Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Mathematical physics methods”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,531 records · Page 85
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Bayesian Entropy Neural Networks for physics-aware prediction

This article addresses the need for deep learning models to integrate well-defined constraints into their outputs, driven by their application in surrogate models, learning with limited data and partial information, and scenarios requiring flexible model behavior to incorporate non-data sample information. We introduce Bayesian Entropy Neural Networks (BENN), a framework grounded in Maximum Entropy (MaxEnt) principles, designed to impose constraints on Bayesian Neural Network (BNN) predictions. BENN is capable of constraining not only the predicted values but also their derivatives and variances, ensuring a more robust and reliable model output. To achieve simultaneous uncertainty quantification and constraint satisfaction, we employ the method of multipliers approach. This allows for the concurrent estimation of neural network parameters and the Lagrangian multipliers associated with the constraints. Our experiments, spanning diverse applications such as beam deflection modeling and microstructure generation, demonstrate the effectiveness of BENN. The results highlight significant improvements over traditional BNNs and showcase competitive performance relative to contemporary constrained deep learning methods.

14 SOLAR ENERGY↗
DOE OSTI2022

AI and extreme scale computing to learn and infer the physics of higher order gravitational wave modes of quasi-circular, spinning, non-precessing black hole mergers

We use artificial intelligence (AI) to learn and infer the physics of higher order gravitational wave modes of quasi-circular, spinning, non precessing binary black hole mergers. We trained AI models using 14 million waveforms, produced with the surrogate model NRHybSur3dq8, that include modes up to $\ell$ ≤ 4 and (5,5), except for (4,0) and (4,1), that describe binaries with mass-ratios $\textit{q}$ ≤ 8, individual spins $s^z_{\{1,2\}} \in$[–0.8,0.8], and inclination angle $θ \in$ [0,π]. Our probabilistic AI surrogates can accurately constrain the mass-ratio, individual spins, effective spin, and inclination angle of numerical relativity waveforms that describe such signal manifold. We compared the predictions of our AI models with Gaussian process regression, random forest, k-nearest neighbors, and linear regression, and with traditional Bayesian inference methods through the PyCBC Inference toolkit, finding that AI outperforms all these approaches in terms of accuracy, and are between three to four orders of magnitude faster than traditional Bayesian inference methods. Our AI surrogates were trained within 3.4 hours using distributed training on 1,536 NVIDIA V100 GPUs in the Summit supercomputer.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Runtime performance of a GAMESS quantum chemistry application offloaded to GPUs

Summary Computational chemistry is at the forefront of solving urgent societal problems, such as polymer upcycling and carbon capture. The complexity of modeling these processes at appropriate length and time scales is mainly manifested in the number and types of chemical species involved in the reactions and may require models of several thousand atoms and large basis sets to accurately capture the chemical complexity and heterogeneity in the physical and chemical processes. The quantum chemistry package General Atomic and Molecular Electronic Structure System (GAMESS) has a wide array of methods that can efficiently and accurately treat complex chemical systems. In this work, we have used the GAMESS Effective Fragment Molecule Orbital (EFMO) method for electronic structure calculation of a challenging mesoporous silica nanoparticle (MSN) model surrounded by about 4700 water molecules to investigate the strong scaling and GPU offloading on hybrid CPU‐GPU nodes. Experiments were performed on the Perlmutter platform at the National Energy Research Scientific Computing Center. Good strong scaling and load balancing have been observed on up to 88 hybrid nodes for different settings of the execution parameters for the calculation considered here. When GPUs are oversubscribed by offloading work from multiple CPU processes, using the NVIDIA multi‐process service (MPS) has consistently reduced time to solution and energy consumed. Additionally, for some configuration parameter settings, oversubscription with MPS improved performance by up to 5.8% over the case without oversubscription.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Mathematical Modeling of Liquid-Phase Alkylation of Benzene with Ethylene Considering the Process Unsteadiness

