Lattice Spring Model & Simulation Based Parameter Inference
Presentation of mathematical content of SDRD project related to subsidence and shock physics
97 MATHEMATICS AND COMPUTING↗
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Results for “parameter inference”
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On the impact of the galaxy window function on cosmological parameter estimation
One important source of systematics in galaxy redshift surveys comes from the estimation of the galaxy window function. Up until now, the impact of the uncertainty in estimating the galaxy window function on parameter inference has not been properly studied. In this paper, we show that the uncertainty and the bias in estimating the galaxy window function will be salient for ongoing and next-generation galaxy surveys using a simulation-based approach. With a specific case study of cross-correlating emission-line galaxies from the DESI Legacy Imaging Surveys and the Planck cosmic microwave background lensing map, we show that neural network-based regression approaches to modelling the window function are superior in comparison to linear regression-based models. Here, we additionally show that the definition of the galaxy overdensity estimator can impact the overall signal-to-noise of observed power spectra. Finally, we show that the additive biases coming from the window functions can significantly bias the modes of the inferred parameters and also degrade their precision. Thus, a careful understanding of the window functions will be essential to conduct cosmological experiments.
79 ASTRONOMY AND ASTROPHYSICS↗
Optimal Cosmic Microwave Background Lensing Reconstruction and Parameter Estimation with SPTpol Data
Here, we perform the first simultaneous Bayesian parameter inference and optimal reconstruction of the gravitational lensing of the cosmic microwave background (CMB), using 100 deg 2 of polarization observations from the SPTpol receiver on the South Pole Telescope. These data reach noise levels as low as 5.8 μK arcmin in polarization, which are low enough that the typically used quadratic estimator (QE) technique for analyzing CMB lensing is significantly suboptimal. Conversely, the Bayesian procedure extracts all lensing information from the data and is optimal at any noise level. We infer the amplitude of the gravitational lensing potential to be ${A}_{\phi }=0.949\,\pm \,0.122$ using the Bayesian pipeline, consistent with our QE pipeline result, but with 17% smaller error bars. The Bayesian analysis also provides a simple way to account for systematic uncertainties, performing a similar job as frequentist "bias hardening" or linear bias correction, and reducing the systematic uncertainty on A Φ due to polarization calibration from almost half of the statistical error to effectively zero. Finally, we jointly constrain A Φ along with A L , the amplitude of lensing-like effects on the CMB power spectra, demonstrating that the Bayesian method can be used to easily infer parameters both from an optimal lensing reconstruction and from the delensed CMB, while exactly accounting for the correlation between the two. These results demonstrate the feasibility of the Bayesian approach on real data, and pave the way for future analysis of deep CMB polarization measurements with SPT-3G, Simons Observatory, and CMB-S4, where improvements relative to the QE can reach 1.5 times tighter constraints on A Φ and seven times lower effective lensing reconstruction noise.
79 ASTRONOMY AND ASTROPHYSICS↗
Characterizing the Sample Selection for Supernova Cosmology
Type Ia supernovae (SNe Ia) are used as distance indicators to infer the cosmological parameters that specify the expansion history of the universe. Parameter inference depends on the criteria by which the analysis SN sample is selected. Only for the simplest selection criteria and population models can the likelihood be calculated analytically, otherwise it needs to be determined numerically, a process that inherently has error. Numerical errors in the likelihood lead to errors in parameter inference. This article presents toy examples where the distance modulus is inferred given a set of SNe at a single redshift. Parameter estimators and their uncertainties are calculated using Monte Carlo techniques. The relationship between the number of Monte Carlo realizations and numerical errors is presented. The procedure can be applied to more realistic models and used to determine the computational and data management requirements of the transient analysis pipeline.
