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At least 721 records · Page 40
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Self-Organizing Map-Based Resilience Quantification and Resilient Control of Distribution Systems Under Extreme Events

Due to climate change, extreme weather events are occurring more frequently and with increasing impact. This trend poses a significant challenge for distribution system operators (DSO) to ensure that there is uninterrupted power supply to critical loads in their networks. To embed resilience into DSO's decision-making, resilience needs to be first quantified and then integrated into the system-level optimization. Therefore, this paper first develops a novel self-organizing map (SOM) based method (called SomRes) to quantify the time-varying resilience index of a system that can leverage the powerful classification property of SOMs and removes some of the disadvantages of subjective weight assignment methods. Using SomRes, a resilient resource allocation and operational dispatch algorithm is further developed to enhance system resilience against extreme events by considering the SomRes resilience index directly as the feedback. Here, the proposed resilience quantification approach is benchmarked with a state-of-the-art approach and the efficacy of the proposed resilient dispatch algorithm is demonstrated through several deterministic and statistical case studies on the IEEE 123-bus distribution system. Simulation studies show that the proposed SomRes quantification method is an appropriate indicator of system resilience, and the resilient resource allocation and dispatch strategy can significantly reduce critical load shedding under varying event propagation scenarios.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

A Synthetic Pathway for Producing Carbon Dots for Detecting Iron Ions Using a Fiber Optic Spectrometer

Iron detection is of growing importance in the critical minerals sector, where unwanted iron ions are typically removed during the processing of target critical metals. The ideal sensor should utilize inexpensive, scalable materials along with a low-cost, robust, and easy-to-use analysis platform. Here, we demonstrate a simple acid–base synthesis of luminescent iron-responsive carbon dots by reacting ethanolamine, phosphoric acid, and m-phenylenediamine. The carbon dots exhibit selective, iron-specific emission quenching, with the ability to detect part-per-billion levels of iron ions even in 0.1 M HCl. After benchmarking the purified materials using a commercial spectrometer, a “low-cost” process is demonstrated in which carbon dots with minimal purification are coupled with a portable fiber-optic spectrometer for analyzing iron content. Carbon dot-coated paper strips are also evaluated as another convenient platform for iron analysis. Taken together, the sensing material and platforms demonstrated here are well-suited for detecting trace quantities of iron in environmentally relevant conditions, with potential applications in tracking iron removal processes during critical mineral production as one exciting area of interest.

acid mine draining↗
DOE OSTI2023

Bayesian sequential optimal experimental design for nonlinear models using policy gradient reinforcement learning

We present a mathematical framework and computational methods for optimally designing a finite sequence of experiments. This sequential optimal experimental design (sOED) problem is formulated as a finite-horizon partially observable Markov decision process (POMDP) under a Bayesian setting and with information-theoretic utilities. The formulation is general and may accommodate continuous random variables, non-Gaussian posteriors, and nonlinear forward models. The sOED design policy incorporates elements of feedback and lookahead simultaneously, and we show it to generalize the commonly-used batch and greedy design strategies. We solve for the sOED policy using the policy gradient (PG) method from reinforcement learning, and provide a derivation for the PG expression in the sOED context. Adopting an actor-critic approach, the policy and value functions are parameterized using deep neural networks and improved via PG estimates produced from simulated episodes of designs and observations. The new PG-sOED algorithm is first validated on a linear-Gaussian benchmark, and then compared against other design baselines on a sensor movement problem for contaminant source inversion in a convection-diffusion field. As a result, we provide explanation for the policy behaviors using knowledge of the underlying physical process.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Distinguishing Surface and Bulk Reactivity: Concentration-Dependent Kinetics of Iodide Oxidation by Ozone in Microdroplets

