Fitting Parameters Research Articles

Class Symbolic Regression: Gotta Fit ’Em All

We introduce “Class Symbolic Regression” (Class SR), the first framework for automatically finding a single analytical functional form that accurately fits multiple data sets—each realization being governed by its own (possibly) unique set of fitting parameters. This hierarchical framework leverages the common constraint that all the members of a single class of physical phenomena follow a common governing law. Our approach extends the capabilities of our earlier Physical Symbolic Optimization (Φ-SO) framework for symbolic regression, which integrates dimensional analysis constraints and deep reinforcement learning for unsupervised symbolic analytical function discovery from data. Additionally, we introduce the first Class SR benchmark, comprising a series of synthetic physical challenges specifically designed to evaluate such algorithms. We demonstrate the efficacy of our novel approach by applying it to these benchmark challenges and showcase its practical utility for astrophysics by successfully extracting an analytic galaxy potential from a set of simulated orbits approximating stellar streams.

Sensitivity of GNSS to vertical land motion over Europe: effects of geophysical loadings and common-mode errors

We perform a statistical sensitivity analysis on a parametric fit to vertical daily displacement time series of 244 European Permanent GNSS stations, with a focus on linear vertical land motion (VLM), i.e., station velocity. We compare two independent corrections to the raw (uncorrected) observed displacements. The first correction is physical and accounts for non-tidal atmospheric, non-tidal oceanic and hydrological loading displacements, while the second approach is an empirical correction for the common-mode errors. For the uncorrected case, we show that combining power-law and white noise stochastic models with autoregressive models yields adequate noise approximations. With this as a realistic baseline, we report improvement rates of about 14% to 24% in station velocity sensitivity, after corrections are applied. We analyze the choice of the stochastic models in detail and outline potential discrepancies between the GNSS-observed displacements and those predicted by the loading models. Furthermore, we apply restricted maximum likelihood estimation (RMLE), to remove low-frequency noise biases, which yields more reliable velocity uncertainty estimates. RMLE reveals that for a number of stations noise is best modeled by a combination of random walk, flicker noise, and white noise. The sensitivity analysis yields minimum detectable VLM parameters (linear velocities, seasonal periodic motions, and offsets), which are of interest for geophysical applications of GNSS, such as tectonic or hydrological studies.

Research on Viscoelastic Impact Damage Constitutive Model and Its Behavioral Characteristics

To investigate the damage characteristics of viscoelastic materials under various impact scenarios, this study presents a viscoelastic impact damage constitutive model that incorporates a material coefficient, a variable fractional-order differential operator, and a damage factor. Split Hopkinson Pressure Bar experiments are conducted under single-impact and repeated-impact conditions. The results indicate that nonlinear features in stress-strain curves at different stages, exhibiting prominent strain rate dependency near the stress peak point in the single-impact scenario. In the repeated-impact scenario, the stress peak points decrease as the impact times increase, resulting in a corresponding decline in the material's load-bearing capacity. Furthermore, strain rate escalates the strain rate increases with an increase in impact times, making the material more susceptible to deformation. Parameter fitting and Sobol sensitivity analysis utilizing experimental data from both scenarios have been employed to explore the effects and patterns of single-parameter and multi-parameter coupling on the model, accurately delineating their influence. The findings reveal a strong coupling relationship among various parameters of the viscoelastic impact damage constitutive model in multiple impact scenarios, showing higher sensitivity to fluctuations in the viscoelastic coefficient and damage factor. These analyses have demonstrated the accuracy of the viscoelastic impact damage constitutive model in capturing dynamic impact damage characteristics of viscoelastic materials across various scenarios.

Deciphering chemical ordering in High Entropy Materials: A machine learning-accelerated high-throughput cluster expansion approach

