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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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At least 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Amorphous 2D Materials – A Novel Platform for Remote Epitaxy and Nanopatterned Epitaxy of III-V Semiconductors with Low Decomposition Temperatures

III-V semiconductor materials such as indium phosphide (InP) offer outstanding photonic properties that outperforms silicon, but the cost of these wafers is extremely expensive. Although reusing original wafers can effectively minimize the cost, current techniques for wafer recycling of these substrates add significant costs in fabrication, nullifying the cost savings by reusing the wafers. Besides, unlike other III-V materials such as gallium arsenide (GaAs), commonly used epitaxial lift-off method for wafer recycling is not well studied for materials like InP due to lack of lattice-matched sacrificial layers, which makes reusing these wafers more difficult. Remote epitaxy and nanopatterned epitaxy are newly discovered methods that enable single-crystal growth of III-V semiconductor thin films and easy exfoliation of these grown films, thus promising for a new cost-effective pathway of reusing wafers. However, previous methods of transferring two-dimensional (2D) materials, which use polymethyl methacrylate (PMMA) or metal stressor layers to transfer 2D materials grown on foreign substrates like copper (Cu) or silicon carbide (SiC), introduce defects and damages on the 2D layer and/or substrates during the transfer process. Remote epitaxial and nanopatterned epitaxial films grown on the damaged 2D layer/substrate suffer from lower crystal quality and imperfect exfoliation, which undermines wafer reusability and device performance. Here we report the MBE growth of amorphous boron nitride (a-BN) on InP wafers at low temperature that enabled improved quality of remote epitaxial and nanopatterned epitaxial films and their perfect exfoliation. We show fully covered a-BN on InP substrates despite their low decomposition temperatures. The surface of a-BN coated InP substrate remains smooth with a RMS roughness of around 3Â. We also demonstrate 100% coverage of single-crystal InP thin films grown on a-BN, with the film's quality significantly improved compared to the case of transferred 2D materials. In addition, the growth and exfoliation were successfully repeated multiple times, proving the feasibility for InP wafer recycling. Through this low temperature MBE growth approach with remote epitaxy and nanopatterned epitaxy, we successfully demonstrate large-scale flexible thin film exfoliation and recycling of InP substrates, which will lead to new opportunities in InP thin film-based photonics and novel heterostructures with significantly reduced cost.

Lu, Kuangye↗
DOE OSTI2022

Amorphous 2D Materials – A Novel Platform for Remote Epitaxy and Nanopatterned Epitaxy of III-V Semiconductors with Low Decomposition Temperatures

III-V semiconductor materials such as indium phosphide (InP) offer outstanding photonic properties that outperforms silicon, but the cost of these wafers is extremely expensive. Although reusing original wafers can effectively minimize the cost, current techniques for wafer recycling of these substrates add significant costs in fabrication, nullifying the cost savings by reusing the wafers. Besides, unlike other III-V materials such as gallium arsenide (GaAs), commonly used epitaxial lift-off method for wafer recycling is not well studied for materials like InP due to lack of lattice-matched sacrificial layers, which makes reusing these wafers more difficult. Remote epitaxy and nanopatterned epitaxy are newly discovered methods that enable single-crystal growth of III-V semiconductor thin films and easy exfoliation of these grown films, thus promising for a new cost-effective pathway of reusing wafers. However, previous methods of transferring two-dimensional (2D) materials, which use polymethyl methacrylate (PMMA) or metal stressor layers to transfer 2D materials grown on foreign substrates like copper (Cu) or silicon carbide (SiC), introduce defects and damages on the 2D layer and/or substrates during the transfer process. Remote epitaxial and nanopatterned epitaxial films grown on the damaged 2D layer/substrate suffer from lower crystal quality and imperfect exfoliation, which undermines wafer reusability and device performance. Here we report the MBE growth of amorphous boron nitride (a-BN) on InP wafers at low temperature that enabled improved quality of remote epitaxial and nanopatterned epitaxial films and their perfect exfoliation. We show fully covered a-BN on InP substrates despite their low decomposition temperatures. The surface of a-BN coated InP substrate remains smooth with a RMS roughness of around 3Å. We also demonstrate 100% coverage of single-crystal InP thin films grown on a-BN, with the film's quality significantly improved compared to the case of transferred 2D materials. In addition, the growth and exfoliation were successfully repeated multiple times, proving the feasibility for InP wafer recycling. Through this low temperature MBE growth approach with remote epitaxy and nanopatterned epitaxy, we successfully demonstrate large-scale flexible thin film exfoliation and recycling of InP substrates, which will lead to new opportunities in InP thin film-based photonics and novel heterostructures with significantly reduced cost.

