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DOE OSTI2026

Concordant Mode Approach (CMA): Vibrational Analysis of New and Upgraded Intermolecular Benchmarks for Noncovalent Bonding

The Concordant Mode Approach (CMA) is a novel method that offers tremendous potential for increasing the system size and the level of theory attainable in quantum chemical computations of molecular vibrational frequencies. To investigate the extension of CMA to intermolecular vibrations, computations with coupled cluster singles and doubles with perturbative triples theory [CCSD(T)] using two augmented correlation-consistent polarized-valence triple-ζ basis sets (aug-cc-pVTZ or h-aug-ccpVTZ) were performed on 17 prototypical loosely bound complexes of hydrogen-bonded, dispersion, and mixed character. These Level A results provide new and upgraded benchmarks for noncovalent bonding and a severe test for CMA vibrational analyses. The Level A target frequencies were recovered remarkably well using second-order Møller−Plesset perturbation theory (MP2) with h-aug-cc-pVTZ for generating the underlying (Level B) normal modes of the CMA scheme. Employing this Level B within the lowest-rung CMA-0A method reproduces the 435 benchmark frequencies with a mean absolute error (MAE) of 0.23 cm −1 and a corresponding standard deviation (σ) of 0.84 cm −1 ; strikingly, the corresponding subset of 106 interfragment frequencies exhibits MAE = 0.34 cm −1 and σ = 0.90 cm −1 . Subsequent application of the higher-rung CMA-2A scheme eliminates all outliers and reduces the overall MAE to a minuscule 0.08 cm −1 with the inclusion of only 3.0% of the off-diagonal couplings not accounted for by CMA-0A. Accordingly, the highly efficient CMA methodology proves to be robust even for vibrations on flat potential energy surfaces.

Aromatic compounds↗

DOE OSTI2022

Ultrafast perturbation of magnetic domains by optical pumping in a ferromagnetic multilayer

Ultrafast optical pumping of spatially nonuniform magnetic textures is known to induce far-from-equilibrium spin transport effects. Here, we use ultrafast x-ray diffraction with unprecedented dynamic range to study the laser-induced dynamics of labyrinth domain networks in ferromagnetic CoFe/Ni multilayers. We detected azimuthally isotropic, odd order, magnetic diffraction rings up to fifth order. The amplitudes of all three diffraction rings quench to different degrees within 1.6 ps. In addition, all three of the detected diffraction rings both broaden by 15% and radially contract by 6% during the quench process. We are able to rigorously quantify a 31% ultrafast broadening of the domain walls via Fourier analysis of the order-dependent quenching of the three detected diffraction rings. Here, the broadening of the diffraction rings is interpreted as a reduction in the domain coherence length, but the shift in the ring radius, while unambiguous in its occurrence, remains unexplained. In particular, we demonstrate that a radial shift explained by domain-wall broadening can be ruled out. With the unprecedented dynamic range of our data, our results provide convincing evidence that labyrinth domain structures are spatially perturbed at ultrafast speeds under far-from-equilibrium conditions, albeit the mechanism inducing the perturbations remains yet to be clarified.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Quantifying the propagation of parametric uncertainty on flux balance analysis

Flux balance analysis (FBA) and associated techniques operating on stoichiometric genome-scale metabolic models play a central role in quantifying metabolic flows and constraining feasible phenotypes. At the heart of these methods lie two important assumptions: (i) the biomass precursors and energy requirements neither change in response to growth conditions nor environmental/genetic perturbations, and (ii) metabolite production and consumption rates are equal at all times (i.e., steady-state). Despite the stringency of these two assumptions, FBA has been shown to be surprisingly robust at predicting cellular phenotypes. In this paper, we formally assess the impact of these two assumptions on FBA results by quantifying how uncertainty in biomass reaction coefficients, and departures from steady-state due to temporal fluctuations could propagate to FBA results. In the first case, conditional sampling of parameter space is required to re-weigh the biomass reaction so as the molecular weight remains equal to 1 g mmol –1 , and in the second case, metabolite (and elemental) pool conservation must be imposed under temporally varying conditions. Results confirm the importance of enforcing the aforementioned constraints and explain the robustness of FBA biomass yield predictions.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