The Cluster Expansion (CE) Method encounters significant computational challenges in multicomponent systems due to the computational expense of generating training data through density functional theory (DFT) calculations. This work aims to refine the cluster and structure selection processes to mitigate these challenges. We introduce a novel method that significantly reduces the computational load associated with the calculation of fitting parameters. This method employs a Graph Neural Network (GNN) model, leveraging the M3GNet network, which is trained using a select subset of DFT calculations at each ionic step. The trained surrogate model excels in predicting the volume and energy of the final structure for a relaxation run. By employing this model, we sample thousands of structures and fit a CE model to the energies of these GNN-relaxed structures. This approach, utilizing a large training dataset, effectively reduces the risk of overfitting, yielding a CE model with a root-mean-square error (RMSE) below 10 meV/atom. We validate our method’s effectiveness in two test cases: the (Ti, Cr, Zr, Mo, Hf, Ta)B2 diboride system and the Refractory High-Entropy Alloy (HEA) AlTiZrNbHfTa system. Our findings demonstrate the significant advantages of integrating a GNN model, specifically the M3GNet network, with CE methods for the efficient predictive analysis of chemical ordering in High Entropy Materials. The accelerating capabilities of the hybrid ML-CE approach to investigate the evolution of Short Range Ordering (SRO) in a large number of stoichiometric systems. Finally, we show how it is possible to correlate the strength of chemical ordering to easily accessible alloy parameters.

Pharmacokinetic/Pharmacodynamic modelling of Saxagliptin and its active metabolite, 5-hydroxy Saxagliptin in rats with Type 2 Diabetes Mellitus

Background and purposesIt is unclear whether the parent Saxagliptin (SAX) in vivo is the same as that in vitro, which is twice that of 5-hydroxy Saxagliptin (5-OH SAX). This study is to construct a Pharmacokinetic-Pharmacodynamic (PK-PD) link model to evaluate the genuine relationship between the concentration of parent SAX in vivo and the effect.MethodsFirst, we established a reliable Ultra Performance Liquid Chromatography-Mass Spectrometry (UPLC-MS/MS) method and DPP-4 inhibition ratio determination method. Then, the T2DM rats were randomly divided into four groups, intravenous injection of 5-OH SAX (0.5 mg/kg) and saline group, intragastric administration of SAX (10 mg/kg) and Sodium carboxymethyl cellulose (CMC-Na) group. Plasma samples were collected at different time points for subsequent testing. Finally, we used the measured concentrations and inhibition ratios to construct a PK-PD link model for 5-OH SAX and parent SAX.ResultsA two-compartment with additive model showed the pharmacokinetic process of SAX and 5-OH SAX, the concentration-effect relationship was represented by a sigmoidal Emax model and sigmoidal Emax with E0 model for SAX and 5-OH SAX, respectively. Fitting parameters showed SAX was rapidly absorbed after administration (Tmax=0.11 h, t1/2, ka=0.07 h), widely distributed in the body (V ≈ 20 L/kg), plasma exposure reached 3282.06 ng*h/mL, and the elimination half-life was 6.13 h. The maximum plasma dipeptidyl peptidase IV (DPP-4) inhibition ratio of parent SAX was 71.47%. According to the final fitting parameter EC50, EC50, 5−OH SAX=0.46EC50, SAX(parent), it was believed that the inhibitory effect of 5-OH SAX was about half of the parent SAX, which is consistent with the literature.ConclusionsThe PK-PD link model of the parent SAX established in this study can predict its pharmacokinetic process in T2DM rats and the strength of the inhibitory effect of DPP-4 based on non-clinical data.

Dispersion Energies with the i-DMFT Method.

The recently proposed i-DMFT method [Wang and Baerends, Phys. Rev. Lett. 128, 013001 (2022)] has been proven to be ideally suited to recover strong static correlation in dissociating covalent bonds. Here, the application to van der Waals bonding is investigated using the prototype van der Waals systems triplet H2 and ground-state He2. It is demonstrated that the i-DMFT orbitals are in this case essentially different from the natural orbitals, and the i-DMFT occupations differ substantially from the NO occupations. This is shown to lead to rather deficient interaction potential curves, even if a reasonable well depth may be obtained by fitting of parameters. If the basis set is extended, however, it may no longer be possible to generate van der Waals bonding at all. The linear behavior of the two-electron cumulant energy Ecum as a function of the "entropy" S along a dissociation coordinate, which was the basis of i-DMFT, is distinctly poorer in the case of van der Waals bonding than for covalent bonding.

Determining the Characteristics of Ultrathin Polymer Films: A Spectroscopic Ellipsometry Approach.