79 ASTRONOMY AND ASTROPHYSICS↗
An implementation of neural simulation-based inference for parameter estimation in ATLAS
Neural simulation-based inference (NSBI) is a powerful class of machine-learning-based methods for statistical inference that naturally handles high-dimensional parameter estimation without the need to bin data into low-dimensional summary histograms. Such methods are promising for a range of measurements, including at the Large Hadron Collider, where no single observable may be optimal to scan over the entire theoretical phase space under consideration, or where binning data into histograms could result in a loss of sensitivity. This work develops a NSBI framework for statistical inference, using neural networks to estimate probability density ratios, which enables the application to a full-scale analysis. It incorporates a large number of systematic uncertainties, quantifies the uncertainty due to the finite number of events in training samples, develops a method to construct confidence intervals, and demonstrates a series of intermediate diagnostic checks that can be performed to validate the robustness of the method. As an example, the power and feasibility of the method are assessed on simulated data for a simplified version of an off-shell Higgs boson couplings measurement in the four-lepton final states. This approach represents an extension to the standard statistical methodology used by the experiments at the Large Hadron Collider, and can benefit many physics analyses.
frequentist statistics↗
Kilonova light-curve interpolation with neural networks
Kilonovae are the electromagnetic transients created by the radioactive decay of freshly synthesized elements in the environment surrounding a neutron star merger. To study the fundamental physics in these complex environments, kilonova modeling requires, in part, the use of radiative transfer simulations. The microphysics involved in these simulations results in high computational cost, prompting the use of emulators for parameter inference applications. Utilizing a training set of 22 248 high-fidelity simulations (composed of 412 unique ejecta parameter combinations evaluated at 54 viewing angles), we use a neural network to efficiently train on existing radiative transfer simulations and predict light curves for new parameters in a fast and computationally efficient manner. Our neural network can generate millions of new light curves in under a minute. We discuss our emulator's degree of off-sample reliability and parameter inference of the AT2017gfo observational data. Finally, we discuss tension introduced by multiband inference in the parameter inference results, particularly with regard to the neural network's recovery of viewing angle. Published by the American Physical Society 2024
79 ASTRONOMY AND ASTROPHYSICS↗
Impact of cross section uncertainties on NOvA oscillation analyses
The NOvA experiment is an off-axis long-baseline neutrino oscillation experiment measuring $\nu_{\mu}$ disappearance and $\nu_{e}$ appearance in a $\nu_{\mu}$ beam originating at Fermilab. Oscillations are observed in the far detector relative to measurements made in the near detector, with a full simulation of the beam line and detectors being used to perform extrapolation between them. The neutrino simulation uses the GENIE event generator, which contains implementations of numerous theoretical neutrino interaction models applied to a variety of nuclear targets. However, recent data, recent reanalysis of extant data, and continued development of theoretical models have brought to light deficiencies in the default GENIE cross section model, which informs the predicted spectra used to infer oscillation parameters. We explore how uncertainties in this model, together with modifications to GENIE version 2.12.2 based on external information and NOvA Near Detector (ND) data, affect NOvA's oscillation parameter inferences. We also discuss how these uncertainties can be mitigated by judicious analysis design, including usage of the ND data.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Comment on "An implementation of neural simulation-based inference for parameter estimation in ATLAS''
The paper titled "An implementation of neural simulation-based inference for parameter estimation in ATLAS" by the ATLAS collaboration (arXiv:2412.01600v1 [hep-ex]) describes the implementation of neural simulation-based inference for a measurement analysis performed by ATLAS. The uncertainties in the analysis arising from the finiteness of the simulated datasets are estimated using a novel double-bootstrapping technique described in that work. In the present comment, it is claimed and demonstrated, using a toy example, that the double-bootstrapping technique does not actually capture the aforementioned uncertainties.