Temperature response and brine availability to heated boreholes in bedded salt

Abstract There is a growing need for disposal of high‐level nuclear waste. To reduce uncertainty associated with brine availability to repository excavations in salt formations, a collaboration between Sandia, Los Alamos, and Lawrence Berkeley National Laboratories is performing a series of borehole‐scale coupled process tests. Here, we report on the first round of the Brine Availability Test in Salt (BATS) project, a “shakedown” experiment called Phase 1s. Experimental testing included placing a resistive heater, a 260‐W radiative heater, and a 750‐W radiative heater within previously drilled horizontal boreholes at the Waste Isolation Pilot Plant (WIPP) while monitoring temperature and water inflow. The experiments successfully achieved the targeted temperature of 120 °C when using the 750‐W radiative heater. Simulations using FEHM (Finite Element Heat and Mass transfer code) and TOUGH‐FLAC (Transport Of Unsaturated Groundwater and Heat–Fast Lagrangian Analysis of Continua) were able to accurately predict the coupled thermo–hydro–mechanical–chemical response of salt, matching the observed temperature and brine production. Due to the extremely low permeability of salt, these systems take many years to reach steady state when perturbed by mining activities. Long‐term numerical simulations are used to develop the initial pressure and saturation conditions. The inclusion of a damaged rock zone with higher permeability around the borehole also affects the saturation and pressure distributions and plays an important role in dissipating the potential for thermal pressurization. Knowledge gained from this round of experimentation and simulation will be used to conduct the next BATS project experiment in new boreholes at WIPP.

58 GEOSCIENCES↗

DOE OSTI2021

Determination of the Collins-Soper Kernel from Lattice QCD

We present lattice results for the non-perturbative Collins-Soper (CS) kernel, which describes the energy-dependence of transverse momentum-dependent parton distributions (TMDs). The CS kernel is extracted from the ratios of first Mellin moments of quasi-TMDs evaluated at different nucleon momenta. The analysis is done with dynamical N f = 2 + 1 clover fermions for the CLS ensemble H101 (a = 0. 0854 fm, m π = m K = 422 MeV). The computed CS kernel is in good agreement with experimental extractions and previous lattice studies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Electrically interfaced Brillouin-active waveguide for microwave photonic measurements

New strategies for converting signals between optical and microwave domains could play a pivotal role in advancing both classical and quantum technologies. Traditional approaches to optical-to-microwave transduction typically perturb or destroy the information encoded on intensity of the light field, eliminating the possibility for further processing or distribution of these signals. In this paper, we introduce an optical-to-microwave conversion method that allows for both detection and spectral analysis of microwave photonic signals without degradation of their information content. This functionality is demonstrated using an optomechanical waveguide integrated with a piezoelectric transducer. Efficient electromechanical and optomechanical coupling within this system permits bidirectional optical-to-microwave conversion with a quantum efficiency of up to -54.16 dB. Leveraging the preservation of the optical field envelope in intramodal Brillouin scattering, we demonstrate a multi-channel microwave photonic filter by transmitting an optical signal through a series of electro-optomechanical waveguide segments, each with distinct resonance frequencies. Such electro-optomechanical systems could offer flexible strategies for remote sensing, channelization, and spectrum analysis in microwave photonics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Three-dimensional hot-spot x-ray emission tomography from cryogenic deuterium–tritium direct-drive implosions on OMEGA