Ethylbenzene is a key intermediate in the manufacture of styrene that is an important industrial monomer. Ethylbenzene is produced by benzene alkylation using either gas-phase or liquid-phase methods. The liquid-phase alkylation that uses liquid acidic catalysts needs to be improved. We develop a mathematical model for the liquid-phase benzene alkylation. The reaction scheme, designed with a due analysis of desired and side reactions, and with the analysis of the formation of deactivating agents, reflects, in particular, the influence of the concentration of heavy hydrocarbons on the catalyst activity. The account of the catalyst deactivation by heavy alkylaromatics allows predictions of the temporal changes in the outputs of the alkylation process. In particular, the decrease of the ethylbenzene concentration by 2–3 wt % and increase of the polyalkylate outlet concentration by 1.5–2 wt % are the results of the catalyst deactivation. These effects, however, can be compensated by 1.3-time increase of polyalkylate supply and by the temperature increase up to 398 K. Finally, the calculations also show that it is possible to decrease the supply of fresh catalyst from 0.498 to 0.472 t/hour without loss in the yield of ethylbenzene.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations

One of the most promising applications of machine learning in computational physics is to accelerate the solution of partial differential equations (PDEs). The key objective of machine-learning-based PDE solvers is to output a sufficiently accurate solution faster than standard numerical methods, which are used as a baseline comparison. Here, we first perform a systematic review of the ML-for-PDE-solving literature. Out of all of the articles that report using ML to solve a fluid-related PDE and claim to outperform a standard numerical method, we determine that 79% (60/76) make a comparison with a weak baseline. Second, we find evidence that reporting biases are widespread, especially outcome reporting and publication biases. We conclude that ML-for-PDE-solving research is overoptimistic: weak baselines lead to overly positive results, while reporting biases lead to under-reporting of negative results. To a large extent, these issues seem to be caused by factors similar to those of past reproducibility crises: researcher degrees of freedom and a bias towards positive results. We call for bottom-up cultural changes to minimize biased reporting as well as top-down structural reforms to reduce perverse incentives for doing so.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Alternative formulation of weak magnetohydrodynamic turbulence theory

In a recent paper, the weak turbulence theory for incompressible magnetohydrodynamics is formulated by employing the method customarily applied in the context of kinetic weak plasma turbulence theory. Such an approach simplified certain mathematical procedures including achieving the closure relationship. The formulation in the above-cited paper starts from the equations of incompressible magnetohydrodynamic (MHD) theory expressed via Elsasser variables. The derivation of nonlinear wave kinetic equation therein is obtained via a truncated solution at the second-order of iteration following the standard practice. In the present paper, the weak MHD turbulence theory is alternatively formulated by employing the pristine form of incompressible MHD equation rather than that expressed in terms of Elsasser fields. The perturbative expansion of the nonlinear momentum equation is carried out up to the third-order iteration rather than imposing the truncation at the second order. Furthermore, it is found that while the resulting wave kinetic equation is identical to that obtained in the previous paper cited above, the third-order nonlinear correction plays an essential role for properly calculating derived quantities such as the total and residual energies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Black Box Equations of State: Creating Semi-analytic Solutions to the Noh Problem and Verifying Equation of State Interfaces

The objective of this report is threefold. First, it details a method for deriving a semi-analytic solution to the Noh Problem when using a “black-box” equation of state. Such capability allows us to perform verification on complicated, more realistic equations of state. Examples include Steinberg equations of state for materials and tabulated equations of state. The second objective is to apply the methodology to verify the singularity-eos equation of state library. We do so by solving the Rankine-Hugoinot jump conditions for the Noh Problem, ensuring singularity derives the correct solution and comparing the error to an exact implementation of the equation of state. The third objective is to perform verification of the xRAGE Eulerian hydrodynamics code when interfaced with singularity. We provide the theory, analysis, documentation for a python implementation of the proposed solver, and verification results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

