeling, namely Operator Inference (OpInf) and sparse Full-Order Model (sFOM) inference. We decompose the domain into two complementary subdomains that exhibit fast and slow singular value decay. The dynamics of the subdomain exhibiting slow singular value decay are learned with sFOM while the dynamics with intrinsically low dimensionality on the complementary subdomain are learned with OpInf. The resulting, coupled OpInf-sFOM formulation leverages the computational efficiency of OpInf and the high resolution of sFOM, and thus enables fast non-intrusive predictions for conditions beyond those sampled in the training data set. A novel regularization technique with a closed-form solution based on the Gershgorin disk theorem is introduced to promote stable sFOM and OpInf models. We also provide a data-driven indicator for subdomain selection and ensure solution smoothness over the interface via a post-processing interpolation step. We evaluate the efficiency of the approach in terms of offline and online speedup through a quantitative, parametric computational cost analysis. We demonstrate the coupled OpInf-sFOM formulation for two test cases: a one-dimensional Burgers’ model for which accurate predictions beyond the span of the training snapshots are presented, and a two-dimensional parametric model for the Pine Island Glacier ice thickness dynamics, for which the OpInf-sFOM model achieves an average prediction error on the order of 1% with an online speedup factor of approximately 8$\times$ compared to the numerical simulation.

42 ENGINEERING↗

DOE OSTI2020

A GPU-based 2D shallow water quality model

In this paper, a 2D shallow water flow solver integrated with a water quality model is presented. The interaction between the main water quality constituents included is based on the Water Quality Analysis Simulation Program. Efficiency is achieved by computing with a combination of a Central Processing Unit (CPU) and a Graphics Processing Unit (GPU) device. This technique is intended to provide robust and accurate simulations with high computation speedups with respect to a single-core CPU in real events. The proposed numerical model is evaluated in cases that include the transport and reaction of water quality components over irregular bed topography and dry–wet fronts, verifying that the numerical solution in these situations conserves the required properties (C-property and positivity). The model can operate in any steady or unsteady form allowing an efficient assessment of the environmental impact of water flows. The field data from an unsteady river reach test case are used to show that the model is capable of predicting the measured temporal distribution of dissolved oxygen and water temperature, proving the robustness and computational efficiency of the model, even in the presence of noisy signals such as wind speed.

54 ENVIRONMENTAL SCIENCES↗