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DOE OSTI2024

A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling

Numerical solvers of partial differential equations (PDEs) have been widely employed for simulating physical systems. However, the computational cost remains a major bottleneck in various scientific and engineering applications, which has motivated the development of reduced-order models (ROMs). Recently, machine-learning-based ROMs have gained significant popularity and are promising for addressing some limitations of traditional ROM methods, especially for advection dominated systems. In this chapter, we focus on a particular framework known as Latent Space Dynamics Identification (LaSDI), which transforms the high-fidelity data, governed by a PDE, to simpler and low-dimensional latent-space data, governed by ordinary differential equations (ODEs). These ODEs can be learned and subsequently interpolated to make ROM predictions. Each building block of LaSDI can be easily modulated depending on the application, which makes the LaSDI framework highly flexible. In particular, we present strategies to enforce the laws of thermodynamics into LaSDI models (tLaSDI), enhance robustness in the presence of noise through the weak form (WLaSDI), select high-fidelity training data efficiently through active learning (gLaSDI, GPLaSDI), and quantify the ROM prediction uncertainty through Gaussian processes (GPLaSDI). We demonstrate the performance of different LaSDI approaches on Burgers equation, a non-linear heat conduction problem, and a plasma physics problem, showing that LaSDI algorithms can achieve relative errors of less than a few percent and up to thousands of times speed-ups.

Computational Engineering, Finance, and Science (c↗

DOE OSTI2026

Integrated Transmission-Distribution Multi-Period Switching for Wildfire Risk Mitigation: Improving Speed and Scalability with Distributed Optimization: Preprint

With increasingly severe wildfire conditions driven by climate change, utilities must manage the risk of wildfire ignitions from electric power lines. During "public safety power shutoff'" events, utilities de-energize power lines to reduce wildfire ignition risk, which may result in load shedding. Distributed energy resources provide flexibility that can help support the system to reduce load shedding when lines are de-energized. We investigate a coordinated transmission-distribution optimization problem that balances wildfire risk mitigation and load shedding. We model distribution systems that include battery energy storage systems which may support loads when transmission lines are de-energized. This multi-period integrated transmission-distribution optimal switching problem jointly optimizes line switching decisions, the generators' setpoints, load shedding, and the batteries' states of charge, resulting in significant computational challenges. To improve scalability, we decompose the problem over both space and time and apply a distributed optimization algorithm. Using a large-scale synthetic California test case with realistic distribution models and real wildfire risk data, we show that distributed optimization can solve large-scale multi-period switching problems that are otherwise intractable for centralized solvers. We also discuss challenges and future directions for improving the distributed algorithm's convergence performance as the number of time periods increases.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2020

DESC: A stellarator equilibrium solver

In this paper, the new code DESC is presented to solve for fixed-boundary ideal magnetohydrodynamic equilibria in stellarators. The approach directly solves the equilibrium force balance as a system of nonlinear equations in the form f(x) = 0. The independent variables x represent nested magnetic flux surfaces expressed in the inverse representation with toroidal flux coordinates, and the equations f(x) quantify equilibrium force balance errors at discrete points in real space. Discretizing with global Fourier–Zernike basis functions properly treats the magnetic axis and minimizes the number of coefficients needed to describe the flux surfaces. The pseudospectral method provides great flexibility in where the errors are evaluated, and the system of equations is efficiently solved with a Newton–Raphson iteration. Equilibria are computed and compared against VMEC for both axisymmetric and non-axisymmetric examples. The results show fast convergence rates and solutions with low errors throughout the plasma volume.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Regional surrogates for predictive control of digital twins