A three-dimensional model of the hot-spot x-ray emission has been developed and applied to the study of low-mode drive asymmetries in direct-drive inertial confinement fusion implosions on OMEGA with cryogenic deuterium–tritium targets. Here, the steady-state model assumes an optically thin plasma and the data from four x-ray diagnostics along quasi-orthogonal lines of sight are used to obtain a tomographic reconstruction of the hot spot. A quantitative analysis of the hot-spot shape is achieved by projecting the x-ray emission into the diagnostic planes and comparing this projection to the measurements. The model was validated with radiation-hydrodynamic simulations assuming a mode-2 laser illumination perturbation resulting in an elliptically shaped hot spot, which was accurately reconstructed by the model using synthetic x-ray images. This technique was applied to experimental data from implosions in polar-direct-drive illumination geometry with a deliberate laser-drive asymmetry, and the hot-spot emission was reconstructed using spherical-harmonic modes of up to ℓ = 3. A 10% stronger drive on the equator relative to that on the poles resulted in a prolate-shaped hot spot at stagnation with a large negative A 2,0 coefficient of A 2,0 = –0.47 ± 0.03, directly connecting the modal contribution of the hot-spot shape with the modal contribution in laser-drive asymmetry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Impact of n > 1 neoclassical tearing modes on fast ions, plasma rotation, and the onset of disruptive tearing modes in DIII-D ITER baseline scenario

We present integrated TRANSP-kick analyses quantitatively characterizing how n > 1 magnetic islands redistribute fast ions (FIs) and modify momentum balance in low-torque DIII-D H-mode scenarios operated with the ITER normalized parameter set and shape (ITER baseline scenario, or IBS). In this plasma scenario, disruptive neoclassical tearing modes (NTMs) are most commonly seeded by nonlinear 3-wave coupling when the differential rotation between the q = 1 and q = 2 surfaces ($δf_{1, 2}$) approaches zero. Analysis of a DIII-D IBS database of shots unstable to the 2/1 NTM demonstrates that the flattening rotation profile is correlated with n > 1 NTM amplitude growth, with a strong drop in $δf_{1, 2}$ occurring when the radial magnetic perturbation amplitude at the rational surface ($δB$ r s ) is estimated to be about 20 G. The interpretive TRANSP-kick simulations show that the experimentally observed reduction in core rotation is due to the fast-ion kicks. Nonlinearity in momentum losses versus NTM amplitude is found to be correlated with overlap of FI island chains, occurring when $δB$ r s is about 35 G, in rough agreement with the experimental results. This agreement suggests the primary mechanism for the conductive momentum loss in the core is due to chaotic FI orbits and FI losses developing from overlapping resonant FI island chains.

ITER baseline scenario↗

DOE OSTI2025

Real-Time Automated pH Control within Batch Processes Relying on Raman pH Measurement

Nuclear fission is an energy source that can provide consistent power with very low associated carbon emissions. However, management of the used nuclear fuel is an important aspect of the application of nuclear power. Recycling of useful components from used fuel is an attractive option, but this involves chemical processing of the fuel. Possible chemical separation technologies that might be used in this regard are sensitive to solution pH. Raman spectroscopy is a promising technique for monitoring the pH of solutions in real time. Classical pH probes are too fragile to be used in the harsh environments encountered in nuclear fuel processing. Raman probes are robust and can withstand these harsh environments to track pH. Coupled with chemometric analysis, the demonstration of the use of Raman spectroscopy to track and predict the pH in carboxylate-buffered systems is made possible. Utilizing this spectroscopy in conjunction with Programmable Logic Controllers mimics industrial control systems used in many modern industrial settings. This showcases a pragmatic approach toward leveraging Raman spectroscopy and chemometric model outputs as inputs for a real-time control system. The model to predict pH created by chemometrics proved to be successful in tracking pH. The optimal pH for TALSPEAK extraction of lanthanides and actinides from aqueous solution is known to proceed in a narrow pH range of around pH = 2.8 ± 0.1. This study uses Raman optical monitoring and automated control to return and maintain solution pH within this range after acid or base perturbations move the solution pH well outside this region. Root-mean-square errors show that pH changes measured using Raman spectroscopy on the batch process solution are reliably measured and used to automatically correct and maintain solution pH. Measurement of solution pH tracks favorably with electrochemical pH probe comparison measurements. As a result, the ability to showcase Raman spectroscopy paired with chemometrics analysis acts as a durable, better alternative data source compared to traditional pH probes to optimize the separation efficiency in the used nuclear fuel processing.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Jet wake from linearized hydrodynamics

