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At least 271 records · Page 15

Uncertainty-aware molecular dynamics from Bayesian active learning for phase transformations and thermal transport in SiC

Abstract Machine learning interatomic force fields are promising for combining high computational efficiency and accuracy in modeling quantum interactions and simulating atomistic dynamics. Active learning methods have been recently developed to train force fields efficiently and automatically. Among them, Bayesian active learning utilizes principled uncertainty quantification to make data acquisition decisions. In this work, we present a general Bayesian active learning workflow, where the force field is constructed from a sparse Gaussian process regression model based on atomic cluster expansion descriptors. To circumvent the high computational cost of the sparse Gaussian process uncertainty calculation, we formulate a high-performance approximate mapping of the uncertainty and demonstrate a speedup of several orders of magnitude. We demonstrate the autonomous active learning workflow by training a Bayesian force field model for silicon carbide (SiC) polymorphs in only a few days of computer time and show that pressure-induced phase transformations are accurately captured. The resulting model exhibits close agreement with both ab initio calculations and experimental measurements, and outperforms existing empirical models on vibrational and thermal properties. The active learning workflow readily generalizes to a wide range of material systems and accelerates their computational understanding.

36 MATERIALS SCIENCE↗

A Bayesian analysis of classical shadows

Abstract The method of classical shadows proposed by Huang, Kueng, and Preskill heralds remarkable opportunities for quantum estimation with limited measurements. Yet its relationship to established quantum tomographic approaches, particularly those based on likelihood models, remains unclear. In this article, we investigate classical shadows through the lens of Bayesian mean estimation (BME). In direct tests on numerical data, BME is found to attain significantly lower error on average, but classical shadows prove remarkably more accurate in specific situations—such as high-fidelity ground truth states—which are improbable in a fully uniform Hilbert space. We then introduce an observable-oriented pseudo-likelihood that successfully emulates the dimension-independence and state-specific optimality of classical shadows, but within a Bayesian framework that ensures only physical states. Our research reveals how classical shadows effect important departures from conventional thinking in quantum state estimation, as well as the utility of Bayesian methods for uncovering and formalizing statistical assumptions.

97 MATHEMATICS AND COMPUTING↗

Bayesian weighting of climate models based on climate sensitivity

Using climate model ensembles containing members that exhibit very high climate sensitivities to increasing CO 2 concentrations can result in biased projections. Various methods have been proposed to ameliorate this ‘hot model’ problem, such as model emulators or model culling. Here, we utilize Bayesian Model Averaging as a framework to address this problem without resorting to outright rejection of models from the ensemble. Taking advantage of multiple lines of evidence used to construct the best estimate of the earth’s climate sensitivity, the Bayesian Model Averaging framework produces an unbiased posterior probability distribution of model weights. The updated multi-model ensemble projects end-of-century global mean surface temperature increases of 2 °C for a low emissions scenario (SSP1-2.6) and 5 °C for a high emissions scenario (SSP5-8.5). These estimates are lower than those produced using a simple multi-model mean for the CMIP6 ensemble. The results are also similar to results from a model culling approach, but retain some weight on low-probability models, allowing for consideration of the possibility that the true value could lie at the extremes of the assessed distribution. Our results showcase Bayesian Model Averaging as a path forward to project future climate change that is commensurate with the available scientific evidence.

59 BASIC BIOLOGICAL SCIENCES↗

Using Flory–Huggins-informed human-in-the-loop Bayesian optimization to map the phase diagram of polymer blends

Mapping the phase diagram of polymer blends is an essential step in controlling the structure–property relationship of polymer-based materials. However, traditional grid-based approaches are inefficient and rely on subjective judgements for terminating the experimental campaign. Artificial intelligence-guided experimentation offers a compelling alternative, especially when data-driven decision-making is interfaced with established polymer thermodynamics to improve efficiency and interpretability. Here, we introduce a physics-informed Bayesian optimization approach to guide the mapping of the phase diagram of a model blend containing poly(methyl methacrylate) and poly(styrene-ran-acrylonitrile). Physical information is derived from a Flory–Huggins representation of the spinodal curve, which is integrated into the Bayesian optimization process as a structured prior mean that acts as a soft constraint. Implemented as a human-in-the-loop workflow, the approach leverages optical imaging of film cloudiness with iterative Gaussian process surrogate modeling and a parameter selection decision policy to identify the composition-temperature conditions for sequential iterations. Convergence of kernel and Flory–Huggins-based hyperparameters provided a stopping criterion, ensuring an objective and interpretable termination of the experimental campaign. The framework recovered the known lower critical solution temperature (∼160 °C), while increasing material efficiency through targeted sampling. This work establishes a proof-of-concept for the application of Bayesian optimization workflows to study polymer blend miscibility.

