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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 523 records · Page 29
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Geophysical monitoring using active seismic techniques at the Citronelle Alabama CO 2 storage demonstration site

Between August 2012 and September 2014, about 114,000 metric tonnes of CO 2 was captured from the coal-fired Plant Barry Power Station at Bucks Alabama and injected into the Paluxy Formation above the oil pool in the southeast unit of the Citronelle Oilfield. Various monitoring methods were deployed at land surface and in project wells to measure system performance, comply with permit requirements and test new and innovative monitoring tools. The monitoring program relied heavily on active seismic methods for subsurface imaging of geologic structure and time-lapse seismic techniques to track the CO 2 migration in the injection interval. Both conventional geophone/hydrophone and fiber-optic based Distributed Acoustic Sensing (DAS) arrays were deployed and tested, allowing a side by side comparison of the equipment and techniques. Geophysical imaging of the subsurface was successful using DAS in the offset vertical seismic profile (OVSP) survey configuration. A high resolution OVSP image of the subsurface was obtained in 2014 with DAS, which exceeded project expectations in comparison to a lower resolution image obtained in 2012 using a conventional 80-level geophone array. A time-lapse image of the redistribution of CO 2 after injection ended in September 2014 was obtained with two DAS OVSP surveys from June 2014 and December 2015, thus successfully demonstrating its proof-of-concept. Unfortunately, a pre-injection baseline survey with DAS, which was in its initial stage of technology development in 2012, did not have sufficient quality for use, making it difficult to interpret the acquired DAS time-lapse difference. Additional research in this area has since demonstrated the utility of time-lapse DAS OVSP. DAS data were also acquired during a cross-well seismic survey conducted in 2014. Unfortunately, the DAS technique was not success in the cross-well survey configuration because the system noise level was too high in the crosswell frequency output range (100–1200 Hz) of the piezoelectric source (increasing by a factor of ten compared to VSP frequency band). Additionally, the cross-well geometry causes sub-horizontal (broadside) incidence on the vertical DAS fiber cable, which is known to be problematic. Current research is focused on improving the DAS cable response to broadside acoustic energy. Time-lapse seismic surveys using commercially available conventional arrays were also acquired. In contrast to the DAS acquired data, the cross-well seismic results obtained with the conventional array was highly successful and clearly showed the CO 2 remained in zone at the end of injection. Time-lapse differencing of the OSVP surveys acquired with the conventional arrays proved to be inconclusive. Finally, changes in wellbore conditions between surveys and unavoidable changes in equipment (the array used for the baseline survey was retired) affected data quality, making it difficult to interpret the OVSP results.

58 GEOSCIENCES↗
DOE OSTI2021

A coupled thermo-hydro-mechanical model for simulating leakoff-dominated hydraulic fracturing with application to geologic carbon storage

A potential risk of injecting CO2 into storage reservoirs with marginal permeability (≲ 10 mD (1 mD = 10 –15 m 2 )) is that commercial injection rates could induce fracturing of the reservoir and/or the caprock. Such fracturing is essentially fluid-driven fracturing in the leakoff-dominated regime. Recent studies suggested that fracturing, if contained within the lower portion of the caprock complex, could substantially improve the injectivity without compromising the overall seal integrity. Modeling this phenomenon entails complex coupled interactions among the fluids, the fracture, the reservoir, and the caprock. Here, we develop a simple method to capture all these interplays in high fidelity by sequentially coupling a hydraulic fracturing module with a coupled thermal-hydrological-mechanical (THM) model for nonisothermal multiphase flow. The model was made numerically tractable by taking advantage of self-stabilizing features of leakoff-dominated fracturing. The model is validated against the PKN solution in the leakoff-dominated regime. Moreover, we employ the model to study thermo-poromechanical responses of a fluid-driven fracture in a field-scale carbon storage reservoir that is loosely based on the In Salah project's Krechba reservoir. The model reveals complex yet intriguing behaviors of the reservoir-caprock-fluid system with fracturing induced by cold CO 2 injection. We also study the effects of the in situ stress contrast between the reservoir and caprock and thermal contraction on the vertical containment of the fracture. The proposed model proves effective in simulating practical problems on length and time scales relevant to geological carbon storage.

