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Parameter estimation in nonlinear distributed systems - Approximation theory and convergence results

An abstract approximation framework and convergence theory is described for Galerkin approximations applied to inverse problems involving nonlinear distributed parameter systems. Parameter estimation problems are considered and formulated as the minimization of a least-squares-like performance index over a compact admissible parameter set subject to state constraints given by an inhomogeneous nonlinear distributed system. The theory applies to systems whose dynamics can be described by either time-independent or nonstationary strongly maximal monotonic operators defined on a reflexive Banach space which is densely and continuously embedded in a Hilbert space. It is demonstrated that if readily verifiable conditions on the system's dependence on the unknown parameters are satisfied, and the usual Galerkin approximation assumption holds, then solutions to the approximating problems exist and approximate a solution to the original infinite-dimensional identification problem.

Banks, H. T.↗

Search for low-energy neutrinos from astrophysical sources with Borexino

We report on searches for neutrinos and antineutrinos from astrophysical sources performed with the Borexino detector at the Laboratori Nazionali del Gran Sasso in Italy. Electron antineutrinos ( $\bar{ν}_e$ ) are detected in an organic liquid scintillator through the inverse β -decay reaction. In the present work we set model-independent upper limits in the energy range 1.8-16.8 MeV on neutrino fluxes from unknown sources that improve our previous results, on average, by a factor 2.5. Using the same data set, we first obtain experimental constraints on the diffuse supernova $\bar{ν}_e$ fluxes in the previously unexplored region below 8 MeV. A search for $\bar{ν}_e$ in the solar neutrino flux is also presented: the presence of $\bar{ν}_e$ would be a manifestation of a non-zero anomalous magnetic moment of the neutrino, making possible its conversion to antineutrinos in the strong magnetic field of the Sun. We obtain a limit for a solar $\bar{ν}_e$ flux of 384 cm -2 s -1 (90% C.L.), assuming an undistorted solar 8 B neutrinos energy spectrum, that corresponds to a transition probability pνe→$\bar{ν}_e$< 7.2 ×10-5 (90% C.L.) for E $\bar{ν}_e$ > 1.8 MeV.At lower energies, by investigating the spectral shape of elastic scattering events, we obtain a new limit on solar 7 Be- ν e conversion into $\bar{ν}_e$ of pνe→$\bar{ν}_e$< 0.14 (90% C.L.) at 0.862 MeV. Last, we investigate solar flares as possible neutrino sources and obtain the strongest up-to-date limits on the fluence of neutrinos of all flavor neutrino below 3–7 MeV. Assuming the neutrino flux to be proportional to the flare’s intensity, we exclude an intense solar flare as the cause of the observed excess of events in run 117 of the Cl-Ar Homestake experiment.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Microstructural characterization of a star-linear polymer blend under shear flow by using rheo-SANS

We present an investigation into the dynamic relaxation mechanisms of a polybutadiene blend composed of a four-arm star (10 wt. %) and a linear polymer matrix in the presence of an applied shear flow. Our focus was the response of the star polymer, which cannot be unambiguously assessed via linear viscoelastic measurements since the signature of the star polymer can barely be detected due to the dominant contribution of the linear matrix. By utilizing small-angle neutron scattering (SANS) coupled with a Couette shear device and a deuterated matrix polymer, we investigated the dynamics of the minority star component of the blend. Our results confirm that the stars deform anisotropically with increasing shear rate. We have compared the SANS data with predictions from the well-established scattering adaptation of the state-of-the-art tube model for entangled linear polymer melts undergoing shear, i.e., Graham, Likhtman, Milner, and McLeish (GLaMM) approach, appropriately modified following earlier studies in order to apply to the star. This modified model, GLaMM-R, includes the physics necessary to understand stress relaxation in both the linear and nonlinear flow regimes, i.e., contour length fluctuations, constraint release, convective constraint release, and chain retraction. The full scattering signal is due to the minority star component and, although the contribution of the linear chains is hidden from the neutron scattering, they still influence the star polymer molecular dynamics, with the applied shear rate ranging from approximately 8 to 24 s –1 , below the inverse relaxation time of the linear component. This study provides another confirmation that the combination of rheology and neutron scattering is an indispensable tool for investigating the nonlinear dynamics of complex polymeric systems.

