Final Report, 2024 DOE SBIR, Phase I, Release I: Leveraging Compadre and MFEM in Geometrically Versatile Numerical Methods
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97 MATHEMATICS AND COMPUTING↗
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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Quantifying local and global mass balance errors in physics-informed neural networks
Physics-informed neural networks (PINN) have recently become attractive for solving partial differential equations (PDEs) that describe physics laws. By including PDE-based loss functions, physics laws such as mass balance are enforced softly in PINN. This paper investigates how mass balance constraints are satisfied when PINN is used to solve the resulting PDEs. We investigate PINN’s ability to solve the 1D saturated groundwater flow equations (diffusion equations) for homogeneous and heterogeneous media and evaluate the local and global mass balance errors. We compare the obtained PINN’s solution and associated mass balance errors against a two-point finite volume numerical method and the corresponding analytical solution. We also evaluate the accuracy of PINN in solving the 1D saturated groundwater flow equation with and without incorporating hydraulic heads as training data. We demonstrate that PINN’s local and global mass balance errors are significant compared to the finite volume approach. Tuning the PINN’s hyperparameters, such as the number of collocation points, training data, hidden layers, nodes, epochs, and learning rate, did not improve the solution accuracy or the mass balance errors compared to the finite volume solution. Mass balance errors could considerably challenge the utility of PINN in applications where ensuring compliance with physical and mathematical properties is crucial.
54 ENVIRONMENTAL SCIENCES↗
Basin-Size Mapping: Prediction of Metastable Polymorph Synthesizability Across TaC–TaN Alloys
The sizes of the basins of attraction on the potential energy surface are helpful indicators in determining the experimental synthesizability of metastable phases. In principle, these basins can be controlled with changes in thermodynamic conditions such as composition, pressure, and surface energy. Herein, we use random structure sampling to computationally study how alloying smoothly perturbs basin of attraction sizes. The TaC 1-x N x pseudobinary is an ideal test system given the structural and polymorphic contrast of its parent compounds and their technological relevance as epitaxial substrates for Al 1-x Ga x N. While we find limited thermodynamic stability across all computationally observed phases, random structure sampling shows a significant composition region where the rocksalt basin dominates. As such, we predict the potential for the nonequilibrium synthesis of metastable rocksalt TaC 1-x N x alloys as substrates for Al 1-x Ga x N. At higher nitrogen concentrations, other low-energy metastable polymorphs emerge that continue to retain the hexagonal close packing suitable for III-N growth. Confidence in these trends was established through uncertainty quantification of the basin sizes and energy distributions; such analysis utilized the Beta and Dirichlet distributions. In conclusion, we also find (a) polymorph basin sizes can be rationalized in terms of energetic preferences for different coordination environments; and (b) basin sizes universally shrink with increasing nitrogen content, making the system more prone to amorphous growth.
36 MATERIALS SCIENCE↗
Tailoring Microbial Fitness Through Computational Steering and CRISPRi-Driven Robustness Regulation
The widespread application of genetically modified microorganisms (GMMs) across diverse sectors underscores the pressing need for robust strategies to mitigate the risks associated with their potential uncontrolled escape. This study merges computational modeling with CRISPR interference (CRISPRi) to refine GMM metabolic robustness. Utilizing ensemble modeling, we achieved high-throughput in silico screening for enzymatic targets susceptible to expression alterations. Translating these insights, we developed functional CRISPRi, boosting fitness control via multiplexed gene knockdown. Our method, enhanced by an insulator-improved gRNA structure and an off-switch circuit controlling a compact Cas12m, resulted in rationally engineered strains with escape frequencies below National Institutes of Health standards. The effectiveness of this approach was confirmed under various conditions, showcasing its ability for secure GMM management. This research underscores the resilience of microbial metabolism, strategically modifying key nodes to halt growth without provoking significant resistance, thereby enabling more reliable and precise GMM control. A record of this paper's transparent peer review process is included in the supplemental information.