Lu, Kuangye↗
DOE OSTI2021

A Detailed Characterization of HR 8799's Debris Disk with ALMA in Band 7

The exoplanetary system of HR 8799 is one of the rare systems in which multiple planets have been directly imaged. Its architecture is strikingly similar to that of the solar system, with the four imaged giant planets surrounding a warm dust belt analogous to the Asteroid Belt, and themselves being surrounded by a cold dust belt analog to the Kuiper Belt. Previous observations of this cold belt with ALMA in Band 6 (1.3 mm) revealed its inner edge, but analyses of the data differ on its precise location. It was therefore unclear whether or not the outermost planet HR 8799 b was dynamically sculpting it. We present here new ALMA observations of this debris disk in Band 7 (340 GHz, 880 μm). These are the most detailed observations of this disk obtained so far, with a resolution of 1″ (40 au) and sensitivity of 9.8 μJy beam{sup −1}, which allowed us to recover the disk structure with high confidence. In order to constrain the disk morphology, we fit its emission using radiative transfer models combined with a Markov Chain Monte Carlo procedure. We find that this disk cannot be adequately represented by a single power law with sharp edges. It exhibits a smoothly rising inner edge and smoothly falling outer edge, with a peak in between, as expected from a disk that contains a high-eccentricity component, hence confirming previous findings. Whether this excited population and inner edge shape stem from the presence of an additional planet remains, however, an open question.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Experimental investigation of surface roughness/wettability pattern effect on crystallization fouling over falling-film flow

In many industries, including desalination, scaling in heat exchangers is a persistent issue, and most methods of scaling control involve environmentally hazardous chemical additives. Exploiting the effects of surface features and flow-imposed shear on salt deposition might introduce a new approach to scale management, opening the possibility of self-cleaning surfaces. In this work, we experimentally explore surface roughness and wettability patterns interaction with salt deposition and flow shear. Heat transfer and scale mass deposition on flat surfaces are measured during thin-film evaporation of calcium sulfate solution. A wide range of surface roughness (0.027–2.66 μm) is studied at fixed flow and heat flux conditions. Due to improved mixing, heat transfer is enhanced with rougher surfaces initially; however, degrades more quickly than smoother surfaces. Following a period of initial mass deposition fluctuation, a steady scaling stage is observed, with rough surfaces scaling more than smooth surfaces. Wettability patterned surfaces can suppress crystal nucleation without sacrificing overall surface wetting, resulting in antifouling performance and heat transfer enhancement. Scale mass deposition on a patterned surface is reduced by 60 %, and 27 % heat transfer improvement over the baseline surface is found. Furthermore, this study provides guidance to surface manipulation for heat transfer improvement and fouling mitigation.

42 ENGINEERING↗
DOE OSTI2021

Preliminary Analysis of Source Physics Experiment Explosion-Triggered Microseismicity Using the Back-Projection Method

A series of four chemical explosions were detonated in a deep borehole within the Yucca Flat Dry Alluvium Geology (DAG) at the Nevada National Security Site between 2018 and 2019. The two larger chemical explosions of 50 tons (DAG-2) and 10 tons (DAG-4) TNT equivalent yield triggered energetic aftershock sequences numbering 1392 and 347 microearthquakes, respectively, within the first 10 days. No significant aftershock activity was observed for the two smaller 1-ton explosions (DAG-1 and DAG-3). Here, we used a back-projection method based on travel-time migration and stacking of signal-to-noise ratio traces to detect, associate and locate aftershocks from a subset of 22-geophones within a larger 2 urn:x-wiley:21699313:media:jgrb54910:jgrb54910-math-0001 2 km seismic array surrounding the borehole. The aftershocks located within 300 m of the borehole and the depths were above the working points of 300 and 50 m depths of DAG-2 and DAG-4, respectively, ruling out triggering slip on geologic faults or disturbances beneath neighboring collapse craters. DAG-2 and DAG-4 aftershocks decayed at similar rates, with power-law exponents of p = 1.48 and p = 1.49, respectively. These decay rates are comparable to aftershocks sequences triggered by earthquakes and historical nuclear explosions at Yucca Flat. A smooth power-law aftershock decay within the first 10 days suggests a triggering mechanism from explosion generated stress relaxation due to the diffusion of high gas pressures in the cavity and radial fractures. A more random and episodic aftershock rate would be expected due to cavity collapse or falling rubble in chimney formation.