36 MATERIALS SCIENCE↗

3+2+X: What Is the Most Useful Depolarization Input for Inverting Lidar Measurements of Non-Spherical Particles to Microphysical Properties?

The typical multiwavelength aerosol lidar data set for inversion of optical to microphysical parameters is composed of three backscatter coefficients (β ) at 355, 532, and 1064 nm and two extinction coefficients (α ) at 355 and 532 nm. This data combination is referred to as 3β +2α or 3+2 data set. This set of data is sufficient for retrieving some important microphysical particle parameters if the particles have spherical shape. Here, we investigate the effect of including the particle linear depolarization ratio (δ) as a third input parameter to the inversion of lidar data. The inversion algorithm is generally not used if measurements show values of δ that exceed 0.10 at 532 nm, i.e. in the presence of non-spherical particles such as desert dust, volcanic ash, and under special circumstances biomass-burning smoke.We use experimental data collected with instruments that are capable of measuring δ at all three lidar wavelengths with an inversion routine that uses the theory of light scattering by randomly oriented spheroids to replicate scattering properties of non-spherical particles. This is the first systematic test of the effect of using all theoretically possible combinations of δ taken at 355, 532, and 1064 nm as input in the lidar data inversion. We find that depolarization information at least at one wavelength already provides useful information in the in version of optical data that describe light-scattering by nonspherical particles. However, any choice of δ(λ) will give lower values of the single-scattering albedo than the traditional 3+2 data set. We find that input data sets that include 355 give a non-spherical fraction that closely resembles the dust ratio we obtain from using β(532) and δ(532) in a methodology applied in aerosol-type separation. The use of 355 in data sets of two or three reduces the fraction of non-spherical particles that is retrieved when using δ(532) and δ(1064). Use of the latter two without accounting for 355 generally leads to high fractions of non-spherical particles that we consider not trustworthy. The use of three δ(λ) instead of two δ(λ) including the constraint that one of these is measured at 355 nm does not provide any advantage over using 3+2+δ(355). Because of the technical challenges involved with accurately measuring δ(1064) we conclude that — depending on measurement capability — the future standard input for inversion using spheroid kernels might be 3+2+δ(355) or 3+2+δ(355)+δ(532).

Tesche, M.↗

Broken symmetries associated with a Kagome chiral charge order

Chirality, or handedness, is ubiquitous in science, from cell biology to physics, and in condensed matter can underlie exotic phases such as chiral charge density waves and chiral superconductivity. However, detecting subtle broken symmetries that define such states is challenging, leading to debate and controversy. Here, using second-order optical response, we reveal the broken symmetries of a chiral charge density wave in the Kagome lattice KV 3 Sb 5 . Polarization-dependent mid-infrared photocurrent microscopy uncovers a longitudinal, helicity-dependent photocurrent associated with the charge order, indicating broken inversion and mirror symmetries. These findings, supported by theoretical analysis, directly establish the intrinsic chiral nature of the ordered state. Moreover, the absence of a circular photogalvanic effect perpendicular to the incident light imposes stringent constraints on the point-group symmetries. Our study not only visualizes the chiral nature of the Kagome charge order, but also highlights the nonlinear photogalvanic effect as a sensitive probe for detecting subtle symmetry breakings.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Evaluation of Space-Based Constraints on Global Nitrogen Oxide Emissions with Regional Aircraft Measurements over and Downwind of Eastern North America