59 BASIC BIOLOGICAL SCIENCES↗
Benchmarking the performance of uncertainty quantification methods for neural network-based interatomic potentials
Machine-learned interatomic potentials (ML-IAPs) continue to gain popularity as accurate, computationally efficient replacements for traditional, physics-based interatomic potentials and expensive ab initio methods. Uncertainty quantification (UQ) of ML-IAPs is a growing area of research as UQ is critical in many applications of IAPs, such as developing curated datasets, active learning-based data augmentation, self-improving models, and estimating the uncertainty of molecular dynamics simulations. In this paper, we construct and benchmark a series of different neural network potentials (NNPs) with varying network architectures to determine the performance of these models with respect to both the mean and uncertainty calibration error. Each NNP method is specifically designed to predict either epistemic or aleatoric uncertainty with particular focus on the differences in behavior between the epistemic and aleatoric uncertainty estimates. We benchmark these methods using multiple datasets common in the ML-IAP literature. The results show that the aleatoric uncertainty from single-shot model architectures is a competitive alternative to ensemble-based epistemic uncertainty predictions in regions of sufficient data-density. However, in regions where the representative data is sparse, aleatoric uncertainty models tend to overpredict and epistemic methods tend to underpredict the actual model error. We conclude that the type of UQ is crucial when discussing performance of probabilistic model results as different methods have different performance characteristics depending on the regime in which they are evaluated. Therefore, the type of UQ method should be carefully evaluated against both the data characteristics and requirements for the intended application.
97 MATHEMATICS AND COMPUTING↗
A robust framework for frictional fault contact in geological formations using a stabilized augmented Lagrangian approach
Numerical simulations are essential to evaluate the performance and safety of engineered subsurface systems such as geological carbon storage sites, enhanced geothermal fields, and oil and gas reservoirs. A key challenge lies in accurately modeling the frictional contact behavior along fault surfaces. This problem involves inequality constraints that arise from the physics of frictional slip, requiring specialized numerical methods to handle the resulting highly nonlinear and path-dependent behavior. Here, in this work, we address this challenge using an Augmented Lagrangian Method (ALM) implemented via the Uzawa algorithm. The formulation employs mixed finite element spaces, combining low-order piecewise linear displacements within the 3D domain cells with piecewise constant tractions defined on the fault surfaces. Furthermore, to ensure stability and satisfy the inf-sup condition, the discrete displacement space is enriched with face bubble functions on both sides of the contact interfaces. This approach offers several advantages over other stabilization techniques that rely on additional terms, and it integrates naturally in the Uzawa framework.
58 GEOSCIENCES↗
Applying the FAIR Principles to computational workflows
Recent trends within computational and data sciences show an increasing recognition and adoption of computational workflows as tools for productivity and reproducibility that also democratize access to platforms and processing know-how. As digital objects to be shared, discovered, and reused, computational workflows benefit from the FAIR principles, which stand for Findable, Accessible, Interoperable, and Reusable. The Workflows Community Initiative’s FAIR Workflows Working Group (WCI-FW), a global and open community of researchers and developers working with computational workflows across disciplines and domains, has systematically addressed the application of both FAIR data and software principles to computational workflows. We present recommendations with commentary that reflects our discussions and justifies our choices and adaptations. These are offered to workflow users and authors, workflow management system developers, and providers of workflow services as guidelines for adoption and fodder for discussion. The FAIR recommendations for workflows that we propose in this paper will maximize their value as research assets and facilitate their adoption by the wider community.
97 MATHEMATICS AND COMPUTING↗
Riemannian Optimization Applied to AC Optimal Power Flow: Preprint
The nonlinear, nonconvex AC optimal power flow problem is of growing importance as the nature of the power grid evolves. This problem can be difficult to solve for interior point methods. However, the advent of optimization algorithms over smooth Riemannian manifolds presents an alternative approach. The nonlinear, nonconvex constraints in the AC power flow problem form an embedded submanifold of Euclidean space. In this paper, the authors explore the performance of Riemannian optimization algorithms for the ACOPF problem where the optimization is performed directly on the AC power flow manifold. They demonstrate that these are viable computational alternatives to interior point methods. This is done by using Julia and the packages PowerModels.jl and Manopt.jl.
