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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

HydraGNN_Predictive_GFM_2024 - Ensemble of predictive graph foundation models for ground state atomistic materials modeling

We provide the ensemble of fifteen pre-trained graph foundation models (GFMs) for atomistic materials modeling applications. Each one of the fifteen GFMs has been trained on five open-source datasets that (once aggregated) amount to over 154 million atomistic structures, which cover over two-thirds of the natural elements of the periodic table and that comprises a broad set of organic and inorganic compounds. This vast set of atomistic structures comprises ground state configurations that are dynamically stable (i.e., equilibrated structures with atomic forces approximately close to zero values) as well as dynamically unstable structures (i.e., non-equilibrium structures with non-negligible non-zero values of atomic forces). The ensemble of datasets aggregated does NOT include excited states. The datasets have been curated to remove atomistic structures with spectral norm of the force tensor above 100 eV/angstrom. Moreover, a linear term of the energy was computed for each dataset using a linear regression model that uses the chemical concentration of each natural element as regressor. The linear term predicted by the linear regression model has been subtracted from each original energy value to perform a re-alignment of the energy values across different electronic structures approximation theories performed to generate the diverse multi-source, multi-fidelity datasets. The folder "ADIOS_files" contains the set of pre-processed datasets in Adaptable I/O System (ADIOS) format (https://www.exascaleproject.org/research-project/adios/) that have been used for the development and training of GFMs in this work. The "ADIOS_files" directory contains 6 sub-directories named as follows: - ANI1x-v3.bp - MPTrj-v3.bp - OC2020-20M-v3.bp - OC2020-v3.bp - OC2022-v3.bp - qm7x-v3.bp Each sub-directory contains the pre-processed datasets converted in Adaptable I/O System (ADIOS) format (https://www.exascaleproject.org/research-project/adios/) that have been used to the development, training, and performance testing of the ensemble go predictive graph foundation models. Each GFM was developed using HydraGNN (https://github.com/ORNL/HydraGNN) as underlying graph neural network (GNN) architecture. The multi-task learning (MTL) capability of HydraGNN was used to simultaneously train the GFMs on labeled values for direct predictions of energy (a total system property of an atomistic structure that measures the chemical stability) and atomic forces (an atomic level property of an atomistic structure that measures the dynamical stability). The hyper parameters of the GFM have been tuned using scalable hyperparameter optimization (HPO) algorithms implemented in the software DeepHyper (https://github.com/deephyper/deephyper). The pre-training of each HPO trial was performed using distributed data parallelism (DDP) to scale the training across 128 compute nodes of the exascale OLCF supercomputer Frontier. Each HPO trial was trained only for 10 epochs and an early stopping was performed to avoid wasting significant computational resources on GNN architectures that were clearly underperforming. For each HPO trial, the 'omnistat' tool developed by (AMD Research - Advanced Micro Device) was used to measure the total energy consumption in kWh. The ensemble of GFMs was obtained by selecting the fifteen best performing HPO trials. Four models have been selected for their clear advantage in accuracy, and these are the GFMs with IDs 229, 156, 147, 260. Additional eleven models have been selected based on judicious balance between accuracy and energy consumption needed for training, and these are the GFMs with IDs 165, 78, 137, 1, 175, 171, 181, 67, 179, 167, 351. Each selected GFM of the ensemble was continued to cumulate a total of at most 30 epochs. In some cases, the total number of epochs actually performed was les than 30 due to two combined factors: (1) the size of the GFM (i.e., the number of model parameters to train) and (2) the total wall-clock time for which the computational resources could be allocated on OLCF-Frontier. The "Ensemble_of_models" directory contains 15 sub-directories named as follows: - gfm_0.229 - gfm_0.156 - gfm_0.147 - gfm_0.260 - gfm_0.165 - gfm_0.78 - gfm_0.137 - gfm_0.1 - gfm_0.175 - gfm_0.171 - gfm_0.181 - gfm_0.67 - gfm_0.179 - gfm_0.167 - gfm_0.351 Each one of these sub-directories refers to one of the fifteen HPO trials that have been selected to continue the pre-training with at most 30 epochs. With each sub-directory associated with a specific HPO trial, the following files can be found: - config.json: file for argument parsing to develop and train an HydraGNN architecture - gfm_0.ID_epoch_N.pk: file with model parameters for HPO ID trial after N epochs of training The ensemble of fifteen GFM architectures was used for (1) ensemble averaging to stabilize the predictions of energy and atomic forces after pre-training for post-processing analysis and (2) ensemble uncertainty quantification (UQ). The code used to develop, pre-train, and load the pre-trained models for post-processing analysis is available on the ORNL-GitHub at the following link: https://github.com/ORNL/HydraGNN/tree/Predictive_GFM_2024

36 MATERIALS SCIENCE↗
DOE OSTI2024

AEOLUS: Advances in Experimental Design, Optimal Control, and Learning for Uncertain Complex Systems