We retrieve tropospheric nitrogen dioxide (NO 2) columns for May 2004 to April 2005 from the SCIAMACHY satellite instrument to derive top-down emissions of nitrogen oxides (NO(x) = NO + NO2) via inverse modeling with a global chemical transport model (GEOS-Chem). Simulated NO 2 vertical profiles used in the retrieval are evaluated with airborne measurements over and downwind of North America (ICARTT); a northern midlatitude lightning source of 1.6 Tg N/yr minimizes bias in the retrieval. Retrieved NO2 columns are validated (r2 = 0.60, slope = 0.82) with coincident airborne in situ measurements. The top-down emissions are combined with a priori information from a bottom-up emission inventory with error weighting to achieve an improved a posteriori estimate of the global distribution of surface NOx emissions. Our a posteriori NOx emission inventory for land surface NOx emissions (46.1 Tg N/yr) is 22% larger than the GEIA-based a priori bottom-up inventory for 1998, a difference that reflects rising anthropogenic emissions, especially from East Asia A posteriori NOx emissions for East Asia (9.8 Tg N/yr) exceed those from other continents. The a posteriori inventory improves the GEOS-Chem simulation of NOx, peroxyacetylnitrate, and nitric acid with respect to airborne in situ measurements over and downwind of New York City. The a posteriori is 7% larger than the EDGAR 3.2FT2000 global inventory, 3% larger than the NEI99 inventory for the United States, and 68% larger than a regional inventory for 2000 for eastern Asia. SCIAMACHY NO2 columns over the North Atlantic show a weak plume from lightning NO(x).

Martin, Randall V.↗

Radiative Losses in the Chromosphere During A C-Class Flare

Context. Solar flares release an enormous amount of energy (~10(exp 32) erg) into the corona. A substantial fraction of this energy is transported to the lower atmosphere, which results in chromospheric heating. The mechanisms that transport energy to the lower solar atmosphere during a flare are still not fully understood. Aims. We aim to estimate the temporal evolution of the radiative losses in the chromosphere at the footpoints of a C-class flare, in order to set observational constraints on the electron beam parameters of a RADYN flare simulation. Methods. We estimated the radiative losses from hydrogen, and singly ionized Ca and Mg using semiempirical model atmospheres, which were inferred from a multiline inversion of observed Stokes profiles obtained with the CRISP and CHROMIS instruments on the Swedish 1-m Solar Telescope. The radiative losses were computed taking into account the effect of partial redistribution and non-local thermodynamic equilibrium. To estimate the integrated radiative losses in the chromosphere, the net cooling rates were integrated between the temperature minimum and the height where the temperature reaches 10 kK. We also compared our time series of radiative losses with those from the RADYN flare simulations. Results. We obtained a high spatial-resolution map of integrated radiative losses around the flare peak time. The stratification of the net cooling rate suggests that the Ca IR triplet lines are responsible for most of the radiative losses in the flaring atmosphere. During the flare peak time, the contribution from Ca II H and K and Mgii h and k lines are strong and comparable to the Ca IR triplet (~32kW m(exp -2)). Since our flare is a relatively weak event, the chromosphere is not heated above 11 kK, which in turn yields a subdued Lyα contribution (~7kW m(exp -2)) in the selected limits of the chromosphere. The temporal evolution of total integrated radiative losses exhibits sharply rising losses (0.4kW m(exp -2) (s(exp -1)) and a relatively slow decay (0.23kW m(exp -2) s(exp -1)). The maximum value of total radiative losses is reached around the flare peak time and can go up to 175kWm􀀀2 for a single pixel located at footpoint. After a small parameter study, we find the best model-data consistency in terms of the amplitude of radiative losses and the overall atmospheric structure with a RADYN flare simulation in the injected energy flux of 5 × 10(exp 10) erg s(exp -1) cm(exp -2).