manifold optimization↗
Effect of Surface Roughness on Dynamic Stall in Pitching Motion
Dynamic stall plays a critical role in determining the performance and stability of a wide range of fluid-dynamics systems in various engineering applications. This unsteady aerodynamic phenomenon is particularly significant for maneuvering aircraft wings, jet aircraft subjected to gust encounters, helicopter rotor blades, and wind turbine blades [1–3]. The prediction of the dynamic stall vortex (DSV) is challenging due to factors such as unsteady aerodynamics, three-dimensional (3-D) effects, turbulence and flow separation, incoming gust, and surface impact effects [4–6]. Hence, advanced computational techniques and modeling approaches in computational fluid dynamics (CFD) would be required to enhance the accuracy and reliability of DSV predictions in dynamic stall scenarios. In the past, Batther and Lee [7] employed delayed detached eddy simulations (DDES) to understand the flow physics associated with the onset of dynamic stall. Their approach demonstrated that DDES achieves results comparable to those obtained from large-eddy simulations at a reduced computational cost. In another study, Khalifa et al. [8] examined the 3-D aspects of dynamic stall on a NACA 0012 airfoil using DES solvers. In conclusion, the findings underlined the superiority of 3-D simulations over two-dimensional approaches, particularly in predicting the lift coefficient values and capturing dynamic stall stages more precisely.
97 MATHEMATICS AND COMPUTING↗
Provable Repair of Vision Transformers
Vision Transformers have emerged as state-of-the-art image recognition tools, but may still exhibit incorrect behavior. Incorrect image recognition can have disastrous consequences in safety-critical real-world applications such as self-driving automobiles. In this paper, we present Provable Repair of Vision Transformers (PRoViT), a provable repair approach that guarantees the correct classification of images in a repair set for a given Vision Transformer without modifying its architecture. PRoViT avoids negatively affecting correctly classified images (drawdown) by minimizing the changes made to the Vision Transformer’s parameters and original output. Here, we observe that for Vision Transformers, unlike for other architectures such as ResNet or VGG, editing just the parameters in the last layer achieves correctness guarantees and very low drawdown. We introduce a novel method for editing these last-layer parameters that enables PRoViT to efficiently repair state-of-the-art Vision Transformers for thousands of images, far exceeding the capabilities of prior provable repair approaches.
97 MATHEMATICS AND COMPUTING↗
Increasing the hardness of posiform planting using random QUBOs for programmable quantum annealer benchmarking
Posiform planting is a method for constructing QUBO instances with a unique planted solution that can be tailored to arbitrary connectivity graphs. In this study we investigate making posiform planted QUBOs computationally harder by fusing many smaller random Ising models, whose global minimum is computed classically, with posiform planted QUBOs. The unique ground state of the resulting QUBO is the concatenation of (exactly one of) the ground states of each smaller problem. Our method generates QUBO instances that have a unique solution, are native to the hardware graph, and have tunable computational hardness. We use our QUBOs to benchmark three D-Wave quantum annealing processors (with 563–5627 qubits), and compare them against simulated annealing and Gurobi. Surprisingly, we find that the D-Wave ground state sampling success rate is not dependent on the glued random QUBO size, and that some QUBO classes are solved at high success rates at short annealing times on the Zephyr processors.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
ENDFtk: A robust tool for reading and writing ENDF-formatted nuclear data
ENDFtk is a recently developed C++ and Python interface to interact with ENDF-6 formatted nuclear data files. It provides a robust and complete interface, allowing the reading and writing of all formats currently part of the ENDF-6 formats manual, as well as some non-ENDF formats used by the NJOY processing code. It provides an interface that mimics the names in the ENDF-6 formats manual as well as an equivalent interface using human-readable attribute names. It is robust and powerful enogh for nuclear data experts to develop complex applications, while also simple enough to be used non-experts to retrieve and manipulate evaluated nuclear data. ENDFtk offers the ability to easily interrogate and manipulate data either in large-scale code projects or in simple Python scripts. Here, in this paper, a brief overview of the interface is given, as well as more substantial examples demonstrating plotting simple data, interacting with more complex data, and writing new data to files. ENDFtk is open source and available for download via GitHub (https://github.com/njoy/ENDFtk).