58 GEOSCIENCES↗
DOE OSTI2024

Can section 45Q tax credit foster decarbonization? A case study of geologic carbon storage at Acid Gas Injection wells in the Permian Basin

Carbon capture, utilization, and storage (CCUS) is an important pathway for meeting climate mitigation goals. While the economic viability of CCUS is well understood, previous studies do not evaluate the economic feasibility of carbon capture and storage (CCS) in the Permian Basin specifically regarding the new Section 45Q tax credits. We developed a technoeconomic analysis method, evaluated the economic feasibility of CCS at the acid gas injection (AGI) wells, and assessed the implication of Section 45Q tax credits for CCS at the AGIs. We find that the compressors, well depth, and the permit and monitoring costs drive the facility costs. Compressors are the predominant contributors to capital and operating expenditure driving the levelized cost of CO 2 storage. Strategic cost reduction measures identified include 1) sourcing of low-cost electricity and 2) optimizing operational efficiency in well operations. In evaluating the impact of the tax credits on CCS projects, facility scale proved decisive. We found that facilities with an annual injection rate exceeding 10,000 MT storage capacity demonstrate economic viability contingent upon the procurement of inputs at the least cost. The new construction of AGI wells were found to be economically viable at a storage capacity of 100,000 MT. The basin is heavily focused on CCUS (tax credit – $\$$65/MT CO 2 ), which overshadows CCS ($\$$85/MT CO 2 ) opportunities. Balancing the dual objectives of CCS and CCUS requires planning and coordination for optimal resource and pore space utilization to attain the basin's decarbonization potential. We also found that CCS on AGI is a lower cost CCS option as compared to CCS on other industries.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2020

Stereoscopic detection of hot spots in superfluid 4 He (He II) for accelerator-cavity diagnosis

Superconducting radio-frequency (SRF) cavities cooled by superfluid 4He (He II) are building blocks of many modern particle accelerators due to their high quality factor. However, Joule heating from sub-millimeter surface defects on cavities can lead to cavity quenching, which limits the maximum acceleration gradient of the accelerators. Developing a non-contacting detection technology to accurately locate these surface hot spots is the key to improve the performance of SRF cavities and hence the accelerators. In a recent proof-of-concept experiment, we demonstrated that a molecular tagging velocimetry (MTV) technique based on the tracking of a He molecular tracer line created nearby a surface hot spot in He II can be utilized to locate the hot spot. In order to make this technique practically useful, here we describe our further development of a stereoscopic MTV setup for tracking the tracer line’s motion in three-dimensional (3D) space. We simulate a quench spot by applying a transient voltage pulse to a small heater mounted on a substrate plate. Images of the drifted tracer line, taken with two cameras from orthogonal directions, are used to reconstruct the line profile in 3D space. Here, a new algorithm for analyzing the 3D line profile is developed, which incorporates the finite size effect of the heater. We show that the center location of the heater can be reproduced on the substrate surface with an uncertainty of only a few hundred microns, thereby proving the practicability of this method.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Hierarchical Bayesian modeling for Inverse Uncertainty Quantification of system thermal-hydraulics code using critical flow experimental data