We explore how to improve the hybrid model description of the particles originating from the wake that a jet produced in a heavy ion collision leaves in the droplet of quark-gluon plasma (QGP) through which it propagates, using linearized hydrodynamics on a background Bjorken flow. Jet energy and momentum loss described by the hybrid model become currents sourcing linearized hydrodynamics. By solving the linearized hydrodynamic equations numerically, we investigate the development of the wake in the dynamically evolving droplet of QGP, study the effect of viscosity, scrutinize energy-momentum conservation, and check the validity of the linear approximation. We find that linearized hydrodynamics works better in the viscous case because diffusive modes damp the energy-momentum perturbation produced by the jet. We calculate the distribution of particles produced from the jet wake by using the Cooper-Frye prescription and find that both the transverse momentum spectrum and the distribution of particles in azimuthal angle are similar in shape in linearized hydrodynamics and in the hybrid model. Their normalizations are different because the momentum-rapidity distribution in the linearized hydrodynamics analysis is more spread out, due to sound modes. Since the Bjorken flow has no transverse expansion, we explore the effect of transverse flow by using local boosts to add it into the Cooper-Frye formula. After including the effects of transverse flow in this way, the transverse momentum spectrum becomes harder: more particles with transverse momenta bigger than 2 GeV are produced than in the hybrid model. Although we defer implementing this analysis in a jet Monte Carlo, as would be needed to make quantitative comparisons to data, we gain a qualitative sense of how the jet wake may modify jet observables by computing proxies for two example observables: the lost energy recovered in a cone of varying open angle, and the fragmentation function. We find that linearized hydrodynamics with transverse flow effects added improves the description of the jet wake in the hybrid model in just the way that comparison to data indicates is needed. Our study illuminates a path to improving the description of the wake in the hybrid model, highlighting the need to take into account the effects of both transverse flow and the broadening of the energy-momentum perturbation in spacetime rapidity on particle production.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Boundary correlators and the Schwarzian mode

The effective low temperature dynamics of near-extremal black holes is governed by the quantum fluctuations of the Schwarzian mode of JT gravity. Utilizing as a proxy a planar charged black hole in asymptotically Anti-de-Sitter spacetime, we investigate the effects of these fluctuations on a probe scalar field. The corresponding holographic real-time boundary correlators are computed following a holographic renormalization procedure, using the dubbed gravitational Schwinger-Keldysh geometry (grSK) and known exact results of boundary correlators from the near-horizon region. This analysis gives rise to a retarded Green’s function that decays as a power law for late Lorentzian times. Its analytic structure indicates the presence of a branch cut in the complex frequency domain at finite temperature. These features are a non-perturbative hallmark that prevails as long as the planar transverse space is kept compact.

2D Gravity↗

DOE OSTI2023

Drought Shifts Sorghum Root Metabolite and Microbiome Profiles and Enriches for Pipecolic Acid

Plant-associated microbial communities shift in composition as a result of environmental perturbations, such as drought. It has been shown that Actinobacteria are enriched in plant roots and rhizospheres during drought stress. However, the correlations between microbiome dynamics and plant response to drought are poorly understood. Here we apply a combination of bacterial community composition analysis and plant metabolite profiling in Sorghum bicolor roots, rhizospheres, and soil during drought and drought recovery to investigate potential contributions of host metabolism to shifts in bacterial composition. Our results provide a detailed view of metabolic shifts across the plant root during drought and show that the response to rewatering differs between root and soil; additionally, we identify drought-responsive metabolites that are highly correlated with the observed changes in Actinobacteria abundance. Furthermore, we find that pipecolic acid is a drought-enriched metabolite in sorghum roots, and that exogenous application of pipecolic acid inhibits root growth. Finally, we show that this activity functions independent of the systemic acquired resistance pathway and has the potential to impact Actinobacterial taxa within the root microbiome.