Sustained advances in the mathematics of modeling and simulation have resulted in the capability today for routine simulation of a number of large scale complex DOE-relevant systems. As remarkable as this capability for solving the so-called forward problem is, it is typically only the first step-an inner loop within an outer loop that explores the simulation model's parameter space and decision space to characterize uncertainty in the model's predictions, learn unknown model parameters from data, design the most informative experiments, determine optimal control strategies, and create optimal designs. Broadly, what unifies all of these outer loop problems is that they are, in one form or another, optimization problems over parameter/control/design space that are constrained by complex uncertain models. To fully realize the power of scientific simulation as a basis for scientific discovery, technological innovation, and rational decision-making, it is imperative to move beyond simulation to tackle the outer loop of optimization for learning from data, experimental design, and control with complex uncertain models. When the models under consideration are large-scale and complex, and when the optimization variable and uncertain parameter spaces are high (or infinite) dimensional, this constitutes a grand challenge of the highest order, and is intractable with conventional methods. To overcome these challenges, the AEOLUS Center was established to develop a unified mathematical, computational, and statistical framework for (1) Learning predictive models from complex data via Bayesian inference and optimization, and (2) Optimizing experiments, processes, and designs using the resulting uncertain models. These problems are intractable with conventional methods, for several reasons: (1) The simulation problems that govern the inner loops of the optimization problems are expensive to execute (due to severe nonlinearity, heterogeneity, multiphysics/multiscale coupling); (2) The optimization variable and uncertain parameter spaces are high dimensional, often stemming from discretizations of infinite dimensional fields such as initial conditions, sources, or material properties. We argue that the key to overcoming these challenges is to develop new mathematical, computational, and statistical methods that exploit the structure of the Bayesian inference and optimization problems mediated by their underlying complex uncertain models. This structure includes the regularity, sparsity, geometry, low intrinsic dimensionality, and multifidelity nature of the maps from uncertain parameter/optimization variable spaces to the specific objectives targeted: Bayesian inference, optimal experimental design, and optimal control design. Black box methods developed as generic tools are incapable of exploiting this structure. To be successful, we must create, integrate, and cross-fertilize ideas across multiple areas of applied math--including approximation theory, Bayesian inference, data science, experimental design, information theory, machine learning, model reduction, optimal control theory, parallel algorithms, PDE-constrained optimization, randomized algorithms, stochastic optimization, and uncertainty quantification--all while exploiting the structure of the problems at hand. With this goal in mind, we have marshaled a team of leading authorities in these areas. While the methods we develop will be broadly applicable across a wide spectrum of DOE problems in which experiments inform models and the systems those models describe must be optimized under uncertainty, we have chosen a specific area, advanced manufacturing and materials, to drive our work. AMM is characterized by complex models across multiple scales, and is a rich source of challenging problems in inference, experimental design, and optimal control, requiring multifaceted and integrated advances in applied mathematics. As such, AMM serves as an excellent vehicle to motivate and demonstrate the advances in applied mathematics developed by our center.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2025

Measurement and Modeling of Electron Temperature in Laboratory Photoionized Plasmas Relevant to Astrophysics

The electron temperature of photoionized plasmas characterizes the thermalization of photoelectrons, impacts the charge-state distribution, emissivity, and opacity through atomic recombination processes, and is needed to perform detailed comparisons with theory predictions. We discuss temperature measurements in laboratory photoionized plasmas and a comparison with model calculations done with several theory approximations and codes. These include a radiation-hydrodynamics simulation and two nonequilibrium heating and ionization models that tracked the evolution of the internal energy of the electrons. Furthermore, for the same physics model and X-ray flux time history, calculations were performed assuming steady-state or time-dependent conditions. The time history of steady-state results correlates with that of the X-ray flux, while that of the time-dependent cases does not, and it is qualitatively and quantitatively different from the steady-state case. Steady-state results significantly overestimated temperature measurements, while time-dependent results produced better approximations, which suggests the importance of transient effects in the experiment and also the need for time-resolved measurements.

Laboratory astrophysics↗
NASA NTRS1972

Discrete-time demodulation of continuous-time signals.

Nonlinear stochastic estimation theory is applied to the problem of obtaining discrete-time demodulator structures for the common types of analog communication signals. A stochastic communication model is presented that can be treated with current results in estimation theory. Approximate algorithms are developed for the estimation problem that yield mathematically realizable receiver structures for the cases of AM, PC, and FM. The digital receivers yield performance characteristics that compare favorably with those of their analog counterparts.

Kelly, C. N.↗
NASA NTRS1972

Effects of circular geometry in simulation of convection in rotating spacecraft tanks

For computational simulation of the convection and mixing of stratified fluid in a rotating tank (such as used in Apollo flights) with time-dependent rotation, the Navier-Stokes convection problem was formulated for a circular tank configuration. The final equations results from a general approximate theory for combined forced and contained natural convection in a time-dependent rotating system. The equations are cast in terms of vorticity and stream function in a form convenient for computation, with a transformed coordinate system, and appropriate boundary conditions are derived. Accurate representations for the cryogenic supercritical oxygen thermodynamic properties are used in the computations, and an efficient numerical finite difference scheme and computational method are employed.