Iodine oxidation reactions play an important role in environmental, biological, and industrial contexts. The multiphase reaction between aqueous iodide and ozone is of particular interest due to its prevalence in the marine atmosphere and unique reactivity at the air–water interface. Here, we explore the concentration dependence of the I – + O 3 reaction in levitated microdroplets under both acidic and basic conditions. To interpret the experimental kinetics, molecular simulations are used to benchmark a kinetic model, which enables insight into the reactivity of the interface, the nanometer-scale subsurface region, and the bulk interior of the droplet. For all experiments, a kinetic description of gas- and liquid-phase diffusion is critical to interpreting the results. We find that the surface dominates the iodide oxidation kinetics under concentrated and acidic conditions, with the reactive uptake coefficient approaching an upper limit of 10 –2 at pH 3. In contrast, reactions in the subsurface dominate under more dilute and alkaline conditions, with inhibition of the surface reaction at pH 12 and an uptake coefficient that is 10× smaller. In conclusion, the origin of a changing surface mechanism with pH is explored and compared to previous ozone-dependent measurements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Melting and density of MgSiO 3 determined by shock compression of bridgmanite to 1254GPa

The essential data for interior and thermal evolution models of the Earth and super-Earths are the density and melting of mantle silicate under extreme conditions. Here, we report an unprecedently high melting temperature of MgSiO 3 at 500 GPa by direct shockwave loading of pre-synthesized dense MgSiO3 (bridgmanite) using the Z Pulsed Power Facility. We also present the first high-precision density data of crystalline MgSiO 3 to 422 GPa and 7200 K and of silicate melt to 1254 GPa. The experimental density measurements support our density functional theory based molecular dynamics calculations, providing benchmarks for theoretical calculations under extreme conditions. The excellent agreement between experiment and theory provides a reliable reference density profile for super-Earth mantles. Furthermore, the observed upper bound of melting temperature, 9430 K at 500 GPa, provides a critical constraint on the accretion energy required to melt the mantle and the prospect of driving a dynamo in massive rocky planets.

58 GEOSCIENCES↗
DOE OSTI2021

End-to-End Simulations of a 3.4-Meter Detector Wall for Neutron-Diagnosed Subcritical Experiments

The Nevada National Security Site, together with Los Alamos National Laboratory and Lawrence Livermore National Laboratory, is developing a novel diagnostic to measure the reactivity of subcritical experiments. This capability is known as neutron-diagnosed subcritical experiments. The decay of the fission gamma rays from the neutron-interrogated subcritical experiment is measured as a function of time with a large (~3-meter diameter) detector wall consisting of 151 individual detector pixels. The data from this current mode measurement inform the neutron multiplication factor, keff, and thus the relative reactivity of the subcritical experiment. The Nevada National Security Site developed the Gamma Array Simulation Toolkit initially to help inform the design of the individual detector pixels and the 3.4-meter diameter detector wall to be fielded as part of neutron-diagnosed subcritical experiments. This toolkit is now being used to simulate and predict the performance of the final design of the individual detector pixels and the aggregate detector wall. Additionally, key detector characteristics evaluated from these simulations include impulse response, pulse height spectrum, number of photoelectrons per MeV, detector efficiency, and cross talk between detector pixels. Collectively, the results of these simulations inform how well the fission gamma ray die-off distribution from a neutron-diagnosed subcritical experiment measurement can be resolved. This is critical to determining the relative reactivity of the experiment. Furthermore, the Gamma Array Simulation Toolkit can be used to aid in the analysis of the experimental data from a neutron-diagnosed subcritical experiment measurement once the simulation has been benchmarked.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS2012

A Look at the Impact of High-End Computing Technologies on NASA Missions

From its bold start nearly 30 years ago and continuing today, the NASA Advanced Supercomputing (NAS) facility at Ames Research Center has enabled remarkable breakthroughs in the space agency s science and engineering missions. Throughout this time, NAS experts have influenced the state-of-the-art in high-performance computing (HPC) and related technologies such as scientific visualization, system benchmarking, batch scheduling, and grid environments. We highlight the pioneering achievements and innovations originating from and made possible by NAS resources and know-how, from early supercomputing environment design and software development, to long-term simulation and analyses critical to design safe Space Shuttle operations and associated spinoff technologies, to the highly successful Kepler Mission s discovery of new planets now capturing the world s imagination.