Digital twins of complex systems must involve a model that is fast, generalizable, and usable for real-time control. For example, high-fidelity nonlinear multiphysics simulations can capture laser-material interactions, but are too slow for optimization or model predictive control (MPC). Reduced-order models, used to accelerate such computation, frequently fail to generalize to unseen inputs or control states. We show theoretically that this failure is intrinsic, i.e., that a learned model is non-unique outside the sampled subspace when its low-rank structure arises from limited excitation and clustered eigenvalues, rather than from a user-imposed truncation alone. Motivated by this result, we propose a control-ready regional surrogate-construction framework for both autonomous and nonautonomous dynamics; it employs Koopman lifting to represent nonlinearities, while preserving spatial locality. We illustrate our approach by constructing a control-ready surrogate for the digital twin of a thermal component of additive-manufacturing process. Our surrogate, localized in space through a von Neumann stencil, is learned from noisy high-fidelity simulations that emulate thermal-camera images collected during the manufacturing. It is linear in thermo-physically augmented states so that MPC reduces to a convex quadratic program. The surrogate requires no online correction, generalizes to unseen scan paths and power profiles of the laser, and is more than three orders of magnitude faster than a finite-difference solver. Furthermore, when the MPC sequence computed on the digital twin is applied to this solver, closed-loop temperature regulation is recovered, showing that the surrogate preserves control-relevant input-output behavior.

Data-driven model↗

DOE OSTI2025

Computational Algorithms for Unit Commitment with AC Power Flows (Final Report)

Security-constrained unit commitment (SCUC) is a key component in power system operations. When AC power flow constraints are considered in the SCUC model (AC-SCUC), the problem becomes extremely difficult due to its discrete and non-convex nature, as described in “Grid Optimization Competition Challenge 3 Problem Formulation (GOCC)”. There are four main challenges: (i) Discrete decisions regarding unit online/offline status and start-up/shut-down procedures for every single unit. The number of discrete decision variables increases considerably when a system integrates multiple generators; (ii) Configuration-based combined-cycle formulations, and multi-commodity models that include ramping products, spin/non-spin products, and regulation up/down products. The combined-cycle units introduce additional discrete decision variables and auxiliary service products further complicate the model by connecting multi-commodity products’ continuous and discrete variables; (iii) SCUC models with AC power flow constraints are far more complex due to massive bilinear terms in the large-scale nonlinear power balance equations. The nonlinear power balance equations are further complicated by the discrete step control variables of shunts; (iv) N − 1 contingency analysis. The size of the model increases linearly with the number of contingencies considered, greatly increasing the size of the optimization model. Accordingly, there is an emergent need to develop a robust algorithm capable of deriving a high-quality solution in a short time and passing through contingency tests simultaneously. In this project, we explore innovative techniques to address this challenging problem by integrating advanced polyhedral theory, approximation methods, relaxation strategies, decomposition techniques, and parallel computing. Each technique approaches the problem from a different perspective, leveraging its specific strengths to tackle distinct challenges. Each individual method has demonstrated its effectiveness in the PI’s previous research. Their integration is expected to significantly reduce the computational time required to solve the proposed complex problem. Successful completion of this project has the potential to transform the industry by enhancing optimization solvers capable of handling large-scale day-ahead energy market clearing models within strict time constraints, while incorporating AC power flow constraints. This advancement will lead to reduced overall generation costs and, consequently, increased social welfare.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2024

ReEDS Performance Improvement

The Regional Energy Deployment System (ReEDS) is an open-source, spatially explicit, long-term capacity expansion model for the bulk electric power system of the contiguous United States, encompassing multiple scenarios with technological and political assumptions (see https://github.com/NREL/ReEDS-2.0). With the increased needs for capabilities, higher temporal and spatial resolutions to model the evolution of the power system with modern technologies and low-carbon pathways, ReEDS' model solution times have increased significantly from 4-6 hours in 2018 to 18-48+ hours in 2023 . Also, the model size for commonly-run ReEDS scenarios reached 22 and 28 million equations and variables, respectively. These runtimes can be especially challenging under certain scenario settings (e.g., very high temporal or spatial resolution) or with limited computational power. In this presentation, we will discuss several methods we used to improve model runtime, including data preparation, model modification, and solver tuning. The implementation of these methods shrank the model size to 7.2 and 7.3 million equations and variables, respectively. Furthermore, this led to a 77% reduction in the model's run time for commonly-run ReEDS scenarios. We will discuss the process of identifying areas for solve time improvements and how the specific enhancements for the ReEDS model might be applied to other similar large-scale models.