36 MATERIALS SCIENCE↗

Inferring adversarial behaviour in cyber‐physical power systems using a Bayesian attack graph approach

Abstract Highly connected smart power systems are subject to increasing vulnerabilities and adversarial threats. Defenders need to proactively identify and defend new high‐risk access paths of cyber intruders that target grid resilience. However, cyber‐physical risk analysis and defense in power systems often requires making assumptions on adversary behaviour, and these assumptions can be wrong. Thus, this work examines the problem of inferring adversary behaviour in power systems to improve risk‐based defense and detection. To achieve this, a Bayesian approach for inference of the Cyber‐Adversarial Power System (Bayes‐CAPS) is proposed that uses Bayesian networks (BNs) to define and solve the inference problem of adversarial movement in the grid infrastructure towards targets of physical impact. Specifically, BNs are used to compute conditional probabilities to queries, such as the probability of observing an event given a set of alerts. Bayes‐CAPS builds initial Bayesian attack graphs for realistic power system cyber‐physical models. These models are adaptable using collected data from the system under study. Then, Bayes‐CAPS computes the posterior probabilities of the occurrence of a security breach event in power systems. Experiments are conducted that evaluate algorithms based on time complexity, accuracy and impact of evidence for different scales and densities of network. The performance is evaluated and compared for five realistic cyber‐physical power system models of increasing size and complexities ranging from 8 to 300 substations based on computation and accuracy impacts.

Sahu, Abhijeet↗

Evidence cross-validation and Bayesian inference of MAST plasma equilibria

In this paper, current profiles for plasma discharges on the mega-ampere spherical tokamak are directly calculated from pickup coil, flux loop, and motional-Stark effect observations via methods based in the statistical theory of Bayesian analysis. By representing toroidal plasma current as a series of axisymmetric current beams with rectangular cross-section and inferring the current for each one of these beams, flux-surface geometry and q-profiles are subsequently calculated by elementary application of Biot-Savart's law. The use of this plasma model in the context of Bayesian analysis was pioneered by Svensson and Werner on the joint-European tokamak [Svensson and Werner,Plasma Phys. Controlled Fusion 50(8), 085002 (2008)]. In this framework, linear forward models are used to generate diagnostic predictions, and the probability distribution for the currents in the collection of plasma beams was subsequently calculated directly via application of Bayes' formula. In this work, we introduce a new diagnostic technique to identify and remove outlier observations associated with diagnostics falling out of calibration or suffering from an unidentified malfunction. These modifications enable a good agreement between Bayesian inference of the last-closed flux-surface with other corroborating data, such as that from force balance considerations using EFIT++[Appel et al., ''A unified approach to equilibrium reconstruction'' Proceedings of the 33rd EPS Conference on Plasma Physics (Rome, Italy, 2006)]. In addition, this analysis also yields errors on the plasma current profile and flux-surface geometry as well as directly predicting the Shafranov shift of the plasma core.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Bayesian soft X-ray tomography using non-stationary Gaussian Processes

In this study, a Bayesian based non-stationary Gaussian Process (GP) method for the inference of soft X-ray emissivity distribution along with its associated uncertainties has been developed. For the investigation of equilibrium condition and fast magnetohydrodynamic behaviors in nuclear fusion plasmas, it is of importance to infer, especially in the plasma center, spatially resolved soft X-ray profiles from a limited number of noisy line integral measurements. For this ill-posed inversion problem, Bayesian probability theory can provide a posterior probability distribution over all possible solutions under given model assumptions. Specifically, the use of a non-stationary GP to model the emission allows the model to adapt to the varying length scales of the underlying diffusion process. In contrast to other conventional methods, the prior regularization is realized in a probability form which enhances the capability of uncertainty analysis, in consequence, scientists who concern the reliability of their results will benefit from it. Under the assumption of normally distributed noise, the posterior distribution evaluated at a discrete number of points becomes a multivariate normal distribution whose mean and covariance are analytically available, making inversions and calculation of uncertainty fast. Additionally, the hyper-parameters embedded in the model assumption can be optimized through a Bayesian Occam's Razor formalism and thereby automatically adjust the model complexity. This method is shown to produce convincing reconstructions and good agreements with independently calculated results from the Maximum Entropy and Equilibrium-Based Iterative Tomography Algorithm methods.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Bayesian uncertainty calculation in neural network inference of ion and electron temperature profiles at W7-X