Biswas, Rupak↗
DOE OSTI2021

End-to-End Simulations of a 3.4-Meter Detector Wall for Neutron-Diagnosed Subcritical Experiments

The Nevada National Security Site, together with Los Alamos National Laboratory and Lawrence Livermore National Laboratory, is developing a novel diagnostic to measure the reactivity of subcritical experiments. This capability is known as neutron-diagnosed subcritical experiments. The decay of the fission gamma rays from the neutron-interrogated subcritical experiment is measured as a function of time with a large (~3-meter diameter) detector wall consisting of 151 individual detector pixels. The data from this current mode measurement inform the neutron multiplication factor, keff, and thus the relative reactivity of the subcritical experiment. The Nevada National Security Site developed the Gamma Array Simulation Toolkit initially to help inform the design of the individual detector pixels and the 3.4-meter diameter detector wall to be fielded as part of neutron-diagnosed subcritical experiments. This toolkit is now being used to simulate and predict the performance of the final design of the individual detector pixels and the aggregate detector wall. Key detector characteristics evaluated from these simulations include impulse response, pulse height spectrum, number of photoelectrons per MeV, detector efficiency, and cross talk between detector pixels. Collectively, the results of these simulations inform how well the fission gamma ray die-off distribution from a neutron-diagnosed subcritical experiment measurement can be resolved. This is critical to determining the relative reactivity of the experiment. Furthermore, the Gamma Array Simulation Toolkit can be used to aid in the analysis of the experimental data from a neutron-diagnosed subcritical experiment measurement once the simulation has been benchmarked.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Sensitivity Coefficients Calculated for the Prompt Neutron Decay Constant At or Near Delayed Critical

The derivation of a non-invasive prompt neutron decay constant sensitivity coefficient is provided in this work. The computation of the sensitivity coefficient derived in this work does not require modification of Monte Carlo source code and is based on capabilities available in Monte Carlo N-Particle R© Code Version 6.2. The prompt neutron decay constant sensitivity coefficients are calculated for 44-group and 252-group energy structures for specific nuclide-reaction pairs in the Jezebel benchmark experiment. The nuclide-reaction pairs investigated in this work include Pu- 239(n,f), Pu-240(n,f), and Pu-241(n,f). Physical explanations of the sensitivity profiles exhibited by the 252-group energy structure are investigated for the prompt neutron multiplication factor, mean neutron lifetime, and prompt neutron decay constant. The prompt neutron decay constant sensitivity coefficients calculated for the 44-group and 252-group energy structure of Pu-239(n,f) are compared. Lastly, the 44-group energy structure sensitivity coefficients calculated are used for nuclear-data induced uncertainty quantification of the neutron multiplication factor. This work shows that a reduction in the nuclear data-induced uncertainty of the neutron multiplication factor is possible for all nuclide-reaction pairs investigated when prompt neutron decay constant sensitivity coefficients are utilized. This is important for new critical experiment design optimization studies of measurement configurations. This work provides a basis for more detailed sensitivity analysis and uncertainty quantification of nuclide, reaction, and energy-specific cross section data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Solvent Dynamics Are Critical to Understanding Carbon Dioxide Dissolution and Hydration in Water

Simulations of carbon dioxide (CO 2 ) in water may aid in understanding the impact of its accumulation in aquatic environments and help advance technologies for carbon capture and utilization (via, e.g., mineralization). Quantum mechanical (QM) simulations based on static molecular models with polarizable continuum solvation poorly reproduce the energetics of CO 2 hydration to form carbonic acid in water, independent of the level of QM theory employed. Only with density-functional-theory-based molecular dynamics and rare-event sampling, followed by energy corrections based on embedded correlated wavefunction theory (in conjunction with density functional embedding theory), can a close agreement between theory and experiment be achieved. Such multilevel simulations can serve as benchmarks for simpler, less costly models, giving insight into potential errors of the latter. The strong influence of sampling/averaging over dynamical solvent configurations on the energetics stems from the difference in polarity of both the transition state and product (both polar) versus the reactant (nonpolar). When a solute undergoes a change in polarity during reaction, affecting its interaction with the solvent, careful assessment of the energetic contribution of the solvent response to this change is critical. Here, we show that static models (without structural sampling) that incorporate three explicit water molecules can yield far superior results than models with more explicit water molecules because fewer water molecules yield less configurational artifacts. Static models intelligently incorporating both explicit (molecules directly participating in the reaction) and implicit solvation, along with a proper QM theory, e.g., CCSD(T) for closed-shell systems, can close the accuracy gap between static and dynamic models.