Chromosphere↗

Spectrum and extension of the inverse-Compton emission of the Crab Nebula from a combined Fermi -LAT and H.E.S.S. analysis

The Crab Nebula is a unique laboratory for studying the acceleration of electrons and positrons through their non-thermal radiation. Observations of very-high-energy γ rays from the Crab Nebula have provided important constraints for modelling its broadband emission. We present the first fully self-consistent analysis of the Crab Nebula’s γ-ray emission between 1 GeV and ∼100 TeV, that is, over five orders of magnitude in energy. Using the open-source software package GAMMAPY, we combined 11.4 yr of data from the Fermi Large Area Telescope and 80 h of High Energy Stereoscopic System (H.E.S.S.) data at the event level and provide a measurement of the spatial extension of the nebula and its energy spectrum. We find evidence for a shrinking of the nebula with increasing γ-ray energy. Furthermore, we fitted several phenomenological models to the measured data, finding that none of them can fully describe the spatial extension and the spectral energy distribution at the same time. Especially the extension measured at TeV energies appears too large when compared to the X-ray emission. Our measurements probe the structure of the magnetic field between the pulsar wind termination shock and the dust torus, and we conclude that the magnetic field strength decreases with increasing distance from the pulsar. We complement our study with a careful assessment of systematic uncertainties.

79 ASTRONOMY AND ASTROPHYSICS↗

Generative Models for Crystalline Materials

Understanding structure-property relationships in materials is fundamental in condensed matter physics and materials science. Over the past few years, machine learning (ML) has emerged as a powerful tool for advancing this understanding and accelerating materials discovery. Early ML approaches primarily focused on constructing and screening large material spaces to identify promising candidates for various applications. More recently, research efforts have increasingly shifted toward generating crystal structures using end-to-end generative models. This review analyzes the current state of generative modeling for crystal structure prediction and de novo generation. It examines crystal representations, outlines the generative models used to design crystal structures, and evaluates their respective strengths and limitations. Furthermore, the review highlights experimental considerations for evaluating generated structures and provides recommendations for suitable existing software tools. Emerging topics, such as modeling disorder and defects, integration in advanced characterization, incorporating synthetic feasibility constraints, and model explainability are explored. Ultimately, this work aims to inform both experimental scientists looking to adapt suitable ML models to their specific circumstances and ML specialists seeking to understand the unique challenges related to inverse materials design and discovery.

Metni, Houssam [Karlsruhe Inst. of Technology (KIT↗

Mass, heat and nutrient fluxes in the Atlantic Ocean determined by inverse methods

Inverse methods are applied to historical hydrographic data to address two aspects of the general circulation of the Atlantic Ocean. The method allows conservation statements for mass and other properties, along with a variety of other constraints, to be combined in a dynamically consistent way to estimate the absolute velocity field and associated property transports. The method was first used to examine the exchange of mass and heat between the South Atlantic and the neighboring ocean basins. The second problem addressed concerns the circulation and property fluxes across the 24 and 36 deg N in the subtropical North Atlantic. Conservation statements are considered for the nutrients as well as mass, and the nutrients are found to contribute significant information independent of temperature and salinity.

Rintoul, Stephen Rich↗

Evidence for an Intermediate Mass Black Hole in NGC 5408 X-1

We report the discovery with XMM-Newton of correlated spectral and timing behavior in the ultraluminous X-ray source (ULX) NGC 5408 X-1. An approx. 100 ksec pointing with XMM/Newton obtained in January, 2008 reveals a strong 10 mHz QPO in the > 1 keV flux, as well as flat-topped, band limited noise breaking to a power law. The energy spectrum is again dominated by two components, a 0.16 keV thermal disk and a power-law with an index of approx. 2.5. These new measurements, combined with results from our previous January 2006 pointing in which we first detected QPOs, show for the first time in a ULX a pattern of spectral and temporal correlations strongly analogous to that seen in Galactic black hole sources, but at much higher X-ray luminosity and longer characteristic time-scales. We find that the QPO frequency is proportional to the inferred disk flux, while the QPO and broad-band noise amplitude (root mean squared, rms) are inversely proportional to the disk flux. Assuming that QPO frequency scales inversely with black hole mass at a given power-law spectral index we derive mass estimates using the observed QPO frequency - spectral index relations from five stellar-mass black hole systems with dynamical mass constraints. The results from all sources are consistent with a mass range for NGC 5408 X-1 from 1000 - 9000 Stellar mass. We argue that these are conservative limits, and a more likely range is from 2000 - 5000 Stellar mass. Moreover, the recent relation from Gierlinski et al. that relates black hole mass to the strength of variability at high frequencies (above the break in the power spectrum), and the variability plane results of McHardy et al. and Koerding et al., are also suggestive of such a. high mass for NGC 5408 X-1. Importantly, none of the above estimates appears consistent with a black hole mass less than approx. 1000 Stellar mass for NGC 5408 X-1. We argue that these new findings strongly support the conclusion that NGC 5408 X-1 harbors an intermediate mass black hole.