Ellipsometry is a powerful and convenient technique that is widely used to determine the thickness and optical characteristics of polymer thin films. The determination is accomplished by modeling the measured change in the polarization of an electromagnetic wave upon interacting with the thin film. However, due to the strong statistical correlations between the fit parameters in the model, simultaneous determination of the thickness and the refractive indices of optically anisotropic ultrathin films using ellipsometry remains a challenge. Here, we propose an approach that can be used to obtain reliable values of both the thickness and the optical anisotropy of ultrathin polymer films. The approach was developed by performing spectroscopic ellipsometry measurements on thin films of hydrophobic polystyrene and hydrophilic chitosan of thickness between a few tens to a few hundred nm and whose absolute value of the birefringence differed by approximately an order of magnitude. Careful consideration of the characteristics of the root mean squared error of the fits obtained by modeling the ellipsometry data and the statistical correlations between the fit parameters formed the basis of the proposed approach.

Estimating Biogeochemical Rates Using a Computationally Efficient Lagrangian Approach

Nutrient concentrations in many estuaries have increased over the past century due to increases in wastewater discharge and increased agricultural intensity, contributing to multiple environmental problems. Numerous biogeochemical and physical processes in estuaries influence nutrient concentrations during transport, resulting in complex spatial and temporal variability and challenges identifying predominant processes and their rates. Mechanistic models which require these rates to quantify biogeochemical processes become complex and difficult to calibrate as the number of processes and parameters grows, owing to the high dimensionality of the parameter space and the computational cost of simultaneously modeling the transport and transformations of constituents. We developed a modeling approach that decouples transport from transformations, enabling fast, data-driven exploration of the parameter space. The approach extracted information including water age, cumulative exposure to specific habitats, and mean water depth exposure from a hydrodynamic model. Using this information, a biogeochemical model was implemented to predict ammonium and nitrate concentrations in a Lagrangian frame. The model performed each simulation in milliseconds on a laptop computer, allowing the fitting of rate parameters for key transformations by optimization. The optimization used fixed station nitrate observations and the model was then validated against high-resolution mapping observations of ammonium and nitrate. The results suggest that the observed spatial and temporal variation can be largely represented with five transformation processes and their associated rates. Dissolved inorganic nitrogen (DIN) losses occurred only in shallow vegetated areas in the model, highlighting that biogeochemical processes in these areas should be included in DIN models.

Topological derivative based sensitivity analysis for three-dimensional discrete variable topology optimization

This study introduces a novel Topological Derivative-based Sensitivity Analysis (TDSA) methodology for three-dimensional (3D) discrete variable topology optimization. Recently, the authors pointed out that the discrete variable sensitivity can be related to the topological derivative, and thus can be rationally approximated by the specially customized topological derivative for plane stress problems. However, the 3D discrete variable sensitivity requires the 3D topological derivative with element-shaped (e.g., unit cube) domain perturbation, whose analytical solution is not available in the literature. This paper proposes a unified parameter fitting framework to calculate the 3D topological derivative with arbitrary shape 3D domain perturbation. The formula for spherical hole perturbation obtained through this parameter fitting framework is identical to the well-known analytical topological derivative formula. Further, the 3D discrete variable sensitivity can be easily obtained through element-shaped domain perturbation. With the recently proposed Sequential Approximate Integer Programming (SAIP), numerical examples demonstrate that TDSA is precise not only for the self-adjoint 3D minimum compliance problems but also for the non-adjoint 3D compliant mechanism design problems. In sum, numerical examples have been conducted by feeding the derived sensitivity to the SAIP optimization algorithms, and the correctness of the sensitivity information has been well demonstrated. This research further solidifies the foundation of rational discrete variable sensitivity analysis in 3D topology optimization.

Theoretical analysis and experimental validation of multi‐level friction damping system

AbstractMost traditional passive friction dampers are limited to the design of single activated energy dissipation mechanism; therefore, when the seismic intensity is not strong enough to activate the mechanism, traditional friction dampers can only increase stiffness of the structure just like braces; only when the mechanism is activated will the energy dissipation elements perform energy absorption and assist the structure to absorb received seismic energy. The objective of this study is to improve this defect of traditional friction dampers, developing a Multi–Level Friction Damper (MFD) with a two‐stage energy dissipation mechanism, helping building structures (e.g., hospitals, high‐tech plants) reduce the acceleration responses of the superstructure. MFDs are proven to provide more comprehensive protection and have higher energy dissipation benefits than traditional friction dampers by the validation of numerical analysis and shaking table test. The study in turn performed parameter fitting with the results of the numerical simulation analysis and shaking table test, and the experimental results turned out to be satisfactory, validating the accuracy of the theoretical formulas.