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

Modernization efforts for the R -Matrix code SAMMY [Abstract]

The R-Matrix code SAMMY is a widely used nuclear data evaluation code focused on the resolved range, which includes corrections for experimental effects. The code is still mostly written in Fortran 77, and uses a memory management system suitable for the time of its initial writing (1984). A modernization effort is under way to bring the code in-line with modern software development practices. A continuous-integration testing framework was added, automating the large existing set of test cases. It is run on every commit. The memory management was updated to current standard practices suitable for modern software analysis tools. The code can be obtained from https://code.ornl.gov/RNSD/SAMMY. The resonance parameters and covariance information are now stored in C++ objects shared by SAMMY and AMPX, the processing code that generates nuclear data libraries for SCALE. This allows for easier maintenance and access to the resonance parameters inside and outside of SAMMY. This feature is already used by accessing and changing parameters in memory in the Bayesian Monte Carlo Evaluation Framework for Cross Sections Nuclear Data and Integral Benchmark Experiments project, Further plans include the switch to the ENDF reading and writing routines in AMPX, as these routines are more robust, easier to maintain, and support more features. Of note here is support for the new GNDS format. Previously it wasn’t easy to share the full covariance matrix for evaluations containing more than one isotope due to limitations on the ENDF format; this is now supported in GNDS. The data are currently available in a binary SAMMY format and can be exported to GNDS to make them more widely available and sharable. The next step will be to use the same resonance processing code at 0K in AMPX and SAMMY as one of the available Reich-Moore R-Matrix formalism. The first step toward this goal is to isolate the reconstruction into a module that takes resonance parameters as its input and does not depend on SAMMY global parameters. This goal has been achieved and it should now be possible to more easily change the resonance formalism and add enhancements as the Phenomenological R-Matrix parameterization of direct, doorway, and compound nuclear reactions discussed elsewhere on this conference. This concerted modernization and enhancement effort provides multiple advantages to the nuclear data community. It will allow parameter optimization using enhanced formalisms, including experimental effects, that better match complex experimental data. Then those evaluated parameters can immediately be passed off to AMPX to be reconstructed with the exact same cross section model and be put into a data library for subsequent testing using SCALE and the Valid Benchmark suite or other suitable benchmark suites.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Design Trade-Offs in Composite Fuel Cell Membranes: Effects of Reinforcement and Chemical Additives

Perfluorosulfonic acid (PFSA) membranes are critical components in proton exchange membrane fuel cells, where performance depends on balancing ionic conductivity, mechanical durability, and chemical stability. This study characterizes a composite membrane (NC700) featuring PFSA-impregnated expanded polytetrafluoroethylene (ePTFE) reinforcement and cerium-based radical scavengers, benchmarked against unreinforced NR211. Complementary techniques, including electron microscopy, X-ray scattering, infrared spectroscopy, thermogravimetric analysis, and dynamic mechanical analysis, identify the structural and compositional strategies employed in NC700. Water sorption isotherms reveal lower water uptake for NC700 across all conditions, attributed to reinforcement and cerium incorporation. Reinforcement reduces in-plane swelling from 11% to 2.1% at 90% RH, confirming strong swelling anisotropy, while maintaining mechanical properties at elevated temperatures. While the ionic conductivity of NC700 is approximately 10% lower than that of NR211, the reduced thickness yields a 40% decrease in calculated area-specific resistance, suggesting the composite architecture can favorably shift the conductivity-stability trade-off. The composite structure also reduces gas permeability, indicating potential for improved separator function alongside favorable transport properties. Systematic deconvolution of reinforcement and additive contributions shows that conductivity losses from cerium incorporation are largely offset by gains from the lower equivalent-weight polymer, providing quantitative relationships that may guide composite membrane design for fuel cells and other electrochemical applications.