An Evolve-Then-Correct Reduced Order Model for Hidden Fluid Dynamics

In this paper, we put forth an evolve-then-correct reduced order modeling approach that combines intrusive and nonintrusive models to take hidden physical processes into account. Specifically, we split the underlying dynamics into known and unknown components. In the known part, we first utilize an intrusive Galerkin method projected on a set of basis functions obtained by proper orthogonal decomposition. We then present two variants of correction formula based on the assumption that the observed data are a manifestation of all relevant processes. The first method uses a standard least-squares regression with a quadratic approximation and requires solving a rank-deficient linear system, while the second approach employs a recurrent neural network emulator to account for the correction term. We further enhance our approach by using an orthonormality conforming basis interpolation approach on a Grassmannian manifold to address off-design conditions. The proposed framework is illustrated here with the application of two-dimensional co-rotating vortex simulations under modeling uncertainty. The results demonstrate highly accurate predictions underlining the effectiveness of the evolve-then-correct approach toward real-time simulations, where the full process model is not known a priori.

long short-term memory↗
DOE OSTI2021

Analytic continuation of noisy data using Adams Bashforth residual neural network

We propose a data-driven learning framework for the analytic continuation problem in numerical quantum many-body physics. Designing an accurate and efficient framework for the analytic continuation of imaginary time using computational data is a grand challenge that has hindered meaningful links with experimental data. The standard Maximum Entropy (MaxEnt)-based method is limited by the quality of the computational data and the availability of prior information. Also, the MaxEnt is not able to solve the inversion problem under high level of noise in the data. Here we introduce a novel learning model for the analytic continuation problem using a Adams-Bashforth residual neural network (AB-ResNet). Additionally, the advantage of this deep learning network is that it is model independent and, therefore, does not require prior information concerning the quantity of interest given by the spectral function. More importantly, the ResNet-based model achieves higher accuracy than MaxEnt for data with higher level of noise. Finally, numerical examples show that the developed AB-ResNet is able to recover the spectral function with accuracy comparable to MaxEnt where the noise level is relatively small.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Impact of cyber attacks on distributed compressive sensing based state estimation in power distribution grids

Modern power distribution grids suffer from multiple vulnerabilities due to the tight integration between the physical system and the cyber infrastructure. Sophisticated and malicious cyber attacks continue to adversely impact the grid operation leading to performance degradation, service interruption, and grid failure. State estimation plays an essential role in grid monitoring and advancing cyber-attack situational awareness. In this regard, this paper first proposes a distributed compressive sensing (CS) state estimation approach for an unobservable distribution grid. Further, the proposed distributed CS approach divides the distribution grid into sub-areas to perform local state estimation. Then an alternating direction method of multipliers (ADMM) based iterative information exchange among neighboring areas is employed to complete the estimation process. In this estimation process, the impact of loss of measurement data, false data injection (FDI), replay, and neighborhood cyber-attacks is analyzed. Extensive simulations are performed on the IEEE 37-bus and IEEE 123-bus standard networks to demonstrate the algorithm’s robustness to the aforementioned cyber-attacks. A quantitative analysis of computational complexity and simulation time of the distributed CS based approach is also presented.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

An finite element analysis surrogate model with boundary oriented graph embedding approach for rapid design

Abstract In this work, we present a boundary oriented graph embedding (BOGE) approach for the graph neural network to assist in rapid design and digital prototyping. The cantilever beam problem has been solved as an example to validate its potential of providing physical field results and optimized designs using only 10 ms. Providing shortcuts for both boundary elements and local neighbor elements, the BOGE approach can embed unstructured mesh elements into the graph and performs an efficient regression on large-scale triangular-mesh-based finite element analysis (FEA) results, which cannot be realized by other machine-learning-based surrogate methods. It has the potential to serve as a surrogate model for other boundary value problems. Focusing on the cantilever beam problem, the BOGE approach with 3-layer DeepGCN model achieves the regression with mean square error (MSE) of 0.011 706 (2.41% mean absolute percentage error) for stress field prediction and 0.002 735 MSE (with 1.58% elements having error larger than 0.01) for topological optimization. The overall concept of the BOGE approach paves the way for a general and efficient deep-learning-based FEA simulator that will benefit both industry and Computer Aided Design (CAD) design-related areas.