43 PARTICLE ACCELERATORS↗
Multimodal parameter spaces of a complex multi-channel neuron model
One of the most common types of models that helps us to understand neuron behavior is based on the Hodgkin–Huxley ion channel formulation (HH model). A major challenge with inferring parameters in HH models is non-uniqueness: many different sets of ion channel parameter values produce similar outputs for the same input stimulus. Such phenomena result in an objective function that exhibits multiple modes (i.e., multiple local minima). This non-uniqueness of local optimality poses challenges for parameter estimation with many algorithmic optimization techniques. HH models additionally have severe non-linearities resulting in further challenges for inferring parameters in an algorithmic fashion. To address these challenges with a tractable method in high-dimensional parameter spaces, we propose using a particular Markov chain Monte Carlo (MCMC) algorithm, which has the advantage of inferring parameters in a Bayesian framework. The Bayesian approach is designed to be suitable for multimodal solutions to inverse problems. We introduce and demonstrate the method using a three-channel HH model. We then focus on the inference of nine parameters in an eight-channel HH model, which we analyze in detail. We explore how the MCMC algorithm can uncover complex relationships between inferred parameters using five injected current levels. The MCMC method provides as a result a nine-dimensional posterior distribution, which we analyze visually with solution maps or landscapes of the possible parameter sets. The visualized solution maps show new complex structures of the multimodal posteriors, and they allow for selection of locally and globally optimal value sets, and they visually expose parameter sensitivities and regions of higher model robustness. We envision these solution maps as enabling experimentalists to improve the design of future experiments, increase scientific productivity and improve on model structure and ideation when the MCMC algorithm is applied to experimental data.
97 MATHEMATICS AND COMPUTING↗
KilonovaNet : Surrogate models of kilonova spectra with conditional variational autoencoders
ABSTRACT Detailed radiative transfer simulations of kilonova spectra play an essential role in multimessenger astrophysics. Using the simulation results in parameter inference studies requires building a surrogate model from the simulation outputs to use in algorithms requiring sampling. In this work, we present kilonovanet, an implementation of conditional variational autoencoders (cVAEs) for the construction of surrogate models of kilonova spectra. This method can be trained on spectra directly, removing overhead time of pre-processing spectra, and greatly speeds up parameter inference time. We build surrogate models of three state-of-the-art kilonova simulation data sets and present in-depth surrogate error evaluation methods, which can in general be applied to any surrogate construction method. By creating synthetic photometric observations from the spectral surrogate, we perform parameter inference for the observed light-curve data of GW170817 and compare the results with previous analyses. Given the speed with which kilonovanet performs during parameter inference, it will serve as a useful tool in future gravitational wave observing runs to quickly analyse potential kilonova candidates.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
A Novel Modeling Framework for Computationally Efficient and Accurate Real-Time Ensemble Flood Forecasting With Uncertainty Quantification
A novel modeling framework that simultaneously improves accuracy, predictability, and computational efficiency is presented. It embraces the benefits of three modeling techniques integrated together for the first time: surrogate modeling, parameter inference, and data assimilation. The use of polynomial chaos expansion (PCE) surrogates significantly decreases computational time. Parameter inference allows for model faster convergence, reduced uncertainty, and superior accuracy of simulated results. Ensemble Kalman filters assimilate errors that occur during forecasting. To examine the applicability and effectiveness of the integrated framework, we developed 18 approaches according to how surrogate models are constructed, what type of parameter distributions are used as model inputs, and whether model parameters are updated during the data assimilation procedure. We conclude that (1) PCE must be built over various forcing and flow conditions, and in contrast to previous studies, it does not need to be rebuilt at each time step; (2) model parameter specification that relies on constrained, posterior information of parameters (so-called Selected specification) can significantly improve forecasting performance and reduce uncertainty bounds compared to Random specification using prior information of parameters; and (3) no substantial differences in results exist between single and dual ensemble Kalman filters, but the latter better simulates flood peaks. The use of PCE effectively compensates for the computational load added by the parameter inference and data assimilation (up to ~80 times faster). Therefore, the presented approach contributes to a shift in modeling paradigm arguing that complex, high-fidelity hydrologic and hydraulic models should be increasingly adopted for real-time and ensemble flood forecasting.