Investigation on thermally assisted optically stimulated luminescence signal in natural CaF2

In this work, thermally assisted OSL (TA-OSL) of natural fluorite was investigated, aiming to understand better the role of traps in both TL and OSL. TA-OSL is the luminescence simultaneously stimulated by light and heat; from this combination it is possible to access deeper traps in the analyzed material, that, in general, need more energy to be accessed. Irradiations were performed at room temperature using the Sr-90/Y-90 source incorporated in the TL/OSL reader at a dose rate of about 10 mGy/s. The optical stimulus was blue light at 470 nm. The dosimeters were also irradiated with X and gamma-rays of various energies (from 20 keV to 1.25 MeV) for comparing the energy dependence of the OSL and the TA-OSL signals. Residual TL curves were acquired after OSL readouts for checking trap participation in OSL emission. The OSL measurements were done at temperatures from 25 °C to 400 °C. For readout temperatures from 25 to ∼185 °C, decay curves were observed, and they were modeled by one stretched-exponential function, giving rise to a good fit to the experimental data. The dependence of the fitting parameter (β) on the photon energy was studied, and it was observed that β increases with the X-ray beam effective energy. The energy dependence of OSL signal is 1.5 times larger than that of TA-OSL signal, pointing to the reduction in energy dependence with the combination of thermal and optical stimuli. The total light emitted (TA-OSL + residual TL) is highly increased by the simultaneous stimulation by light and heat, indicating that light promotes charges to thermally active traps (phototransfer), and heat promotes charges to optically active traps, facilitating their release during illumination.

An updated variable RBE model for proton therapy

Objective. While a constant relative biological effectiveness (RBE) of 1.1 forms the basis for clinical proton therapy, variable RBE models are increasingly being used in plan evaluation. However, there is substantial variation across RBE models, and several new in vitro datasets have not yet been included in the existing models. In this study, an updated in vitro proton RBE database was collected and used to examine current RBE model assumptions, and to propose an up-to-date RBE model as a tool for evaluating RBE effects in clinical settings. Approach. A proton database (471 data points) was collected from the literature, almost twice the size of the previously largest model database. Each data point included linear-quadratic model parameters and linear energy transfer (LET). Statistical analyses were performed to test the validity of commonly applied assumptions of phenomenological RBE models, and new model functions were proposed for RBEmax and RBEmin (RBE at the lower and upper dose limits). Previously published models were refitted to the database and compared to the new model in terms of model performance and RBE estimates. Main results. The statistical analysis indicated that the intercept of the RBEmax function should be a free fitting parameter and RBE estimates were clearly higher for models with free intercept. RBEmin increased with increasing LET, while a dependency of RBEmin on the reference radiation fractionation sensitivity ( α/βx ) did not significantly improve model performance. Evaluating the models, the new model gave overall lowest RMSE and highest R2 score. RBE estimates in the distal part of a spread-out-Bragg-peak in water ( α/βx = 2.1 Gy) were 1.24–1.51 for original models, 1.25–1.49 for refits and 1.42 for the new model. Significance. An updated RBE model based on the currently largest database among published phenomenological models was proposed. Overall, the new model showed better performance compared to refitted published RBE models.

Automated data-driven method for creating digital building models from dense point clouds and images through semantic segmentation and parametric model fitting

This paper proposes an automated method for creating semantic digital building models using dense point clouds and images. The method employs a hybrid bottom-up, top-down approach, integrating artificial intelligence capabilities in scene understanding with domain engineering knowledge to overcome challenges in indoor 3D reconstruction. The pre-trained PointTransformer semantic segmentation model extracts thirteen building objects, where the wall and ceiling segments are utilized in a 3D space parsing algorithm. The parameterized floor plan map is then generated using a data-driven approach, enabling the creation of an extruded volumetric digital model. Additionally, the YOLOV8 object detection network recognizes doors and windows in images derived from projected points of the wall instances. The validation results for six building datasets with different layouts showcase the effectiveness of the proposed model reconstruction algorithm, with a mean error of about 7 cm between the parameters of elements in digital reference models and reconstructed models. This highlights AI’s potential in automating the creation of digital models for the real world.