42 ENGINEERING↗
DOE OSTI2021

Geo Thermal Cloud: Cloud Fusion of Big Data and Multi-Physics Models using Machine Learning for Discovery, Exploration, and Development of Hidden Geothermal Resources

The project is motivated by the challenges, risks, and costs associated with geothermal exploration and production. Many processes and parameters impacting geothermal conditions are poorly understood. Diverse datasets are available to help characterize subsurface geothermal conditions (public and proprietary; satellite, airborne surveys, vegetation/water sampling, geological, geophysical, etc.). Yet, it is not clear how to properly leverage these datasets for geothermal exploration due to an incomplete understanding of how physical processes impacting subsurface geothermal conditions are represented in these observations. Recent advancements in machine learning (ML) provide great promise to resolve these issues. The tremendous challenges and risks of geothermal exploration and production bring the demand for novel ML methods and tools that can (1) analyze large field datasets, (2) assimilate model simulations (large inputs and outputs), (3) process sparse datasets, (4) perform transfer learning (between sites with different exploratory levels), (5) extract hidden geothermal signatures in the field and simulation data, (6) label geothermal resources and processes, (7) identify high-value data acquisition targets, and (8) guide geothermal exploration and production by selecting optimal exploration, production, and drilling strategies. Our goals and work under Phases 1 and 2 (as proposed) of this project address all these needs.

15 GEOTHERMAL ENERGY↗
DOE OSTI2024

Mathematical Modeling of Multi-Phenomena Anisotropic Systems: Ejection of Primary Aerosols during the Fast Pyrolysis of Biomass

This study introduces a novel particle model for biomass fast pyrolysis, incorporating an anisotropic cylindrical particle to address mass and energy transport coupled with aerosol ejection, which previous models have overlooked. The main contribution lies in developing a model that considers aerosol generation in anisotropic cylindrical particles for the first time, addressing bubbling dynamics and bursting within the liquid phase. The population balance equation describes bubble dynamics and aerosol formation, capturing phenomena like nucleation, growth, coalescence, and bursting. The model employs the method of moments with bubble volume as an internal variable, substantially reducing computational costs by eliminating dependence on this variable. Results highlight the significant impact of anisotropy and particle size on aerosol ejection: smaller, less elongated particles experience faster heating, quicker conversion, and the increased accumulation of the liquid intermediate phase. Specifically, 1 mm diameter particles yield higher concentrations of metaplast and bio-oil aerosols, exceeding 15%, compared to concentrations below 11% for 3 mm particles. This model provides insights into aerosol structure (volume, surface area), aiding in understanding aerosol reactivity at the reactor scale.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Unleashed from constrained optimization: quantum computing for quantum chemistry employing generator coordinate inspired method

Hybrid quantum-classical approaches offer potential solutions to quantum chemistry problems, yet they often manifest as constrained optimization problems. Here, we explore the interconnection between constrained optimization and generalized eigenvalue problems through the Unitary Coupled Cluster (UCC) excitation generators. Inspired by the generator coordinate method, we employ these UCC excitation generators to construct non-orthogonal, overcomplete many-body bases, projecting the system Hamiltonian into an effective Hamiltonian, which bypasses issues such as barren plateaus that heuristic numerical minimizers often encountered in standard variational quantum eigensolver (VQE). Diverging from conventional quantum subspace expansion methods, we introduce an adaptive scheme that robustly constructs the many-body basis sets from a pool of the UCC excitation generators. This scheme supports the development of a hierarchical ADAPT quantum-classical strategy, enabling a balanced interplay between subspace expansion and ansatz optimization to address complex, strongly correlated quantum chemical systems cost-effectively, setting the stage for more advanced quantum simulations in chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Grassmannian diffusion maps based surrogate modeling via geometric harmonics

Abstract A novel surrogate model based on the Grassmannian diffusion maps (GDMaps) and utilizing geometric harmonics (GH) is developed for predicting the response of complex physical phenomena. The method utilizes GDMaps to obtain a low‐dimensional representation of the underlying behavior of physical/mathematical systems with respect to uncertain input parameters. Using this representation, GH, an out‐of‐sample extension technique, is employed to create a global map from the input parameter space to a Grassmannian diffusion manifold. GH is further employed to locally map points on the diffusion manifold onto the tangent space of a Grassmann manifold. The exponential map is then used to project the points in the tangent space onto the Grassmann manifold, where reconstruction of the full solution is performed. The performance of the proposed surrogate model is verified with three examples. The first problem is a toy example used to illustrate the technique. In the second example, errors associated with the various mappings are assessed by studying response predictions of the electric potential of a dielectric cylinder in a homogeneous electric field. The last example applies the method for uncertainty prediction in the strain field evolution in a model amorphous material using the shear transformation zone theory of plasticity.