25 ENERGY STORAGE↗
NASA NTRSDate not supplied

Exploring Airfoil Table Generation using XFOIL and OVERFLOW

The rotorcraft design process is a continuously evolving field of research that incorporates a number of software programs. An accurate airfoil table is critical in the design and testing process for rotorcraft. With multiple flow solvers available and flow conditions of multirotor UAM vehicles potentially covering a wide range of Reynolds and Mach numbers, a documented approach for developing airfoil tables is needed. Using benchmark data from legacy airfoil tables and wind tunnel tests for comparison, simulations for a comprehensive test matrix could guide rotorcraft design engineers in generating their own airfoil tables using the XFOIL and OVERFLOW solvers. The motivation for this study is to investigate flow solver features to develop a best practices document for airfoil table generation. The study uses the OVERFLOW and XFOIL flow solvers, coupled with the airfoil table generator AFTGen, to analyze three airfoils for a specific Reynolds numbers flow regime and provide details on how well each flow solver performs within a specific angle of attack range, Mach number range, Reynolds number range, and in different flow conditions, such as turbulent and transitional flow. OVERFLOW analyses in AFTGen for fully turbulent and transition flow are compared with XFOIL results and experimental test data for the section lift, section drag, and pressure coefficients. XFOIL ultimately yields results that are accurate within the linear angle of attack range and below a Mach number of 0.4 but tends to overpredict lift and underpredict drag unless the flow is in the compressible regime. XFOIL cannot accurately model stall and post-stall conditions due to the nature of the solver. This is evident in nearly every case run with XFOIL, where the linear range is usually predicted acceptably and the lift coefficient is overpredicted as the stall angle of attack is approached (with the exception being the generally poor correlation with most of the SSC-A09 cases). OVERFLOW is limited at low Mach numbers, and appears to perform best at Mach numbers of 0.4 and above. The exploration of airfoil table generation using XFOIL and OVERFLOW yielded moderately successful results for the NACA 0012 airfoil, reasonably good results for the RC(4)-10 airfoil, and less accurate results for the SSC-A09 airfoil.

Airfoil Table Generation↗
NASA NTRSDate not supplied

Surrogate Modeling of Subgrid Turbulent Transport Based on 3D Radiative Hydrodynamic Simulations of the Quiet Sun

Turbulent Transport: Plays a critical role in astrophysical plasmas, such as the solar interior, spanning multiple scales and challenging traditional modeling approaches. Objective: Develop machine learning (ML) models—MLP and CNN—to predict subgrid Reynolds stress tensors from StellarBox 3D simulations of the solar atmosphere. Benchmarking: Compare ML-driven models against physics-based Gradient and Smagorinsky approaches.

SMD↗
DOE OSTI2025

Status of the n+ 234 U evaluation in the resolved resonance region (*), (**)

In natural uranium, the 234 U isotope represents only 0.0055%, however, this minor isotope can affect highly enriched uranium metal benchmark calculations. In fact, enriched uranium contains more 234 U than natural uranium as the result of the uranium enrichment process. Therefore, the n+ 234 U nuclear data evaluation is one of the milestones of the APPENDIX B within the Nuclear Criticality Safety Program (NCSP).

AMPX↗
DOE OSTI2022

Evaluated 238 U(n,f) Average Prompt Fission Neutron Multiplicities Including the CGMF Model