58 GEOSCIENCES↗
DOE OSTI2022

Enhancing Surface Finish of Additively Manufactured 316L Stainless Steel with Pulse/Pulse Reverse Electropolishing

To improve the reliable integration of additively manufactured (AM) metal components, there is an urgent need for surface finishing methods capable of processing rough, “as-printed” surfaces. Here, we present a new and scalable electropolishing (EP) technique for use on AM 316L stainless steel (SS) that is capable of achieving a surface roughness equivalent to a machined finish, with arithmetic mean heights (S a ) as low as 1.0 µm. This technique utilizes the sequential application of a new, NaCl/H 2 O pulse/pulse reverse (P/PR) EP step along with a conventional DC (direct current) EP step, where P/PR expands the capability of EP by removing roughness features > 1 µm, which has been previously unattainable with DC EP alone without substantial material removal. This is achieved by independently varying pulse parameters, such as pulse width and height, allowing more control over electrodynamic processes at the part-electrolyte interface. Additionally, P/PR EP resulted in higher smoothing efficiency, where a higher degree of smoothing was achieved with less material removal when compared with conventional DC EP alone. This minimizes unwanted change in geometry from excessive metal dissolution.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Learning together: Towards foundation models for machine learning interatomic potentials with meta-learning

Abstract The development of machine learning models has led to an abundance of datasets containing quantum mechanical (QM) calculations for molecular and material systems. However, traditional training methods for machine learning models are unable to leverage the plethora of data available as they require that each dataset be generated using the same QM method. Taking machine learning interatomic potentials (MLIPs) as an example, we show that meta-learning techniques, a recent advancement from the machine learning community, can be used to fit multiple levels of QM theory in the same training process. Meta-learning changes the training procedure to learn a representation that can be easily re-trained to new tasks with small amounts of data. We then demonstrate that meta-learning enables simultaneously training to multiple large organic molecule datasets. As a proof of concept, we examine the performance of a MLIP refit to a small drug-like molecule and show that pre-training potentials to multiple levels of theory with meta-learning improves performance. This difference in performance can be seen both in the reduced error and in the improved smoothness of the potential energy surface produced. We therefore show that meta-learning can utilize existing datasets with inconsistent QM levels of theory to produce models that are better at specializing to new datasets. This opens new routes for creating pre-trained, foundation models for interatomic potentials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Effect of 3D-printed surface textures on wear mechanism in 3-body abrasion of soil

This study systematically investigates the enhancement of wear resistance in 3D printed surface textures through both experimental and theoretical approaches. Three distinct surface morphologies (Smooth Surface, Surface with uniformly distributed Pits, and Surface with uniformly distributed Bumps) were fabricated using High-Impact Polystyrene, where the meso-scale textures were precisely controlled through the 3D printing process. Wear behavior was evaluated using a 3-body wear tester in an abrasive particle environment, analyzing the influence of surface textures under various operating conditions. Systematic wear tests revealed that optimally designed surface textures achieved a remarkable 77 % reduction in wear compared to the worst-performing sample. The wear mechanisms were comprehensively characterized through weight loss measurements, Scanning Electron Microscopy (SEM), and Energy Dispersive Spectroscopy (EDS) analyses, elucidating the surface morphology changes and their interaction with wear particles. Notably, the study identified how the geometric characteristics of surface textures influence the movement of wear particles and the distribution of contact stresses. Discrete element method simulations corroborated the experimental findings, providing theoretical validation for the enhanced wear resistance of the optimal structure. The high correlation between simulated wear patterns and experimental results validates the reliability of the proposed design methodology. In conclusion, these results demonstrate that 3D printed surface texturing offers a cost-effective and scalable approach to significantly improve wear resistance in engineering applications, presenting a practical alternative to conventional, high-cost surface engineering methods.