ENERGY PLANNING, POLICY, AND ECONOMY,MATHEMATICS A↗

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 OSTI2022

SNICAR-ADv4: a physically based radiative transfer model to represent the spectral albedo of glacier ice

Abstract. Accurate modeling of cryospheric surface albedo is essential for our understanding of climate change as snow and ice surfaces regulate the global radiative budget and sea-level through their albedo and mass balance. Although significant progress has been made using physical principles to represent the dynamic albedo of snow, models of glacier ice albedo tend to be heavily parameterized and not explicitly connected with physical properties that govern albedo, such as the number and size of air bubbles, specific surface area (SSA), presence of abiotic and biotic light absorbing constituents (LACs), and characteristics of any overlying snow. Here, we introduce SNICAR-ADv4, an extension of the multi-layer two-stream delta-Eddington radiative transfer model with the adding–doubling solver that has been previously applied to represent snow and sea-ice spectral albedo. SNICAR-ADv4 treats spectrally resolved Fresnel reflectance and transmittance between overlying snow and higher-density glacier ice, scattering by air bubbles of varying sizes, and numerous types of LACs. SNICAR-ADv4 simulates a wide range of clean snow and ice broadband albedo (BBA), ranging from 0.88 for (30 µm) fine-grain snow to 0.03 for bare and bubble-free ice under direct light. Our results indicate that representing ice with a density of 650 kg m−3 as snow with no refractive Fresnel layer, as done previously, generally overestimates the BBA by an average of 0.058. However, because most naturally occurring ice surfaces are roughened “white ice”, we recommend modeling a thin snow layer over bare ice simulations. We find optimal agreement with measurements by representing cryospheric media with densities less than 650 kg m−3 as snow and larger-density media as bubbly ice with a Fresnel layer. SNICAR-ADv4 also simulates the non-linear albedo impacts from LACs with changing ice SSA, with peak impact per unit mass of LACs near SSAs of 0.1–0.01 m2 kg−1. For bare, bubble-free ice, LACs actually increase the albedo. SNICAR-ADv4 represents smooth transitions between snow, firn, and ice surfaces and accurately reproduces measured spectral albedos of a variety of glacier surfaces. This work paves the way for adapting SNICAR-ADv4 to be used in land ice model components of Earth system models.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

GPU-acceleration of the ELPA2 distributed eigensolver for dense symmetric and hermitian eigenproblems

The solution of eigenproblems is often a key computational bottleneck that limits the tractable system size of numerical algorithms, among them electronic structure theory in chemistry and in condensed matter physics. Large eigenproblems can easily exceed the capacity of a single compute node, thus must be solved on distributed-memory parallel computers. We here present GPU-oriented optimizations of the ELPA two-stage tridiagonalization eigensolver (ELPA2). On top of cuBLAS-based GPU offloading, we add a CUDA kernel to speed up the back-transformation of eigenvectors, which can be the computationally most expensive part of the two-stage tridiagonalization algorithm. Furthermore, we benchmark the performance of this GPU-accelerated eigensolver on two hybrid CPU–GPU architectures, namely a compute cluster based on Intel Xeon Gold CPUs and NVIDIA Volta GPUs, and the Summit supercomputer based on IBM POWER9 CPUs and NVIDIA Volta GPUs. Consistent with previous benchmarks on CPU-only architectures, the GPU-accelerated two-stage solver exhibits a parallel performance superior to the one-stage counterpart. Finally, we demonstrate the performance of the GPU-accelerated eigensolver developed in this work for routine semi-local KS-DFT calculations comprising thousands of atoms.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

An Algebraic Sparsified Nested Dissection Algorithm Using Low-Rank Approximations