Strohmayer, Tod E.↗

Constraints on Variability of Brightness and Surface Magnetism on Time Scales of Decades to Centuries in the Sun and Sun-Like Stars: A Source of Potential Terrestrial Climate Variability

The following summarizes the most important, results of our research: (1) Conciliation of solar and stellar photometric variability; (2) Demonstration of an inverse correlation between the global temperature of the terrestrial lower troposphere, inferred from the NASA Microwave Sounding Unit (MSU)) radiometers, and the total area of the Sun covered by coronal holes from January 1979 to present (up to May 2000); (3) Identification of a possible climate mechanism amplifying the impact of solar ultraviolet irradiance variations; (4) Exploration of natural variability in an ocean-atmosphere climate model; (5) Presentation of a review of the sun's coronal influence on the terrestrial space environment; (6) Quantification of stellar variability as an influence on the analysis of periodic radial velocities that imply the presence of a planetary companion.

Baliunas, Sallie L.↗

Rotating-Pump Design Code

Pump Design (PUMPDES) is a computer program for designing a rotating pump for liquid hydrogen, liquid oxygen, liquid nitrogen, water, methane, or ethane. Using realistic properties of these fluids provided by another program called GASPAK, this code performs a station-by-station, mean-line analysis along the pump flow path, obtaining thermodynamic properties of the pumped fluid at each station and evaluating hydraulic losses along the flow path. The variables at each station are obtained under constraints that are consistent with the underlying physical principles. The code evaluates the performance of each stage and the overall pump. In addition, by judiciously choosing the givens and the unknowns, the code can perform a geometric inverse design function: that is, it can compute a pump geometry that yields a closest approximation of given design point. The code contains two major parts: one for an axial-rotor/inducer and one for a multistage centrifugal pump. The inducer and the centrifugal pump are functionally integrated. The code can be used in designing and/or evaluating the inducer/centrifugal-pump combination or the centrifugal pump alone. The code is written in standard Fortran 77.

Walker, James F.↗

Subsurface fluvial sediments beneath InSight on Mars from geophysical constraints

Subsurface structure investigation on Mars is crucial for understanding its geological evolution and past hydrological conditions. Elysium Planitia (EP), located near the hypothesized ancient ocean shorelines, could contain clues for past water activity and paleoclimate. Here we present better-constrained subsurface models beneath InSight extending to ~800 m depth, obtained from joint inversion of seismic and seismoacoustic coupling data, and use the well-resolved subsurface structure to explore the lithological profile through rock physics models. The derived subsurface lithology agrees well with local geological context and exhibits a shallow 60-m-thick low-rigidity layer consistent with hydrated sedimentary materials. Despite possible contributions of aeolian and volcanic deposits, we favor the interpretation that the low-rigidity layer originated from fluvial activity in EP during the Hesperian or Hesperian-to-Amazonian epoch, as supported by adjacent paleo-shoreline morphology observations. These results hint at a period of warmer paleoclimate at low latitudes, possibly during high-obliquity phases of Mars’ rotational axis.