54 ENVIRONMENTAL SCIENCES↗
Cosmic Inference: Constraining Parameters with Observations and a Highly Limited Number of Simulations
We look at cosmological probes that pose an inverse problem where the measurement result is obtained through observations, and the objective is to infer values of model parameters that characterize the underlying physical system-our universe, from these observations and theoretical forward-modeling. The only way to accurately forward-model physical behavior on small scales is via expensive numerical simulations, which are further “emulated” due to their high cost. Emulators are commonly built with a set of simulations covering the parameter space with Latin hypercube sampling and an interpolation procedure; the aim is to establish an approximately constant prediction error across the hypercube. In this paper, we provide a description of a novel statistical framework for obtaining accurate parameter constraints. The proposed framework uses multi-output Gaussian process emulators that are adaptively constructed using Bayesian optimization methods with the goal of maintaining a low emulation error in the region of the hypercube preferred by the observational data. In this paper, we compare several approaches for constructing multi-output emulators that enable us to take possible inter-output correlations into account while maintaining the efficiency needed for inference. Using a Lyα forest flux power spectrum, we demonstrate that our adaptive approach requires considerably fewer-by a factor of a few in the Lyα P(k) case considered here-simulations compared to the emulation based on Latin hypercube sampling, and that the method is more robust in reconstructing parameters and their Bayesian credible intervals.
79 ASTRONOMY AND ASTROPHYSICS↗
Simulation-based inference for parameter estimation of complex watershed simulators
High-resolution, spatially distributed process-based (PB) simulators are widely employed in the study of complex catchment processes and their responses to a changing climate. However, calibrating these PB simulators using observed data remains a significant challenge due to several persistent issues, including the following: (1) intractability stemming from the computational demands and complex responses of simulators, which renders infeasible calculation of the conditional probability of parameters and data, and (2) uncertainty stemming from the choice of simplified representations of complex natural hydrologic processes. Here, we demonstrate how simulation-based inference (SBI) can help address both of these challenges with respect to parameter estimation. SBI uses a learned mapping between the parameter space and observed data to estimate parameters for the generation of calibrated simulations. To demonstrate the potential of SBI in hydrologic modeling, we conduct a set of synthetic experiments to infer two common physical parameters – Manning's coefficient and hydraulic conductivity – using a representation of a snowmelt-dominated catchment in Colorado, USA. We introduce novel deep-learning (DL) components to the SBI approach, including an “emulator” as a surrogate for the PB simulator to rapidly explore parameter responses. We also employ a density-based neural network to represent the joint probability of parameters and data without strong assumptions about its functional form. While addressing intractability, we also show that, if the simulator does not represent the system under study well enough, SBI can yield unreliable parameter estimates. Approaches to adopting the SBI framework for cases in which multiple simulator(s) may be adequate are introduced using a performance-weighting approach. The synthetic experiments presented here test the performance of SBI, using the relationship between the surrogate and PB simulators as a proxy for the real case.
54 ENVIRONMENTAL SCIENCES↗
Dealing with Measurement Uncertainties as Nuisance Parameters in Bayesian Model Calibration
In the presence of model discrepancy, the calibration of physics-based models for physical parameter inference is a challenging problem. Lack of identifiability between calibration parameters and model discrepancy requires additional identifiability constraints to be placed on the model discrepancy to obtain unique physical parameter estimates. If these assumptions are violated, the inference for the calibration parameters can be systematically biased. In many applications, such as in dynamic material property experiments, many of the calibration inputs refer to measurement uncertainties. Here, we develop a metric for identifying overfitting of these measurement uncertainties, propose a prior capable of reducing this overfitting, and show how this leads to a diagnostic tool for validation of physical parameter inference. The approach is demonstrated for a benchmark example and applied for a material property application to perform inference on the equation of state parameters of tantalum.
97 MATHEMATICS AND COMPUTING↗
Inferring Structural Parameters of Low-Surface-Brightness-Galaxies with Uncertainty Quantification using Bayesian Neural Networks
Measuring the structural parameters (size, total brightness, light concentration, etc.) of galaxies is a significant first step towards a quantitative description of different galaxy populations. In this work, we demonstrate that a Bayesian Neural Network (BNN) can be used for the inference, with uncertainty quantification, of such morphological parameters from simulated low-surface-brightness galaxy images. Compared to traditional profile-fitting methods, we show that the uncertainties obtained using BNNs are comparable in magnitude, well-calibrated, and the point estimates of the parameters are closer to the true values. Our method is also significantly faster, which is very important with the advent of the era of large galaxy surveys and big data in astrophysics.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Differentiable stochastic halo occupation distribution
ABSTRACT In this work, we demonstrate how differentiable stochastic sampling techniques developed in the context of deep reinforcement learning can be used to perform efficient parameter inference over stochastic, simulation-based, forward models. As a particular example, we focus on the problem of estimating parameters of halo occupation distribution (HOD) models that are used to connect galaxies with their dark matter haloes. Using a combination of continuous relaxation and gradient re-parametrization techniques, we can obtain well-defined gradients with respect to HOD parameters through discrete galaxy catalogue realizations. Having access to these gradients allows us to leverage efficient sampling schemes, such as Hamiltonian Monte Carlo, and greatly speed up parameter inference. We demonstrate our technique on a mock galaxy catalogue generated from the Bolshoi simulation using a standard HOD model and find near-identical posteriors as standard Markov chain Monte Carlo techniques with an increase of ∼8× in convergence efficiency. Our differentiable HOD model also has broad applications in full forward model approaches to cosmic structure and cosmological analysis.