Here, we propose a new algorithm for the fast solution of large, sparse, symmetric positive-definite linear systems, spaND (sparsified Nested Dissection). It is based on nested dissection, sparsification, and low-rank compression. After eliminating all interiors at a given level of the elimination tree, the algorithm sparsifies all separators corresponding to the interiors. This operation reduces the size of the separators by eliminating some degrees of freedom but without introducing any fill-in. This is done at the expense of a small and controllable approximation error. The result is an approximate factorization that can be used as an efficient preconditioner. We then perform several numerical experiments to evaluate this algorithm. We demonstrate that a version using orthogonal factorization and block-diagonal scaling takes fewer CG iterations to converge than previous similar algorithms on various kinds of problems. Furthermore, this algorithm is provably guaranteed to never break down and the matrix stays symmetric positive-definite throughout the process. We evaluate the algorithm on some large problems show it exhibits near-linear scaling. The factorization time is roughly $\mathcal{O}$(N), and the number of iterations grows slowly with N.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

INTEGRATE - Inverse Network Transformations for Efficient Generation of Robust Airfoil and Turbine Enhancements

The INTEGRATE (Inverse Network Transformations for Efficient Generation of Robust Airfoil and Turbine Enhancements) project is developing a new inverse-design capability for the aerodynamic design of wind turbine rotors using invertible neural networks. This AI-based design technology can capture complex non-linear aerodynamic effects while being 100 times faster than design approaches based on computational fluid dynamics. This project enables innovation in wind turbine design by accelerating time to market through higher-accuracy early design iterations to reduce the levelized cost of energy. INVERTIBLE NEURAL NETWORKS Researchers are leveraging a specialized invertible neural network (INN) architecture along with the novel dimension-reduction methods and airfoil/blade shape representations developed by collaborators at the National Institute of Standards and Technology (NIST) learns complex relationships between airfoil or blade shapes and their associated aerodynamic and structural properties. This INN architecture will accelerate designs by providing a cost-effective alternative to current industrial aerodynamic design processes, including: - Blade element momentum (BEM) theory models: limited effectiveness for design of offshore rotors with large, flexible blades where nonlinear aerodynamic effects dominate - Direct design using computational fluid dynamics (CFD): cost-prohibitive - Inverse-design models based on deep neural networks (DNNs): attractive alternative to CFD for 2D design problems, but quickly overwhelmed by the increased number of design variables in 3D problems AUTOMATED COMPUTATIONAL FLUID DYNAMICS FOR TRAINING DATA GENERATION - MERCURY FRAMEWORK The INN is trained on data obtained using the University of Marylands (UMD) Mercury Framework, which has with robust automated mesh generation capabilities and advanced turbulence and transition models validated for wind energy applications. Mercury is a multi-mesh paradigm, heterogeneous CPU-GPU framework. The framework incorporates three flow solvers at UMD, 1) OverTURNS, a structured solver on CPUs, 2) HAMSTR, a line based unstructured solver on CPUs, and 3) GARFIELD, a structured solver on GPUs. The framework is based on Python, that is often used to wrap C or Fortran codes for interoperability with other solvers. Communication between multiple solvers is accomplished with a Topology Independent Overset Grid Assembler (TIOGA). NOVEL AIRFOIL SHAPE REPRESENTATIONS USING GRASSMAN SPACES We developed a novel representation of shapes which decouples affine-style deformations from a rich set of data-driven deformations over a submanifold of the Grassmannian. The Grassmannian representation as an analytic generative model, informed by a database of physically relevant airfoils, offers (i) a rich set of novel 2D airfoil deformations not previously captured in the data , (ii) improved low-dimensional parameter domain for inferential statistics informing design/manufacturing, and (iii) consistent 3D blade representation and perturbation over a sequence of nominal shapes. TECHNOLOGY TRANSFER DEMONSTRATION - COUPLING WITH NREL WISDEM Researchers have integrated the inverse-design tool for 2D airfoils (INN-Airfoil) into WISDEM (Wind Plant Integrated Systems Design and Engineering Model), a multidisciplinary design and optimization framework for assessing the cost of energy, as part of tech-transfer demonstration. The integration of INN-Airfoil into WISDEM allows for the design of airfoils along with the blades that meet the dynamic design constraints on cost of energy, annual energy production, and the capital costs. Through preliminary studies, researchers have shown that the coupled INN-Airfoil + WISDEM approach reduces the cost of energy by around 1% compared to the conventional design approach. This page will serve as a place to easily access all the publications from this work and the repositories for the software developed and released through this pr...