97 MATHEMATICS AND COMPUTING↗
Science & Technology Review June 2026: Predicting Tsunamis
At Lawrence Livermore National Laboratory, we focus on science and technology research to ensure our nation’s security. We also apply that expertise to solve other important national problems in energy, bioscience, and the environment. Science & Technology Review is published eight times a year to communicate, to a broad audience, the Laboratory’s scientific and technological accomplishments in fulfilling its primary missions. The publication’s goal is to help readers understand these accomplishments and appreciate their value to the individual citizen, the nation, and the world.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Selection of Global Climate Model Data for Downscaling With Generative Machine Learning and Use in the Power Planning for Alignment of Climate and Energy Systems Project
The range of results from climate models and scenarios is important to the understanding of uncertainty in power planning analysis. A U.S. Department of Energy-funded analytic project called Power Planning for Alignment of Climate and Energy Systems is developing data and analytic methods to reflect the effects of climate change on key variables for power system planning, as part of the Grid Modernization Lab Consortium. This project will select and prepare global climate model results for use in power system planning models. A related report (Evaluation of Global Climate Models for Use in Energy Analysis) assesses the performance of various global climate models from the Coupled Model Intercomparison Project Phase 6 data archive for their historical skill with respect to energy system performance and for their future projections under multiple climate change scenarios. Building from that report, we describe the selection of a climate scenario (Shared Socioeconomic Pathway [SSP] 2-4.5) and five climate models: TaiESM1, EC-Earth3-CC, GFDL-CM4, EC-Earth3-Veg, and MPI-ESM1-2-HR. We describe the model selection criteria, which were based on the quality of the match between model results under historical conditions and on the representation of the range of future values for several variables. These results will be downscaled via an open-source generative machine learning method called Super-Resolution for Renewable Energy Resource Data with Climate Change Impacts.
29 ENERGY PLANNING, POLICY, AND ECONOMY↗
Adaptive Computing for Scale-Up Problems
Adaptive Computing is an application-agnostic outer loop framework to strategically deploy simulations and experiments to guide decision making for scale-up analysis. Resources are allocated over successive batches, which makes the allocation adaptive to some objective such as optimization or model training. The framework enables the characterization and management of uncertainties associated with predictive models of complex systems when scale-up questions lead to significant model extrapolation. A key advancement of this framework is its integration of multi-fidelity surrogate modeling, uncertainty management, and automated orchestration of various computing and experimentation resources into a single integrated software package. This enables efficient multi-fidelity modeling across multiple computing resources by incorporating real-world constraints such as relative queue times and throughput on individual machines into the multi-fidelity sampling decision. We discuss applications of this framework to problems in the renewable energy space, including biofuels production, material synthesis, perovskite crystal growth, and building electrical loads.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
Demonstration Trials of AI/ML Edge+Cloud Suite (CRADA Final Report)
PACE AI and LBNL partnered under this CRADA to test and evaluate the PACE5 edge node prototype, an AI/ML edge and cloud-based suite, at FLEXLAB.The objective of the test was to evaluate the PACE5 edge node prototype's ability to perform demand shed and take to dynamic price signals, and to demonstrate advanced fault detection and microgrid monitoring capabilities.
97 MATHEMATICS AND COMPUTING↗
Automated and Accelerated Continuum Model Development for Electrochemical Systems (Abbreviated Report)
Despite the availability of computational resources and advancements in numerical computing capabilities, the multiscale models core to understanding, predicting the behaviors of, and designing energy and environmental systems involving porous media are still 1.) developed through by-hand derivations and 2.) limited by many methodological assumptions employed during model derivation. As a result, the advancement of effective media models for engineering DOE mission-critical systems (e.g., batteries, flow batteries, electrolyzers, geothermal systems, subsurface chemical storage systems, etc.) is slow (i.e., it takes years for models to traverse from stages of “development” to “practical utilization”), hindering our ability to effectively optimize such systems and stay at the cutting-edge of the energy frontier. In this work, we aimed to address these limitations by 1.) automating and accelerating multiscale model derivation via symbolic computing and 2.) develop a novel multiscale modeling methodology for flow and transport through porous media that avoids the typical assumptions hindering previous models. As a result of our efforts, we 1.) developed a hybrid symbolic-numeric code called Fouriera for fully-automating the implementation of multiphysical and phase-field models via the Fourier spectral method for materials science research, and 2.) advanced a multiscale modeling methodology called The Method of Finite Averages that rigorously predicts the behaviors of flow and transport through heterogeneous porous media under the influence of non-local effects and strong advection. Ultimately, these deliverables provide strong foundations from which further efforts can advance multiscale modeling tools and capabilities that do not intrinsically rely on 1.) the speed and mathematical capabilities of humans, nor 2.) the methodological assumptions limiting current models.
36 MATERIALS SCIENCE↗
Mathematics and physics at the quantum-classical interface
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general physics↗