The best estimate plus uncertainty methodology in nuclear system thermal-hydraulic studies necessitates a comprehensive understanding of uncertainties in system code predictions. The forward uncertainty quantification (UQ) process involves the propagation of input uncertainties through the computational models to obtain uncertainties in the outputs. To this end, achieving an accurate estimation of input uncertainties is important, which is the focus of inverse UQ (IUQ). Traditionally, research in Bayesian IUQ within the nuclear engineering domain has largely relied on single-level Bayesian inference. While being effective for relatively small datasets, this approach encounters limitations for cases with large datasets. The use of a single-level model may prove inefficient, as the resultant posterior distributions can significantly differ when distinct subsets of data are employed. To address this issue, we employ an hierarchical Bayesian model for IUQ. Furthermore, this approach involves organizing observations into different groups based on the test conditions, thereby accommodating varying calibration parameters across these distinct groups. In this study, we developed and implemented a hierarchical Bayesian IUQ method to consider the grouping effect of critical flow measurement data from various geometries. Comparing the outcomes of IUQ under different selections of test data using hierarchical Bayesian IUQ against those obtained from single-level Bayesian IUQ, the forward propagation of hierarchical Bayesian IUQ results demonstrates a notably improved agreement with the experimental data.

42 ENGINEERING↗
DOE OSTI2026

Facile synthesis of Co(OH)2 nanoneedle arrays grown on stainless steel for industrial electrochemical oxygen evolution reaction

The electrochemical oxygen evolution reaction (OER) is a critical half-reaction in a variety of energy conversion and storage applications, however, OER suffers from sluggish kinetics due to the four proton-electron transfer processes. To remedy this, interfacial engineering proves an effective strategy to design high active OER catalysts. Herein, we report a facile synthesis of Co(OH)2 nanoneedle (Co-NN) arrays grown on stainless steel (SS) via a one-step hydrothermal reaction, and the resultant impressive OER performance. Particularly, the Co-NN/SS needs 267, 307, and 576 mV overpotentials to reach 10, 100, and 1000 mA cm−2 in 1 M KOH & room temperature, and the overpotentials drop to 199, 257, and 283 mV to achieve the same current densities in 30 wt% KOH & 80 °C. Additionally, an alkaline water electrolysis (AWE) cell coupled with Co-NN/SS anode and PtRu/NiMo cathode only requires 1.65 and 1.73 V iR-free cell voltage to reach 1.0 and 2.0 A cm−2, respectively. The sterling OER performance could be attributed to four possible reasons, the Fe in SS surface tailoring the electronic properties of Co(OH)2, the mixed metal oxides on SS surface accelerating surface reconstruction of Co(OH)2 nanoneedles into CoOOH active species, a Ni-rich surface layer formation cooperatively boosting the OER activity, and a local electric field effect concentrating reactants on the tip surface and accelerating the mass transfer. This work provides a facile approach for synthesizing highly efficient OER catalysts for industrial applications by interfacial engineering.

Lyu, Xiang [ORNL] (ORCID:0000000208673248)↗
DOE OSTI2021

A hierarchical gray-box dynamic modeling methodology for direct-expansion cooling systems to support control stability analysis; Méthodologie de modélisation dynamique hiérarchique de type boîte grise pour les systèmes de refroidissement à détente directe afin de soutenir l'analyse de stabilité de la commande

In this paper, a gray-box dynamic modeling approach for direct-expansion cooling systems is presented. The overall approach incorporates a multi-stage training procedure that consists of 1) identification of component sub-models from quasi-steady-state performance data, 2) system model integration with estimation of refrigerant charge and 3) fine tuning of thermal capacitances of the evaporator and condenser to capture the system dynamic responses. Compared to traditional physics-based models, the proposed modeling approach has advantages including reduced engineering efforts in the model development phase, improved computational efficiency and enhanced prediction accuracy. The modeling method was validated using a 3-ton variable-speed heat pump and proved to be capable of accurately predicting the system transient behaviors over a wide range of operating conditions. The established dynamic model was then applied for control stability analysis, with a specific goal of determining a proper control execution time step. The case study results showed that the stable control execution time step could change significantly, from 3 sec to 19 sec, as the operating conditions and control settings vary, and a proper selection of the execution time step is critical to ensure stable and reliable operations.