165 RRNA↗

DOE OSTI2022

Impact of Increased Latent Generations on Sensitivity Calculations with SCALE

Analyses of cross section sensitivity data from systems with fissile material allow analysts to associate an importance for each material, nuclide, reaction, and neutron energy by simulating real world criticality scenarios. Although criticality safety validation efforts can be guided by the cross-section sensitivity and uncertainty data generated for a particular system, these calculations can often be computationally expensive and sometimes cumbersome without proper guidance. The TSUNAMI suite within the SCALE code package has several methods for generating sensitivity data, including multigroup and continuous energy (CE) capabilities. The release of SCALE 6.3 has three different CE methods for generating cross section sensitivity data: (1) the Iterated Fission Probability (IFP) method with the KENO Monte Carlo transport solver, (2) the IFP method with the Shift Monte Carlo transport solver, and (3) the Contributon-Linked eigenvalue sensitivity/Uncertainty estimation via Tracklength importance CHaracterization (CLUTCH) method with the KENO Monte Carlo transport solver. Although the CLUTCH method has additional parameters for generating sensitivity data files relative to the IFP method, all three methods use latent generations, which are the generations between an event (i.e., fission) and the assessment of importance based on the asymptotic population of progeny neutrons. Increasing the number of latent generations in a calculation leads to increased discrimination of the sensitivity coefficients but at the cost of the increased uncertainty associated with those generated values. Analysts must balance the accuracy of the sensitivity calculations and its uncertainty with the associated computational cost involved in generating the values. This paper discusses the impact of adjusting the latent generation parameter for a range of sensitivity values and how these changes compare with the direct perturbation values obtained from a change of ±0.5% Δ k in both benchmark and safety application models. Two benchmarks from the International Handbook of Evaluated Criticality Safety Benchmark Experiments and the MPC-32 dual purpose canister for spent nuclear fuel are used for analysis.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Systematic Study of the Self-Renormalized Nucleon Gluon PDF in Large-Momentum Effective Theory

We present a systematic study of the nucleon gluon parton distribution function (PDF) using the self-renormalized large-momentum effective theory (LaMET) approach in lattice QCD. This work extends previous gluon-PDF extractions by performing a detailed analysis of key systematic effects, including gauge-link smearing, lattice spacing, pion mass, and nucleon boost momentum. The self-renormalization framework mitigates ultraviolet divergences associated with Wilson-line self-energy and renormalon contributions by combining lattice matrix elements with perturbative short-distance information, thereby preserving the correct infrared structure. Calculations are performed on $N_f=2+1+1$ HISQ ensembles generated by the MILC Collaboration at three lattice spacings and two pion masses, with boosted nucleon states reaching momenta up to 2.2~GeV. We determine renormalization factors from zero-momentum matrix elements and apply hybrid renormalization to suppress discretization artifacts. After extrapolating large-separation behavior and performing Fourier transforms, we reconstruct quasi-PDFs and match them to lightcone PDFs using next-to-leading order Wilson coefficients. Our results demonstrate that smearing and lattice-spacing effects are under control, and pion-mass and lattice-spacing dependence is mild relative to the current $O(10^6)$ statistics; however, momentum dependence remains a significant source of uncertainty. Future work including even larger boost momenta will be essential to reduce systematics in lattice determinations of the gluon PDF and to advance toward precision QCD phenomenology at the LHC and the future Electron-Ion Collider.

FOS: Physical sciences↗

DOE OSTI2024

Shock wave formation in radiative plasmas

The temporal evolution of weak shocks in radiative media is theoretically investigated in this work. The structure of radiative shocks has traditionally been studied in a stationary framework. Their systematic classification is complex because layers of optically thick and thin regions alternate to form a radiatively-driven precursor and a temperature-relaxation layer, between which the hydrodynamic shock is embedded. In this work, we analyze the formation of weak shocks when two radiative plasmas with different pressures are put in contact. Applying a reductive perturbative method yields a Burgers-type equation that governs the temporal evolution of the perturbed variables including the radiation field. The conditions upon which optically thick and thin solutions exist have been derived and expressed as a function of the shock strength and Boltzmann number. Below a certain Boltzmann number threshold, weak shocks always become optically thick asymptotically in time, while thin solutions appear as transitory structures. The existence of an optically thin regime is related to the presence of an overdense layer in the compressed material. Scaling laws for the characteristic formation time and shock width are provided for each regime. The theoretical analysis is supported by FLASH simulations, and a comprehensive testcase has been designed to benchmark radiative hydrodynamic codes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

A Multiyear Gridded Data Ensemble of Surface Biogenic Carbon Fluxes for North America: Evaluation and Analysis of Results