Effects of Specific Physical Fitness Regimen on Selected Motor Fitness Parameters among Tribal Girls in Andhra Pradesh

Effects of Specific Physical Fitness Regimen on Selected Motor Fitness Parameters among Tribal Girls in Andhra Pradesh

High precision wavefront correction method in interferometer testing

A wavefront correction method is proposed for high-precision optic surfacing, addressing the discrepancy between wavefront and real surface errors in Fizeau interferometer testing. We believe this to be a proposed novel method that encompasses optical surface function parameters fitting, lateral distortion correction, misalignment error removal, and sag surface error calculation. The method's error has been thoroughly analyzed, including aspects of function parameters fitting, ray tracing, and interpolation. The effectiveness of the method was demonstrated by correcting the wavefront of an off-axis parabolic mirror in null testing configurations, significantly reducing artificially created annular errors and improving off-axis direction errors from 0.23λ to 0.05λ (λ=632.8 nm), with the PV of aspheric departures exceeding 8.5 mm.

Bayes_Opt-SWMM: A Gaussian process-based Bayesian optimization tool for real-time flood modeling with SWMM

Real-time flood model plays a pivotal role in averting urban flood damage, particularly when there is minimal lead time for preparatory measures. However, urban flood modeling in real-time often contends with inherent uncertainties arising from input data uncertainty and parameter ambiguities. This study introduces a real-time calibration (RTC) tool called Bayes_Opt-SWMM , specifically tailored for real-time urban flood modeling and uncertainty optimization. This tool leverages the Gaussian process-based Bayesian optimization algorithm and interfaces seamlessly with the Stormwater Management Model (SWMM). It integrates real-time model forcing data and flood monitoring collected through sensors and gauges which are strategically placed within critical locations of urban drainage systems. Our approach hinges on the Surrogate Model based Uncertainty Optimization (SMUO) concept, providing an avenue for enhancing real-time flood modeling. Bayes_Opt-SWMM runs the optimization process using a surrogate model called Gaussian Process emulator with two inference methods: (1) the Gaussian Process (GP) model and (2) Markov Chain Monte Carlo (MCMC) algorithm in GP model (GP_MCMC). Furthermore, three acquisition functions, namely Expected Improvement (EI), Maximum Probability of Improvement (MPI), and Lower Confidence Bound (LCB), facilitate optimal parameter fitting within the surrogate models. The efficiency of GP-based surrogate models in learning SWMM model parameters, leads to an improved uncertainty quantification and accelerated real-time flood modeling in urban areas. Overall, Bayes_Opt-SWMM emerges as a cost-effective and valuable tool for real-time flood modeling and monitoring, with significant potential for managing intelligent storm water systems in urban environments.

A new activity coefficient model for describing adsorbed phase nonidealities

The following study introduces a new adsorbed phase activity coefficient model, the SPLINT model, for describing nonideal multicomponent systems. The derivation is presented and simplification to the thermodynamically robust ABC model in the low‑coverage limit is shown. Both the SPLINT and ABC models are fit to 25 binary systems. Thermodynamic consistency of the data is established through multiple consistency tests including the intersection rule, closed‑loop reduced spreading pressure integration, the Gibbs‑Duhem integral equality, and alignment of pure and binary data. Regressed parameters are used in Real Adsorbed Solution Theory to predict both binary and ternary adsorption. The ABC and SPLINT models accurately describe systems with considerable nonideality when the activity coefficients are symmetric; however, the SPLINT model is required for accurate description of systems with complex, asymmetric activity coefficient behavior. The new model includes one more fitting parameter than the ABC model for a single binary system, but less across multiple data sets and higher‑order systems due to the theoretical basis. The importance of capturing activity coefficient asymmetry is demonstrated with a highly nonideal system across various pressures and temperatures measured by the present authors using the Integral Mass Balance method with HFC‑125 (pentafluoroethane), HFC‑32 (difluoromethane), and zeolite H‑ZSM‑5. The theoretical basis of the SPLINT model is further enforced by presenting two methods for predicting activity coefficients with the SPLINT model: correlating the fitting parameters individually and simultaneously regressing pure isosteric heat data to extract SPLINT fitting parameters. The study concludes with a discussion of pure and binary HFC‑125/HFC‑32 data with zeolite H‑ZSM‑5. A possible binary adsorption mechanism is proposed based on isosteric heat and excess enthalpy predictions and observed system irreversibility.