42 ENGINEERING↗
DOE OSTI2022

A review on nearly isothermal compression technology

Compressors can be described as the heart of a vapor compression refrigeration system, circulating the working fluid in the system. Significant benefits can be gained from improving its efficiency since energy consumption is responsible for almost the entire system's power input. An effort has been made to achieve isothermal compression through liquid refrigerant injection or inter-stage cooling in refrigeration systems. In recent years, much effort has been invested into isothermal compression technology for air compressors or compressed air energy storage systems with the rise of renewable energy. Here, this work has explored the advancements made in this area and categorized them to discuss the benefits, limitations, and tradeoffs. Evidently, increasing heat transfer area is a significant aid in improving heat transfer, resulting in better isothermal compression. However, liquid pistons open more avenues for this to be pursued, and therefore, are limited to air compression applications. In addition, water injection proved to be the most effective among the methods. Finally, there is a need for more experimental research on refrigeration applications and the field is still in its infancy.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2022

The role of lignin in the conversion of wheat straw to cellobionic acid by Neurospora crassa HL10

An engineered Neurospora crassa strain (HL10) naturally produces cellulases, cellobiose dehydrogenase (CDH), and heterologously expresses laccase. It can convert Avicel (cellulose) to cellobionic acid (cellobionate) without any enzyme addition at high yields. However, the addition of a catalytic amount of artificial redox mediators was required to achieve a high yield conversion. When a lignocellulosic substrate like wheat straw was used as the carbon source, it was found that adding exogenous artificial redox mediators did not improve cellobionate yield. We hypothesized that lignin and lignin degradation products were able to serve as redox mediators for the CDH-laccase conversion system. Experiments were designed to prove the hypothesis. When N. crassa HL10 was grown on Avicel, the addition of enzyme hydrolyzed lignin (EHL) can achieve a similar level of cellobionate production as with ABTS addition. The addition of EHL can increase the cellobionate production rate in the CDH-laccase bi-enzyme system using cellobiose as the substrate. The formation of lignin radicals, and the quenching of lignin radicals by reduced CDH, were verified by an electron paramagnetic resonance (EPR) experiment, providing further evidence that lignin radicals can serve as the electron acceptor of reduced CDH. Hence, lignocellulosic biomass is a self-sufficient substrate for the production of cellobionate. The conversion of the lignocellulosic substrate to cellobionate using N. crassa HL10 can be achieved without any exogenous enzyme addition or redox mediator addition.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Indirectly probing the structural change in ion-irradiated Zr-Based metallic glasses from small scale mechanical tests

Ion irradiation was applied to tailor the structural heterogeneities in Zr-based metallic glasses at room temperature. Experimental methods of X-ray diffraction, nanoindentation, and micropillar compression were conducted to examine the irradiation effects on their structural and mechanical property changes. It is found that the irradiated materials retained amorphous structure after room-temperature Ni ion irradiation. The reduction of elastic modulus and hardness measured by nanoindentation indicated the irradiation-induced mechanical degradation. A unified statistic model was employed to quantitatively predict the density and strength of irradiation defects, although their specific structural and physical nature is not explicitly included in this model. The transition of non-intersecting shear bands to multiple intersecting shear bands was observed on compression tests of irradiated micropillars with the increase of irradiation dose. Furthermore, the analysis of the displacement excursion of micropillar compression tests indicated a different deformation mode from the unirradiated state. These results from nanoindentation pop-in and micro-pillar compression tests suggested that irradiation eventually leads to a new state with different types and characteristics of structural heterogeneities from violent displacement cascades and non-equilibrium energy deposition/dissipation processes, which also proves ion irradiation as an effective method to tune the structure and mechanical properties of metallic glasses.