Martin, E. D.↗
NASA NTRS1973

Graphite oxidation at low temperature in subsonic air.

Coupled mass loss and heat transfer was studied experimentally for thin two inch diameter graphite disks heated as high as 2800 F in a flow of ambient air at velocities of 97 to 717 ft/sec. Oxidation was predominately reaction rate controlled with rate constants which were determined experimentally for POCO AXF 5Q, ATJ, ATJS, and an AVCO 3D Orthogonal material. The specimen thermal response was used with an energy balance to obtain the influence of mass loss and chemical reactions on the heat transfer. Specimen heating due to exothermic reactions correlates qualitatively with an approximate theory.

Knight, D. D.↗
NASA NTRS1973

Short-term frequency stability of the Rb-87 maser.

Measurements of the short-term stability of the Rb-87 maser as a function of the maser power output and the receiver cutoff frequency are reported. The experimental data are compared to theoretical results obtained from an approximate theory. In this theory the transfer function of the maser for thermal noise is derived, and the spectral density of the phase fluctuations is calculated. An analytical expression for the 'Allan variance' is also given. A comparison of the stability of the Rb-87 maser with existing frequency standards shows its superiority for averaging times less than 1 sec.

Tetu, M.↗
NASA NTRS1973

Stress wave calculations in composite plates using the fast Fourier transform.

The protection of composite turbine fan blades against impact forces has prompted the study of dynamic stresses in composites due to transient loads. The mathematical model treats the laminated plate as an equivalent anisotropic material. The use of Mindlin's approximate theory of crystal plates results in five two-dimensional stress waves. Three of the waves are flexural and two involve in-plane extensional strains. The initial value problem due to a transient distributed transverse force on the plate is solved using Laplace and Fourier transforms. A fast computer program for inverting the two-dimensional Fourier transform is used. Stress contours for various stresses and times after application of load are obtained for a graphite fiber-epoxy matrix composite plate. Results indicate that the points of maximum stress travel along the fiber directions.

Moon, F. C.↗
NASA NTRS1974

Optimal design of an unsupervised adaptive classifier with unknown priors

An adaptive detection scheme for M hypotheses was analyzed. It was assumed that the probability density function under each hypothesis was known, and that the prior probabilities of the M hypotheses were unknown and sequentially estimated. Each observation vector was classified using the current estimate of the prior probabilities. Using a set of nonlinear transformations, and applying stochastic approximation theory, an optimally converging adaptive detection and estimation scheme was designed. The optimality of the scheme lies in the fact that convergence to the true prior probabilities is ensured, and that the asymptotic error variance is minimum, for the class of nonlinear transformations considered. An expression for the asymptotic mean square error variance of the scheme was also obtained.

Kazakos, D.↗
NASA NTRS1973

Sonic boom analysis for high altitude flight at high Mach number

Numerical programs are presented which take into account the nonlinear effects of high Mach number, the entropy change across the shock, the entropy and enthalpy variations in the atmospheric layer and the gravitational effect. Extension of the programs for the axisymmetric problems to handle nonaxisymmetric terms is described. The asymmetry can be caused by the geometry of the body, the lift and also the fact that the variations in the atmospheric layer are two-dimensional. Numerical results demonstrating the influences of these effects and comparison with existing approximate theories are presented.

Ferri, A.↗
NASA NTRS1977

Sonic boom analysis for high-altitude flight at high Mach number

Numerical programs for the computation of the flow field from the airplane at the flight altitude to the ground are presented. They take into account the nonlinear effects of high Mach number, the entropy change across the shock, the entropy and enthalpy variations in the atmospheric layer, and the gravitational effect. Extension of the programs for the axisymmetric problems to handle nonaxisymmetric terms is described. The asymmetry can be caused by the geometry of the body and the lift, and also by the fact that the variations in the atmospheric layer are two-dimensional. Numerical results for ground level signatures of several configurations at various flight conditions are presented and compared with existing approximate theories to demonstrate the influences of these nonlinear effects.

Ferri, A.↗
NASA NTRS1977

Stress intensities for cracks emanating from pin-loaded holes

A series of stress freezing photoelastic experiments were conducted on large plates containing central holes with cracks emanating from the edge formed by the intersection of the hole with the plate surface. Loads were applied through rigid pins with neat fits in the holes. Stress-intensity factors (SIF) were estimated by a computer assisted least squares analysis of the photoelastic data taken from slices near the points of intersection of the flaw border with the hole boundary and the plate surface. Results indicate that the local mode of loading changes from Mode 1 near the hole boundary to mixed mode near the plate surface. The analysis is extended to include mixed mode loading, and results are compared with an existing approximate theory.

Smith, C. W.↗