Accurate and fine-scale estimates of biogenic carbon fluxes are critical for measuring and monitoring the biosphere's responses and feedback to the climate system. Currently available data products from flux towers and model-intercomparison projects struggle to adequately represent spatiotemporal dynamics of surface biogenic carbon fluxes, and to quantify their uncertainties, which also are crucial to atmospheric inversion systems. To address these gaps, we introduce a new perturbed-parameter model ensemble with the CASA model to estimate surface biogenic carbon fluxes at monthly and 3-hourly scales for North America at ~500-m and 5-km resolutions. We first use the Extended Fourier Amplitude Sensitivity Testing to choose the three most sensitive parameters to be perturbed, maximum light use efficiency (E max ), optimal temperature of photosynthesis (T opt ), and temperature response of respiration (Q 10 ). The initial range for each parameter is broadly sampled for the L1 ensemble, but then we pruned E max with site-level primary productivity to derive an L2 ensemble with narrower uncertainty ranges. Ensembles are strongly correlated with site-level results at both monthly and 3-hourly scales, and the spread across L1/L2 ensemble members encompasses the range of AmeriFlux observations. Monthly variability in the L2 ensemble mean is 85% of the observed variability. The L2 ensemble outperforms diverse data products with the highest Taylor skill scores at diurnal to annual scales. Finally, the ensemble's seasonality agrees well with other models for most biome types and in high and middle latitudes, but inconsistencies are found in subtropical and tropical ecoregions and for annual totals over North America.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Coupled neutronic-thermal-hydraulic simulations of the European SFR core

Within the European SFR (Sodium-cooled Fast Reactor) - Safety Measures Assessment and Research Tools (ESFR-SMART) project, steady-state coupled simulation of the ESFR core has been performed using several core analysis packages, with the objective of quantifying the coupling effect. Focus is on the fuel Doppler effect and coolant expansion effect. Standalone neutronics calculations in TRACE/PARCS (PSI), DYN3D (HZDR) and WIMS (Jacobs) showed superb agreement with the reference Serpent power distribution (root mean square - rms discrepancies of 1.3%, 1.5% and 0.7% respectively). Results for COUNTHER (CIEMAT) were also in reasonable agreement, but with a somewhat higher discrepancy of 3.7%. Temperature distributions from thermal-hydraulic calculations were also compared and are found to be in good agreement. The effect of Doppler and coolant density feedback on core power distribution was predicted by TRACE/PARCS, DYN3D and WIMS to be between 0.4% and 0.8% rms difference in assembly powers. Reactivity coefficients for perturbations in the inlet temperature, flow rate and core power were shown to be negative for these three codes, with values of roughly -0.5 pcm/C. degree, -0.3 pcm/C. degree and -3.5 pcm/C. degree respectively. A preliminary investigation of differential thermal expansion effects indicates that this may have a significant effect on core power distribution of a few %, greater than anticipated a priori and may warrant inclusion in coupled core analysis to ensure the accurate calculation of power distributions. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2026

Identifying Differential Equations in Fourier Domain (FourierIdent)

We investigate identifying differential equations in the frequency domain. Fourier analysis is an important tool in theoretical analysis and numerical solvers of differential equations, yet there is limited work in exploring this connection in the identification of differential equations. This paper aims to identify the underlying differential equation in the frequency domain, from a given single realization of the differential equation perturbed by noise. Such setting imposes difficulties which are different from other identification methods where computation is carried out in the physical domain. We propose several ways to mitigate the challenges arising from noise in data and large differences in the magnitudes of frequency responses. The main takeaways are that identifying differential equations solely in the frequency domain is challenging, the method we propose is based on a form of domain partitions in the frequency domain, and this method shows benefits for complex data even with high level of noise. We introduce a Fourier feature denoising, and define the meaningful data region and the core regions of features to reduce the effect of noise in the frequency domain and to enhance the accuracy in coefficient identification. The proposed method is tested on various differential equations with linear, nonlinear, and high-order derivative feature terms, and shows advantages on complex data with many frequency modes, even under high level of noise.

97 MATHEMATICS AND COMPUTING↗