This report documents an evaluation of the average prompt fission neutron multiplicity, $\overline{v}_p$, of 238 U from 800 keV to MeV. This evaluation had to be re-done from “scratch” as the input to previous $\overline{v}_p$ evaluations, specifically ENDF/B-VIII.0, was not found. That means that all available experimental data were re-analyzed and uncertainties were re-estimated. The new evaluated 238 U $\overline{v}_p$ based on only experimental data differs distinctly from ENDF/B-VIII.0 $\overline{v}_p$ from 2 to 4.5 MeV, and from 6 to 7 MeV, and is otherwise similar. The difference from 2 to 4.5 MeV stems from the fact that ENDF/B-VIII.0 was tweaked in this energy range to data of Frehaut, while two other, equally trustworthy, data sets would indicate an evaluated 238 U $\overline{v}_p$ that is up to 2% higher. Also, second chance fission in ENDF/B-VIII.0 was smoothed over from 6–7 MeV. Another major difference to ENDF/B-VIII.0 is that one of the evaluations presented here includes model information from the Hauser-Feshbach fission fragment decay code CGMF, while ENDF/B-VIII.0 is based purely on experimental data. CGMF links several fission quantities with each other; $\overline{v}_p$ is predicted by assumptions made on, e.g., pre-neutron emission yields as a function of mass, the total kinetic energy, or spin and parity of fission fragments. This allows to validate the new 238 U $\overline{v}_p$ by using CGMF parameters obtained from fitting to experimental 238 U $\overline{v}_p$ to predict yields as a function of mass, the average total kinetic energy, or the mean energy of the prompt fission neutron spectrum. These model-predicted values can then be compared to experimental and evaluated data. The model-predicted fission-observable values using evaluated parameters obtained here are reasonably close to experimental data for some observables, but are farther away from experimental data related to TKE observables. In addition to that, the evaluated 238 U(n,f) $\overline{v}_p$ shows similar deviations from ENDF/B-VIII.0 as for the evaluation with only experimental data. This difference is expected to lead to changes in simulated effective neutron multiplication factor, $k_{eff}$ of ICSBEP critical assemblies that are sensitive to 238 U in the fast range (BigTen, Flattop, Flattop-Pu). These changes in $k_{eff}$ need to be counter-balanced. Chi-Nu PFNS experimental data are expected to be released in the next few months that might lead to the needed changes in the PFNS. Until then, we hold off in benchmarking the new 238 U(n,f) $\overline{v}_p$ as well as submitting it to ENDF/B-VIII.1. Also, new high-precision 238 U $\overline{v}_p$ are expected to be measured by the CEA in the next two years that will shed further light on question on 238 U $\overline{v}_p$ from 2–4.5 and 6–7 MeV.

238U↗
NASA NTRS2010

Climate Benchmark Missions: CLARREO

CLARREO (Climate Absolute Radiance and Refractivity Observatory) is one of the four Tier 1 missions recommended by the recent NRC decadal survey report on Earth Science and Applications from Space (NRC, 2007). The CLARREO mission addresses the need to rigorously observe climate change on decade time scales and to use decadal change observations as the most critical method to determine the accuracy of climate change projections such as those used in the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC AR4). A rigorously known accuracy of both decadal change observations as well as climate projections is critical in order to enable sound policy decisions. The CLARREO mission accomplishes this critical objective through highly accurate and SI traceable decadal change observations sensitive to many of the key uncertainties in climate radiative forcings, responses, and feedbacks that in turn drive uncertainty in current climate model projections. The same uncertainties also lead to uncertainty in attribution of climate change to anthropogenic forcing. The CLARREO breakthrough in decadal climate change observations is to achieve the required levels of accuracy and traceability to SI standards for a set of observations sensitive to a wide range of key decadal change variables. These accuracy levels are determined both by the projected decadal changes as well as by the background natural variability that such signals must be detected against. The accuracy for decadal change traceability to SI standards includes uncertainties of calibration, sampling, and analysis methods. Unlike most other missions, all of the CLARREO requirements are judged not by instantaneous accuracy, but instead by accuracy in large time/space scale average decadal changes. Given the focus on decadal climate change, the NRC Decadal Survey concluded that the single most critical issue for decadal change observations was their lack of accuracy and low confidence in observing the small but critical climate change signals. CLARREO is the recommended attack on this challenge, and builds on the last decade of climate observation advances in the Earth Observing System as well as metrological advances at NIST (National Institute of Standards and Technology) and other standards laboratories.

Wielicki, Bruce A.↗
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↗