We make use of a Bayesian description of the neural network (NN) training for the calculation of the uncertainties in the NN prediction. Having uncertainties on the NN prediction allows having a quantitative measure for trusting the NN outcome and comparing it with other methods. Within the Bayesian framework, the uncertainties can be calculated under different approximations. The NN has been trained with the purpose of inferring ion and electron temperature profile from measurements of a X-ray imaging diagnostic at W7-X. The NN has been trained in such a way that it constitutes an approximation of a full Bayesian model of the diagnostic, implemented within the Minerva framework. Finally, the network has been evaluated using measured data and the uncertainties calculated under different approximations have been compared with each other, finding that neglecting the noise on the NN input can lead to an underestimation of the error bar magnitude in the range of 10%–30%.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Hybrid Parameter Search and Dynamic Model Selection for Mixed-Variable Bayesian Optimization

Herein this article presents a new type of hybrid model for Bayesian optimization (BO) adept at managing mixed variables, encompassing both quantitative (continuous and integer) and qualitative (categorical) types. Our proposed new hybrid models (named hybridM) merge the Monte Carlo Tree Search structure (MCTS) for categorical variables with Gaussian Processes (GP) for continuous ones. hybridM leverages the upper confidence bound tree search (UCTS) for MCTS strategy, showcasing the tree architecture’s integration into Bayesian optimization. Our innovations, including dynamic online kernel selection in the surrogate modeling phase and a unique UCTS search strategy, position our hybrid models as an advancement in mixed-variable surrogate models. Numerical experiments underscore the superiority of hybrid models, highlighting their potential in Bayesian optimization.

97 MATHEMATICS AND COMPUTING↗

LOCAL NON-GAUSSIANITY IN THE COSMIC MICROWAVE BACKGROUND THE BAYESIAN WAY

We introduce an exact Bayesian approach to search for non-Gaussianity of local type in cosmic microwave background (CMB) radiation data. Using simulated CMB temperature maps, the newly developed technique is compared against the conventional frequentist bispectrum estimator. Starting from the joint probability distribution, we obtain analytic expressions for the conditional probabilities of the primordial perturbations given the data, and for the level of non-Gaussianity, f{sub NL}, given the data and the perturbations. We propose Hamiltonian Monte Carlo sampling as a means to derive realizations of the primordial fluctuations from which we in turn sample f{sub NL}. Although computationally expensive, this approach allows us to construct exactly the full target posterior probability distribution. When compared to the frequentist estimator, applying the Bayesian method to Gaussian CMB maps provides consistent results. For the analysis of non-Gaussian maps, however, the error bars on f{sub NL} do not show excess variance within the Bayesian framework. This finding is of particular relevance in the light of upcoming high-precision CMB measurements obtained by the Planck satellite mission.

79 ASTRONOMY AND ASTROPHYSICS↗

Methods for Bayesian power spectrum inference with galaxy surveys

We derive and implement a full Bayesian large scale structure inference method aiming at precision recovery of the cosmological power spectrum from galaxy redshift surveys. Our approach improves upon previous Bayesian methods by performing a joint inference of the three-dimensional density field, the cosmological power spectrum, luminosity dependent galaxy biases, and corresponding normalizations. We account for all joint and correlated uncertainties between all inferred quantities. Classes of galaxies with different biases are treated as separate subsamples. This method therefore also allows the combined analysis of more than one galaxy survey. In particular, it solves the problem of inferring the power spectrum from galaxy surveys with non-trivial survey geometries by exploring the joint posterior distribution with efficient implementations of multiple block Markov chain and Hybrid Monte Carlo methods. Our Markov sampler achieves high statistical efficiency in low signal-to-noise regimes by using a deterministic reversible jump algorithm. This approach reduces the correlation length of the sampler by several orders of magnitude, turning the otherwise numerically unfeasible problem of joint parameter exploration into a numerically manageable task. We test our method on an artificial mock galaxy survey, emulating characteristic features of the Sloan Digital Sky Survey data release 7, such as its survey geometry and luminosity-dependent biases. These tests demonstrate the numerical feasibility of our large scale Bayesian inference frame work when the parameter space has millions of dimensions. This method reveals and correctly treats the anti-correlation between bias amplitudes and power spectrum, which are not taken into account in current approaches to power spectrum estimation, a 20% effect across large ranges in k space. In addition, this method results in constrained realizations of density fields obtained without assuming the power spectrum or bias parameters in advance.