3-body abrasion↗
DOE OSTI2026

Stochastic Microgrid Scheduling With Chance‐Constrained Resilience Consideration

Traditionally, it is assumed that microgrids transition seamlessly from grid‐connected operation to islanded mode in the event of sudden main grid outages. In reality, the islanding process, especially unintentional islanding, is rarely seamless. Instead, it is subject to voltage and frequency fluctuations caused by the instantaneous disconnection of the point of common coupling (PCC) switch, variations in loads and renewable generation output and even the protection tripping of distributed energy resources (DERs). To mitigate these fluctuations and facilitate a smooth islanding process, we propose a stochastic microgrid scheduling model that incorporates chance‐constrained resilience measures. Specifically, the resilience measure is defined as the probability of successful islanding (PSI), that is, the probability that a microgrid can mitigate the generation‐demand imbalance caused by the disconnection of the PCC switch, variations in load and renewable generation and DER tripping. This measure is modelled using chance constraints. Unlike existing reliability and resilience indices, which typically neglect the possibility of microgrid/DER failure under extreme events and assume their survival while primarily focussing on reducing impact duration or magnitude, the proposed PSI‐based framework explicitly addresses microgrid and DER survival during the islanding transition. The formulated nonlinear chance constraints are approximated using a multiinterval approach and equivalently represented as a mixed‐integer linear programming (MILP) formulation. Case study results validate the proposed method, showing that the PSI estimation error is reduced to less than 8%, compared to approximately 28% with existing methods. Various sensitivity analyses on the DER tripping rate and PSI settings were performed to validate the robustness of the proposed method. In particular, the necessity of accounting for DER tripping in the PSI calculation was demonstrated.

chance constrained optimization↗
DOE OSTI2024

Planarizing Spalled GaAs(100) Surfaces by MOVPE Growth

III-V photovoltaic devices have demonstrated exceptional performance across various applications, with controlled crystal fracturing, known as controlled spalling, emerging as a promising method to reduce costs by enabling substrate reuse. Spalling GaAs(100) substrates, a commonly used substrate in III-V photovoltaics, results in faceted ridges that must be planarized to grow high-quality photovoltaic devices. Here, in this study, we demonstrate that a GaAs(100) wafer offcut toward [$0\bar{11}$] and spalled toward [$011$] can be efficiently planarized by growing C:GaAs by metal-organic vapor phase epitaxy (MOVPE) on the surface, with up to 95% of the nominally deposited material used to fill the valleys between ridges. We find that reducing the offcut to 2° enhances the planarizing capability of C:GaAs. A surface morphology model indicates that the density of surface dangling bonds significantly influences the growth evolution of undoped GaAs surfaces. In contrast, the model suggests that the effectiveness of C:GaAs as a smoothing layer stems from modifying the atomic surface structure and, consequently, the associated sticking coefficients of the facets, which can alter the evolution of surface morphology. Our findings provide guidelines for the epitaxial planarization of semiconductor surfaces and improve the understanding of MOVPE growth on nonplanar surfaces.

14 SOLAR ENERGY↗
DOE OSTI2024

Warm boundary-layer cloud properties and cloud susceptibilities product at the ARM ENA observatory

Cloud liquid water path, albedo, and cloud fraction susceptibilities for marine warm boundary-layer clouds are quantified using the Meteosat retrieved cloud microphysical properties at the ARM Eastern North Atlantic (ENA) observatory in the Azores. The Meteosat cloud retrievals are based on the methods applied by the Clouds and the Earth’s Radiant Energy System (CERES) project, which are specifically tailored to support the ARM user facility over the ARM ground-based observation sites (enavisstpx2dm11minnisX1.c1). Cloud susceptibility is quantified as the slope between cloud properties and Nd within a 1-degree-by-1-degree grid box at each satellite time step using a least-square regression. To reduce uncertainties associated with the adiabatic assumption in the Nd retrieval, for each cloud object, we exclude cloudy pixels at the cloud edge, defined as those adjacent to cloud-free pixels. To minimize influence of cloud heterogeneity and co-variability on the retrieved cloud susceptibility, cloud properties are averaged to 0.25-degree resolution using the 3-km pixel-level retrieval, and the 1-degree cloud susceptibilities are estimated using the smoothed data. Cloud type classification is applied to distinct cloud object, labeling all contiguous cloudy pixels. Marine warm boundary-layer clouds are defined as clouds with 90% of cloud tops below 3km, and Meteosat retrieved cloud phase as liquid.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

A Boundary Topology Optimization Approach for Lightweighting Electric Machines Inspired by Additive Manufacturing