36 MATERIALS SCIENCE↗
DOE OSTI2022

The effect of 10 at.% Al addition on the hydrogen storage properties of the Ti 0.33 V 0.33 Nb 0.33 multi-principal element alloy

We report here a thorough study on the effect of 10 at.% Al addition into the ternary equimolar Ti 0.33 V 0.33 Nb 0.33 alloy on the hydrogen storage properties. Despite a decrease of the storage capacity by 20%, several other properties are enhanced by the presence of Al. The hydride formation is destabilized in the quaternary alloy as compared to the pristine ternary composition, as also confirmed by machine learning approach. The hydrogen desorption occurs at lower temperature in the Al-containing alloy relative to the initial material. Moreover, the Al presence improves the stability during hydrogen absorption/desorption cycling without significant loss of the capacity and phase segregation. Finally, this study proves that Al addition into multi-principal element alloys is a promising strategy for the design of novel materials for hydrogen storage.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Intrinsic Bulk Quantum Oscillations in a Bulk Unconventional Insulator SmB 6

The finding of bulk quantum oscillations in the Kondo insulator SmB 6 proved a considerable surprise. Subsequent measurements of bulk quantum oscillations in other correlated insulators including YbB 12 lent support to our discovery of a class of bulk unconventional insulators that host bulk quantum oscillations. Here we perform a series of experiments to examine evidence for the intrinsic character of bulk quantum oscillations in floating zone-grown single crystals of SmB 6 that have been the subject of our quantum oscillation studies. We present results of thermodynamic, transport, and composition analysis experiments on pristine floating zone-grown single crystals of SmB 6 and compare quantum oscillations with metallic LaB 6 and elemental aluminum. These results establish the intrinsic origin of quantum oscillations from the insulating bulk of floating zone-grown SmB 6 . The similarity of the Fermi surface in insulating SmB 6 with the conduction-electron Fermi surface in metallic hexaborides is at the heart of a theoretical mystery.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Development and characterization of an aerosol-generated multi-method analytical particle test material

Ceria (CeO 2 ) particles with low to ultra-low loading of nickel dopant were produced using an aerosol-based, droplet-to-particle synthesis via an in-line calcination technique. This aerosol-based synthesis method enables the production of particles with a monodisperse size distribution. These produced and well-characterized, multi-element, ceria-based particles demonstrate a material exemplar for multi-method analytical testing. They were prepared from a cerium nitrate feedstock where low loading nickel dopant was added at target Ni/(Ni + Ce) atomic percents of 1 %, 0.1 %, and 0.01 %, using a nickel nitrate spike. This methodology proved to produce ceria particles doped with a dynamic range of low to ultra-low loadings of nickel over a 24-h period, with consistent size distribution, morphology, and composition. The successful incorporation of nickel was demonstrated with bulk and single particle inductively coupled plasma mass spectroscopy and revealed notable particle-to-particle elemental homogeneity. X-ray photoelectron spectroscopy demonstrated the presence of a high concentration of nickel dopant incorporated preferentially toward the surface of the particles, and that this dopant aided oxidation of surface Ce(III) atoms to Ce(IV). These particle test materials were then validated through X-ray absorption near edge spectroscopy, comparing the ultra-low 0.01 % Ni and low 1 % Ni-doped ceria samples. This revealed a more-reduced oxidation state of the nickel with an increase in dopant concentration. Finally, this work demonstrates a synthesis and systematic characterization scheme to produce multi-method analytical test particulates.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Diurnal variation of the fair-weather atmospheric electric field in Binchuan, China

With the purpose of understanding the variation of fair-weather atmospheric electric field, the vertical component of atmospheric electric field (recorded as Ez) has been measured in the town Binchuan (25°50'N, 100°34'E, 1438.7 m asl) of Dali city, Yunnan, China from June 14, 2017 to December 1, 2020. Automatic measured visual range is used as a proxy of aerosol concentration. The mean diurnal variation curve of the fair-weather Ez in Binchuan, having two peaks occurred at around 9LT and 20LT, shows little correlation with the well-known Carnegie Curve and other two high-latitude sites' Curves. While strong negative correlation between fair-weather Ez and visual range is found, indicating the variation of fair-weather is dominated by aerosol concentration. The main source of aerosol concentration variation probably sunrise and sunset effect. We support our findings by comparing Ez, visual range with sunrise and sunset times. The peaks (troughs) of Ez (visual range) are proved to have weak correlations with anthropogenic pollution through comparing the Ez, visual range under workdays and holidays.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Dilute Pd-in-Au alloy RCT-SiO 2 catalysts for enhanced oxidative methanol coupling