58 GEOSCIENCES↗

Shedding light on shadow generalized parton distributions

The feasibility of extracting generalized parton distributions (GPDs) from deeply virtual Compton scattering (DVCS) data has recently been questioned because of the existence of an infinite set of so-called “shadow GPDs” (SGPDs). These SGPDs depend on the process and manifest as multiple solutions (at a fixed scale 𝑄 2 ) to the inverse problem that needs to be solved to infer GPDs from DVCS data. SGPDs therefore pose a significant challenge for extracting GPDs from DVCS data. With this motivation we study the extent to which QCD evolution can provide constraints on SGPDs. This is possible because the known classes of SGPDs begin to contribute to observables after evolution, and can then be constrained (at the input scale 𝑄$^{2}_{0}$) by data that has a finite 𝑄 2 range. The impact that SGPDs could have on determining the total angular momentum, pressure and sheer force distributions, and tomography is also discussed. We find that 𝑄 2 evolution, given empirical data over a wide range of skewness (𝜉 ) and 𝑄 2 scales, constrains the SGPDs studied at low 𝑥 and low 𝜉. If this finding generalizes to all SGPDs—and we have not been able to find any SGPDs with qualitatively different behavior—then this potentially makes extraction of GPDs from DVCS possible over a limited range of 𝑥 and 𝜉.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Co-evolution for Problem Simplification

This paper explores a co-evolutionary approach applicable to difficult problems with limited failure/success performance feedback. Like familiar "predator-prey" frameworks this algorithm evolves two populations of individuals - the solutions (predators) and the problems (prey). The approach extends previous work by rewarding only the problems that match their difficulty to the level of solut,ion competence. In complex problem domains with limited feedback, this "tractability constraint" helps provide an adaptive fitness gradient that, effectively differentiates the candidate solutions. The algorithm generates selective pressure toward the evolution of increasingly competent solutions by rewarding solution generality and uniqueness and problem tractability and difficulty. Relative (inverse-fitness) and absolute (static objective function) approaches to evaluating problem difficulty are explored and discussed. On a simple control task, this co-evolutionary algorithm was found to have significant advantages over a genetic algorithm with either a static fitness function or a fitness function that changes on a hand-tuned schedule.

Haith, Gary L.↗

Where did the tumor start? An inverse solver with sparse localization for tumor growth models

In this work, we present a numerical scheme for solving an inverse problem for parameter estimation in tumor growth models for glioblastomas, a form of aggressive primary brain tumor. The growth model is a reaction–diffusion partial differential equation (PDE) for the tumor concentration. We use a PDE-constrained optimization formulation for the inverse problem. The unknown parameters are the reaction coefficient (proliferation), the diffusion coefficient (infiltration), and the initial condition field for the tumor PDE. Segmentation of magnetic resonance imaging (MRI) scans drive the inverse problem where segmented tumor regions serve as partial observations of the tumor concentration. Like most cases in clinical practice, we use data from a single time snapshot. Moreover, the precise time relative to the initiation of the tumor is unknown, which poses an additional difficulty for inversion. We perform a frozen-coefficient spectral analysis and show that the inverse problem is severely ill-posed. We introduce a biophysically motivated regularization on the structure and magnitude of the tumor initial condition. In particular, we assume that the tumor starts at a few locations (enforced with a sparsity constraint on the initial condition of the tumor) and that the initial condition magnitude in the maximum norm is equal to one. We solve the resulting optimization problem using an inexact quasi-Newton method combined with a compressive sampling algorithm for the sparsity constraint. Our implementation uses PETSc and AccFFT libraries. We conduct numerical experiments on synthetic and clinical images to highlight the improved performance of our solver over a previously existing solver that uses standard two-norm regularization for the calibration parameters. The existing solver is unable to localize the initial condition. Our new solver can localize the initial condition and recover infiltration and proliferation. In clinical datasets (for which the ground truth is unknown), our solver results in qualitatively different solutions compared to the two-norm regularized solver.

97 MATHEMATICS AND COMPUTING↗