Minimizing the mass in electric machines while maintaining superior performance has become a new requirement for the advancement of drivetrains used in wind energy and electric mobility. Topology optimization for light-weighting electric machines using traditional approaches typically explore a restricted design space allowed by standard parametrizable geometry and manufacturing, while advanced methods like cell-based density approaches suffer from a lack of robust manufacturability constraints during the optimization process. To overcome these drawbacks, we explore a grid-independent, boundary TO where the outer shape of the magnet is parameterized using Bezier curves. We conduct a design of experiments (DOE) to study the effect of different magnet shapes on machine performance by varying the control points on the Bezier curves. A machine-learning based surrogate model is constructed using the data from the DOE to quantify the relationship between the control points, air-gap torque and mass. The control points are then optimized to maximize the torque density. The approach is used for minimizing electrical steel mass in the IEA-15MW radial flux direct-drive wind turbine generator. The free-from boundary TO resulted in smooth and concise shapes that can be easily additively manufactured with upto 20-ton reduction in electrical steel mass.

additive manufacturing↗
DOE OSTI2025

Assessing the difficulty of capturing the distribution function of neutrinos in neutron star merger simulations

The collision of two neutron stars is a rich source of information about nuclear physics. In particular, the kilonova signal following a merger can help us elucidate the role of neutron stars in nucleosynthesis, and informs us about the properties of matter above nuclear saturation. Approximate modeling of neutrinos remains an important limitation to our ability to make predictions for these observables. Part of the problem is the fermionic nature of neutrinos. By the exclusion principle, the expected value 𝑓 𝜈 for the number of neutrinos in a quantum state is at most 1. Any process producing neutrinos is suppressed by a blocking factor (1 −𝑓 𝜈 ). Recent simulations focused on neutrino physics mostly use a gray two-moment scheme to evolve neutrinos. This evolves integrals of 𝑓 𝜈 over momentum space, preventing direct calculations of blocking factors. Monte Carlo methods may be an attractive alternative, providing access to the full distribution of neutrinos. Their current implementation is, however, inadequate to estimate 𝑓 𝜈 : in our most recent simulations, a single Monte Carlo packet causes, in the worst cases, estimates of 𝑓 𝜈 to jump from 𝑓 𝜈 =0 to 𝑓 𝜈 ∼10 5 . While this is concerning, this brazen violation of the fermionic nature of neutrinos has been largely inconsequential, as the interactions used in simulations avoid direct calculations of 𝑓 𝜈 . We are, however, reaching a level of modeling at which this problem can no longer be ignored. Here, we discuss the relatively simple origin of this issue. We then show that very rough estimates of 𝑓 𝜈 can in theory be obtained in merger simulations, but that they will require a combination of unintuitive weighting schemes for Monte Carlo packets and smoothing of the neutrino distribution at coarser resolution than what the merger simulation uses.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

A New Shape Optimization Approach for Lightweighting Electric Machines Inspired by Additive Manufacturing

Minimizing the mass in electric machines while maintaining superior performance is a new requirement for the advancement of drivetrains used in wind energy and electric mobility. Topology optimization (TO) for lightweighting electric machines using traditional approaches typically explores a restricted design space allowed by standard parametrizable geometry and manufacturing, while advanced methods, such as cell-based density approaches, suffer from a lack of robust manufacturability constraints during the optimization process. To overcome these drawbacks, we explore a grid-independent, boundary optimization where the outer shape of the magnet is parameterized using Bezier curves. We conduct a design of experiments (DOE) to study the effect of different magnet shapes on machine performance by varying the control points on the Bezier curves. A machine-learning-based surrogate model is constructed using the data from the DOE to quantify the relationship between the control points, air-gap torque, and mass. The control points are then optimized to maximize the torque density. The approach is used for minimizing electrical steel mass in the International Energy Agency (IEA) 15-MW radial flux direct-drive wind turbine generator. The new approach to shape optimization resulted in smooth and concise shapes that can be easily additively manufactured with up to a 20-ton reduction in electrical steel mass.

additive manufacturing↗
DOE OSTI2022

A New Shape Optimization Approach for Lightweighting Electric Machines Inspired by Additive Manufacturing: Preprint

Minimizing the mass in electric machines while maintaining superior performance is a new requirement for the advancement of drivetrains used in wind energy and electric mobility. Topology optimization (TO) for lightweighting electric machines using traditional approaches typically explores a restricted design space allowed by standard parametrizable geometry and manufacturing, while advanced methods, such as cell-based density approaches, suffer from a lack of robust manufacturability constraints during the optimization process. To overcome these drawbacks, we explore a grid-independent, boundary TO where the outer shape of the magnet is parameterized using Bezier curves. We conduct a design of experiments (DOE) to study the effect of different magnet shapes on machine performance by varying the control points on the Bezier curves. A machine-learning-based surrogate model is constructed using the data from the DOE to quantify the relationship between the control points, air-gap torque, and mass. The control points are then optimized to maximize the torque density. The approach is used for minimizing electrical steel mass in the International Energy Agency (IEA) 15-MW radial flux direct-drive wind turbine generator. The free-form boundary TO resulted in smooth and concise shapes that can be easily additively manufactured with up to a 20-ton reduction in electrical steel mass.