Inclusivity of thermal performance parameters for evaluation of solar cookers and the necessity of uniformity in the appraisal using generalized test procedure for different designs

Solar cookers play a vital role in decentralized energy solutions. Therefore, their appropriate rating is essential. The present work reviews and emphasizes the usefulness of thermal performance parameters (TPPs) for assessing solar cookers, such as box type, parabolic dish, panel type, Fresnel lens-based, and their hybrids. Although the TPPs are extensively used for testing solar cookers, several research studies depicted ambiguities, non-uniformities, and inconsistencies in their use. Interestingly, Cooker Opto-Thermal Ratio (COR) is one of the most generalized and, hence, useful TPP for the optical and thermal performance evaluation and rating/grading of multiple designs of solar cookers. In view of non-uniformities and inconsistencies found in determining TPPs, current work provides crucial insights into the existing TPPs, including COR, corresponding test standards/protocols, and quantification of test load(s) for solar cookers. Also, this work justifies the appropriate use of the different TPPs for solar cookers, and the usefulness and robustness of COR determined using linear regression fit of experimental data and derivate COR-dependent objective parameters. Finally, it includes insightful information for researchers, designers, and manufacturers on the future research pathways based on COR and corresponding test procedure and provide useful visions to avoid its deceptive, inconsistent, and inappropriate use.

DIFFERENCE IN SURFACE FITTING WITH STANDARD AND MATRIX TOPOLOGY

This paper presents the impact of the surface topology of the scanned 3D object on parametric fitting. Whether it is a simple NURBS (Non-uniform rational B-spline) or a more complex hierarchical spline version, it is important to apply the fitting procedure. Here we describe the differences between fitting a surface with a given topology as a result of a 3D scanning system and a matrix topology of the surface, where the original surface is replaced by the result of a preset number of sections of the original geometry. We use the matrix and the free-form distribution. The former is more stable with respect to the distribution of the control point, the latter is numerically more suitable. In the future, we plan to adopt the free-form distribution to utilize the advantages of both distributions.

Spatial Prediction of Diameter Distributions for the Alpine Protection Forests in Ebensee, Austria, Using ALS/PLS and Spatial Distributional Regression Models

A novel Bayesian spatial distributional regression model is presented to predict forest structural diversity in terms of the distributions of the stem diameter at breast height (DBH) in the protection forests in Ebensee, Austria. The distributional regression approach overcomes the limitations and uncertainties of traditional regression modeling, in which the conditional mean of the response is regressed against explanatory variables. The distributional regression addresses the complete conditional response distribution, instead. In total 36,338 sample trees were measured via a handheld mobile personal laser scanning system (PLS) on 273 sample plots each having a 20 m radius. Recent airborne laser scanning (ALS) data were used to derive regression covariates from the normalized digital vegetation height model (DVHM) and the digital terrain model (DTM). Candidate models were constructed that differed in their linear predictors of the two gamma distribution parameters. In the distributional regression approach, covariates can enter the model in a flexible form, such as via nonlinear smooth curves, cyclic smooths, or spatial effects. Supported by Bayesian diagnostics DIC and WAIC, nonlinear smoothing splines outperformed linear parametric slope coefficients, and the best implementation of spatial structured effects was achieved by a Gaussian process smooth. Model fitting and posterior parameter inference was achieved by using full Bayesian methodology and MCMC sampling algorithms implemented in the R-package BAMLSS. With BAMLSS, spatial interval predictions of the DBH distribution at any new geo-locations were enabled via straightforward access to the posterior predictive distributions of the model terms and by offering simple plug-in solutions for new covariate values. A cross-validation analysis validated the robustness of the proposed method’s parameter estimation and out-of-sample prediction. Spatial predictions of stem count proportions per DBH classes revealed that regeneration of smaller trees was lacking in certain areas of the protection forest landscape. Therefore, the intensity of final felling needs to be increased to reduce shading from the dense, overmature shelter trees and to promote sunlight for the young regeneration trees.