42 ENGINEERING↗
DOE OSTI2023

Machine learning surrogate of physics-based building-stock simulator for end-use load forecasting

Building energy models are used to simulate heat and mass transfer and estimate end-use load in buildings. With the proliferation of solar photovoltaics on residential and commercial buildings, increasingly, buildings are expected to provide grid services, for which accurate and computationally efficient building energy simulations and end-use load prediction are imperative. Existing building energy simulation tools, however, have significant computational overhead that make them less practical in real-time deployment for optimization, design, uncertainty quantification and control in building energy management systems. Here this article presents a data-driven machine learning model based on light gradient boosting method (LightGBM) as a surrogate for a physics-based simulator for residential buildings to predict end-use load. The machine learning based surrogate model accounts for time-series related variables, seasonality and trend component of end-use load, and history of end-use load. The accuracy of the surrogate model is assessed on the prediction of the load profiles of 100 different houses in Cook County, Illinois, USA. The LightGBM surrogate model is shown to reduce the root-mean-squared error by 53% relative to a reference decision tree (DT) based model reported previously in the literature. Moreover, the model predicts the load spikes and high-ramp rate events throughout the year which are often the Achilles heel of other models in the literature. The machine learning based surrogate model is demonstrated to be computationally efficient, with a ten-fold reduction in the computational time compared to a physics-based building energy simulation, and suitable for uncertainty analysis and real-time control of building characteristics in response to uncertainty.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

Z-Target Radiography Postprocessing With A Deep Convolution Neural Network

Analyzing X-ray radiographs is crucial for understanding target behavior in Inertial Confinement Fusion (ICF) and High Energy Density (HED) platforms. However, the density of Magneto Raleigh Taylor (MRT) bands and limitations of target materials often obscure relevant spike growth and density information. To address this issue, machine learning postprocessing techniques can be applied to remove darkened regions in radiography images. In this study, a novel method is presented for removing MRT darkened regions from z-target radiographs using a convolutional neural network (CNN). The CNN, consisting of six layers, treats the darkened regions as noise and employs a mixed loss function and end-to-end frameworks to suppress them while preserving sharpness. The six-layer architecture is designed to effectively learn features when provided with a larger volume of learning space. Each layer is optimized using a mixed loss function that combines a standard loss pixel approach with a multi-scaled structural similarity index loss, which considers luminance, contrast, and structure in local neighborhoods. This approach is particularly beneficial for capturing the stochastic structure of MRT limbs. Due to the limited availability of experimental data, training is conducted using synthetic target radiography from 3D Alegra simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

A Structure-Preserving Decorated Particle Method for the Vlasov-Poisson System

We revisit the Scovel-Weinstein framework (Scovel & Weinstein, CPAM 1994) for reducing the Vlasov-Poisson system while preserving its Hamiltonian structure. Standard particle-in-cell (PIC) algorithms approximate the distribution function by macro-particles with position and velocity. In contrast, Scovel-Weinstein decorated particles involve additional shape degrees of freedom, while maintaining a finite-dimensional reduction with Hamiltonian structure inherited from the continuum model. Although the original work established this structure three decades ago, its computational potential has remained largely unexplored. We present a practical implementation of the Scovel-Weinstein model and compare it with a standard PIC algorithm. Numerical experiments demonstrate that macro-particles in standard PIC can be replaced by far fewer decorated particles while retaining comparable accuracy. This decorated particle approach offers a new structure-preserving paradigm for kinetic plasma simulation.

65M75, 70H05, 70G65↗