Dilute alloy catalysts have the potential to enhance selectivity and activity for large-scale reactions. Highly dilute Pd-in-Au nanoparticle alloys partially embedded in porous silica (“raspberry colloid templated” (RCT)-SiO 2 ) prove to be robust and selective catalysts for oxidative coupling of methanol. Palladium concentrations in the bimetallic nanoparticles as low as ~3.4 at.% catalyze the production of methyl formate with a selectivity of ~95% at conversions of ~55%, whereas conversions are low (<10%) for ~1.7 at.% Pd-in-Au nanoparticle and pure Au nanoparticle catalysts. Fractional reaction orders for both CH 3 OH and O 2 measured for ~3.4 at.% Pd-in-Au nanoparticles supported on RCT-SiO 2 indicated a complex mechanism in which the sites for O 2 dissociation are not saturated. Optimal methyl formate production was found for an equimolar mixture. There is no conversion of methanol in the absence of O 2 between 360 and 450 K. Finally, all observations are consistent with a mechanism derived from model studies, requiring that clusters of Pd be available on the catalyst for O 2 dissociation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Identification and evolution of active sites in isomorphously substituted Fe-ZSM-5 catalysts for methane dehydroaromatization (MDA)

Methane dehydroaromatization (MDA) enables the catalytic conversion of methane into aromatics, mainly benzene, along with hydrogen, in a single-step process under non-oxidative conditions. In this study, we prepared a series of isomorphously substituted Fe-ZSM-5 catalysts with exclusively isolated or low-oligomerized sites up to 3.2% Fe weight loading by adding ethylenediaminetetraacetic acid (EDTA) to the crystallization gel. These catalysts exhibit no induction/activation period and a significantly higher maximum product yield compared to Fe/ZSM-5 catalysts prepared by the incipient wetness impregnation method and containing extensively aggregated FeOx. This investigation focuses on the evolution of Fe sites during the post-synthetic treatments. Most importantly, we demonstrate the quantitative relation between Fe site isolation and catalytic activity, proving that isolated or low-oligomerized Fe species at the exchange sites formed during post-synthetic retreatment are the active sites for methane activation.

02 PETROLEUM↗
DOE OSTI2023

Amorphous 1-D nanowires of calcium phosphate/pyrophosphate: A demonstration of oriented self-growth of amorphous minerals

Amorphous inorganic solids are traditionally isotropic, thus, it is believed that they only grow in a non-preferential way without the assistance of regulators, leading to the morphologies of nanospheres or irregular aggregates of nanoparticles. However, in the presence of (ortho)phosphate (Pi) and pyrophosphate ions (PPi) which have synergistic roles in biomineralization, the highly elongated amorphous nanowires (denoted ACPPNs) form in a regulator-free aqueous solution (without templates, additives, organics, etc). Based on thorough characterization and tracking of the formation process (e.g., Cryo-TEM, spherical aberration correction high resolution TEM, solid state NMR, high energy resolution monochromated STEM-EELS), the microstructure and its preferential growth behavior are elucidated. In ACPPNs, amorphous calcium orthophosphate and amorphous calcium pyrophosphate are distributed at separated but close sites. The ACPPNs grow via either the preferential attachment of ~2 nm nanoclusters in a 1-dimension way, or the transformation of bigger nanoparticles, indicating an inherent driving force-governed process. Here, we propose that the anisotropy of ACPPNs microstructure, which is corroborated experimentally, causes their oriented growth. This study proves that, unlike the conventional view, amorphous minerals can form via oriented growth without external regulation, demonstrating a novel insight into the structures and growth behaviors of amorphous minerals.

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