79 ASTRONOMY AND ASTROPHYSICS↗
Impact of Varying Dark Energy on Future Large-Scale Structure Studies
The cosmos withholds multiple mysteries such as dark forms of matter and energy that are yet beyond human comprehension. In the standard cosmological model, $\Lambda$CDM, the cosmological constant $\Lambda$ is thought to be responsible for the late accelerated expansion of the Universe. However, recent results from the Dark Energy Spectroscopic Instrument (DESI) suggest the possibility of evolving dark energy, which warrants further exploration. Future surveys such as the Rubin Observatory Legacy Survey of Space and Time (LSST) will map the large-scale structure (LSS) with unprecedented precision, giving us valuable statistical information about the cosmos. The goal of this research is to investigate the potential impact of an evolving dark energy scenario on cosmological parameters constrained by LSS probes, as will be mapped by the LSST. For this, we examine the power spectra of lens galaxies, source galaxies, and cross-power spectra between lens galaxies and source galaxies. The combination of these statistics is commonly referred to as '3 $\times$ 2 points'. For this investigation, we created a set of simulations resembling LSST data and used them to perform cosmological parameter inference in two scenarios: one in which the simulated data is based on the fiducial model and another on evolving dark energy. We then examined the degeneracy between the cosmological parameters and checked for potential shifts in the parametric space when the data contains dynamical dark energy but the modeling assumes $\Lambda$CDM. Our findings indicate that mismodeling the dark energy equation of state can significantly impact parameter inference, particularly affecting the total matter density, $\Omega_m$, and the growth of structures, as represented by the $S_8$ parameter. These results highlight the importance of further exploring extensions of the $\Lambda$CDM model in future LSS studies.
Yaman Acharya, A.↗
Feasibility of Vascular Parameter Estimation for Assessing Hypertensive Pregnancy Disorders
Abstract Hypertensive pregnancy disorders (HPDs), such as pre-eclampsia, are leading sources of both maternal and fetal morbidity in pregnancy. Noninvasive imaging, such as ultrasound (US) and magnetic resonance imaging (MRI), is an important tool for predicting and monitoring these high risk pregnancies. While imaging can measure hemodynamic parameters, such as uterine artery pulsatility and resistivity indices (PI and RI), the interpretation of such metrics for disease assessment relies on ad hoc standards, which provide limited insight to the physical mechanisms underlying the emergence of hypertensive pregnancy disorders. To provide meaningful interpretation of measured hemodynamic data in patients, advances in computational fluid dynamics can be brought to bear. In this work, we develop a patient-specific computational framework that combines Bayesian inference with a reduced-order fluid dynamics model to infer parameters, such as vascular resistance, compliance, and vessel cross-sectional area, known to be related to the development of hypertension. The proposed framework enables the prediction of hemodynamic quantities of interest, such as pressure and velocity, directly from sparse and noisy MRI measurements. We illustrate the effectiveness of this approach in two systemic arterial network geometries: an aorta with branching carotid artery and a maternal pelvic arterial network. For both cases, the model can reconstruct the provided measurements and infer parameters of interest. In the case of the maternal pelvic arteries, the model can make a distinction between the pregnancies destined to develop hypertension and those that remain normotensive, expressed through the value range of the predicted absolute pressure.
Biophysics↗