aerodynamics↗

DOE OSTI2023

COMPUTATIONAL MODELING OF IGNITION AND PREMIXED FLAME PROPAGATION INITIATED BY A PRE-CHAMBER TURBULENT JET

Addressing the pressing need for reduced carbon emissions, Turbulent Jet Ignition (TJI) emerges as a promising technology for ultra-lean combustion, offering enhanced thermal efficiencies and minimized cyclic variability in spark-ignited engines. To facilitate rapid testing and integration of this technology, a robust computational modeling framework is crucial. This study delves into the predictive capabilities of computational models for main-chamber ignition and premixed flame propagation using a single-cycle TJI rig measured by Biswas et al. (Applied Thermal Engineering, vol 106, 2016). Employing an open-source compressible flow simulation solver with Large Eddy Simulation (LES) for turbulence modeling, the investigation integrates the conventional Laminar Finite Rate Chemistry (LFRC) model alongside the transported Probability Density Method (PDF) for turbulence-chemistry interaction. A fully-consistent Eulerian Monte-Carlo Fields (EMCF) method is utilized to approximate the transported PDF, while Interaction by Exchange with Mean is employed to close micro-mixing terms in stochastic differential equations. A reduced chemical reaction mechanism with 21 species and 84 reactions (DRM-19) is used for solving chemical kinetics, and a double Gaussian energy deposition model is used to approximate the spark ignition in the pre-chamber. An unstructured O-grid mesh with 0.3 million cells in the prechamber and 1 million cells in the main chamber is employed. Results are divided into two phases: pre-chamber initialization and full TJI simulations. Validation of the predicted pre-chamber flame propagation and the lean ignition in the main-chamber is carried out by using available experimental data. Under quiescent conditions, both the LFRC and transported PDF methods largely underestimate the flame speed and subsequent pressure growth in the pre-chamber. A linear momentum forcing technique is applied to investigate the impact of initial turbulence in the pre-chamber, demonstrating a notable influence on flame propagation. Fine-tuning of the forcing coefficient reproduces the sudden pressure growth observed in the experiment. The experimentally validated pre-chamber simulation serves as the initial condition for the full TJI simulations. It is found that the LFRC model fails to predict lean-ignition in the main-chamber, resulting in a misfiring event. Incorporation of turbulence-chemistry interaction using the transported PDF method substantially improves the prediction of the ignition event in the main-chamber, achieving fair qualitative agreement and quantitative validation of combustion parameters within ±10% of the reported experimental data. The rich simulation results consisting of a full set of statistical description of the thermo-chemical states enable us to gain deep insights into the ignition mechanisms in the main chamber, which is limited when done experimentally. A novel dual ignition phenomenon is revealed in the TJI rig for the first time. Initially, a primary ignition kernel is formed at a downstream location which eventually detaches from the main jet. As the jet momentum decreases, a secondary ignition event follows, this time at a more upstream location which eventually combines with the primary ignition kernel to form a single connected flame front. Investigation of these ignition sequences in chemical composition space reveal distinct differences between the two. The primary ignition event in the main-chamber is followed by a large concentration of active radicals from the pre-chamber jet, accelerating the chain-branching steps, characterizing what has been referred to as flame ignition. In contrast, the secondary ignition occurs in the absence of active radicals in the pre-chamber jet, hence characterized as jet ignition. Further analysis of the effect of pre-chamber jet characteristics on lean ignition in the main-chamber is conducted by setting up cases with different initial pressure ratios (por) between the two chambers, a non-dimensional parameter, ranging from 1.2 to 3.2. As the initial pressure ratio increases, jet momentum increases, with dual ignition observed in cases above por= 2.2. Case with por= 3.2 lead to misfiring. The effect of ignition sequence on global combustion characteristics of TJI is analyzed. Dual ignition events lead to non-monotonicity in combustion characteristics such as global reaction progress variable, flame penetration, and global heat release rate. In dual ignition events, although the rate of fuel consumption and global heat release rate is initially lower, the secondary ignition leads to a sudden increase in flame surface area, resulting in a sudden jump and promoting the overall performance of the TJI system.

42 ENGINEERING↗