additive manufacturing↗
DOE OSTI2024

"Hierarchical Speed Planner for Automated Vehicles: A Framework for Lagrangian Variable Speed Limit in Mixed Autonomy Traffic"

This paper introduces a novel control framework for Lagrangian variable speed limits in hybrid traffic flow environments utilizing automated vehicles (AVs). The framework was validated using a fleet of 100 connected automated vehicles as part of the largest coordinated open-road test designed to smooth traffic flow. The framework includes two main components: a high-level controller deployed on the server side, named Speed Planner, and low-level controllers called vehicle controllers deployed on the vehicle side. The Speed Planner designs and updates target speeds for the vehicle controllers based on real-time Traffic State Estimation (TSE) [1]. The Speed Planner comprises two modules: a TSE enhancement module and a target speed design module. The TSE enhancement module is designed to minimize the effects of inherent latency in the received traffic information and to improve the spatial and temporal resolution of the input traffic data. The target speed design module generates target speed profiles with the goal of improving traffic flow. The vehicle controllers are designed to track the target speed meanwhile responding to the surrounding situation. The numerical simulation indicates the performance of the proposed method: the bottleneck throughput has increased by 5.01%, and the speed standard deviation has been reduced by a significant 34.36%. We further showcase an operational study with a description of how the controller was implemented on a field-test with 100 AVs and its comprehensive effects on the traffic flow.

Wang, Han↗
DOE OSTI2020

Adaptive Activation Functions Accelerate Convergence in Deep and Physics-informed Neural Networks

We employ adaptive activation functions for regression in deep and physics-informed neural networks (PINNs) to approximate smooth and discontinuous functions as well as solutions of linear and nonlinear partial differential equations. In particular, we solve the nonlinear Klein-Gordon equation, which has smooth solutions, the nonlinear Burgers equation, which can admit high gradient solutions, and the Helmholtz equation. We introduce a scalable hyper-parameter in the activation function, which can be optimized to achieve best performance of the network as it changes dynamically the topology of the loss function involved in the optimization process. The adaptive activation function has better learning capabilities than the traditional one (fixed activation) as it improves greatly the convergence rate, especially at early training, as well as the solution accuracy. To better understand the learning process, we plot the neural network solution in the frequency domain to examine how the network captures successively different frequency bands present in the solution. We consider both forward problems, where the approximate solutions are obtained, as well as inverse problems, where parameters involved in the governing equation are identified. Our simulation results show that the proposed method is a very simple and effective approach to increase the efficiency, robustness and accuracy of the neural network approximation of nonlinear functions as well as solutions of partial differential equations, especially for forward problems. We theoretically prove that in the proposed method, gradient descent algorithms are not attracted to suboptimal critical points or local minima.

machine leaning, Bad minima, Inverse problems, Phy↗
DOE OSTI2025

High-order limiting methods using maximum principle bounds derived from the Boltzmann equation I: Euler equations

The use of limiting methods for high-order numerical approximations of hyperbolic conservation laws generally requires defining an admissible region/bounds for the solution. In this work, we present a novel approach for computing solution bounds and limiting for the Euler equations through the kinetic representation provided by the Boltzmann equation, which allows for extending limiters designed for linear advection directly to the Euler equations. Given an arbitrary set of solution values to compute bounds over (e.g., numerical stencil) and a desired linear advection limiter, the proposed approach yields an analytic expression for the admissible region of particle distribution function values, which may be numerically integrated to yield a set of bounds for the density, momentum, and total energy. Further, these solution bounds are shown to preserve positivity of density/pressure/internal energy and, when paired with a limiting technique, can robustly resolve strong discontinuities while recovering high-order accuracy in smooth regions without any ad hoc corrections (e.g., relaxing the bounds). This approach is demonstrated in the context of an explicit unstructured high-order discontinuous Galerkin/flux reconstruction scheme for a variety of difficult problems in gas dynamics, including cases with extreme shocks and shock-vortex interactions. Furthermore, this work presents a foundation for limiting techniques for more complex macroscopic governing equations that can be derived from an underlying kinetic representation for which admissible solution bounds are not well-understood.

42 ENGINEERING↗