79 ASTRONOMY AND ASTROPHYSICS↗

EXONEST: Bayesian model selection applied to the detection and characterization of exoplanets via photometric variations

EXONEST is an algorithm dedicated to detecting and characterizing the photometric signatures of exoplanets, which include reflection and thermal emission, Doppler boosting, and ellipsoidal variations. Using Bayesian inference, we can test between competing models that describe the data as well as estimate model parameters. We demonstrate this approach by testing circular versus eccentric planetary orbital models, as well as testing for the presence or absence of four photometric effects. In addition to using Bayesian model selection, a unique aspect of EXONEST is the potential capability to distinguish between reflective and thermal contributions to the light curve. A case study is presented using Kepler data recorded from the transiting planet KOI-13b. By considering only the nontransiting portions of the light curve, we demonstrate that it is possible to estimate the photometrically relevant model parameters of KOI-13b. Furthermore, Bayesian model testing confirms that the orbit of KOI-13b has a detectable eccentricity.

79 ASTRONOMY AND ASTROPHYSICS↗

Goal-oriented optimal design of experiments for large-scale Bayesian linear inverse problems

We develop a framework for goal-oriented optimal design of experiments (GOODE) for large-scale Bayesian linear inverse problems governed by PDEs. This framework differs from classical Bayesian optimal design of experiments (ODE) in the following sense: we seek experimental designs that minimize the posterior uncertainty in the experiment end-goal, e.g. a quantity of interest (QoI), rather than the estimated parameter itself. This is suitable for scenarios in which the solution of an inverse problem is an intermediate step and the estimated parameter is then used to compute a QoI. In such problems, a GOODE approach has two benefits: the designs can avoid wastage of experimental resources by a targeted collection of data, and the resulting design criteria are computationally easier to evaluate due to the often low-dimensionality of the QoIs. We present two modified design criteria, A-GOODE and D-GOODE, which are natural analogues of classical Bayesian A- and D-optimal criteria. We analyze the connections to other ODE criteria, and provide interpretations for the GOODE criteria by using tools from information theory. Then, we develop an efficient gradient-based optimization framework for solving the GOODE optimization problems. Additionally, we present comprehensive numerical experiments testing the various aspects of the presented approach. The driving application is the optimal placement of sensors to identify the source of contaminants in a diffusion and transport problem. As a result, we enforce sparsity of the sensor placements using an L1-norm penalty approach, and propose a practical strategy for specifying the associated penalty parameter.

97 MATHEMATICS AND COMPUTING↗

A practical and efficient approach for Bayesian quantum state estimation

Bayesian inference is a powerful paradigm for quantum state tomography, treating uncertainty in meaningful and informative ways. Yet the numerical challenges associated with sampling from complex probability distributions hampers Bayesian tomography in practical settings. In this article, we introduce an improved, self-contained approach for Bayesian quantum state estimation. Leveraging advances in machine learning and statistics, our formulation relies on highly efficient preconditioned Crank–Nicolson sampling and a pseudo-likelihood. We theoretically analyze the computational cost, and provide explicit examples of inference for both actual and simulated datasets, illustrating improved performance with respect to existing approaches.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Bayesian analysis of CCDM models

Creation of Cold Dark Matter (CCDM), in the context of Einstein Field Equations, produces a negative pressure term which can be used to explain the accelerated expansion of the Universe. In this work we tested six different spatially flat models for matter creation using statistical criteria, in light of SNe Ia data: Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and Bayesian Evidence (BE). These criteria allow to compare models considering goodness of fit and number of free parameters, penalizing excess of complexity. We find that JO model is slightly favoured over LJO/ΛCDM model, however, neither of these, nor Γ = 3α H {sub 0} model can be discarded from the current analysis. Three other scenarios are discarded either because poor fitting or because of the excess of free parameters. A method of increasing Bayesian evidence through reparameterization in order to reducing parameter degeneracy is also developed.

79 ASTRONOMY AND ASTROPHYSICS↗

A Bayesian interpretation of inconsistency measures in cosmology

Abstract Measures of inconsistency and tension between datasets have become an essential part of cosmological analyses. It is important to accurately evaluate the significance of such tensions when present. We propose here a Bayesian interpretation of inconsistency measures that can extract information about physical inconsistencies in the presence of data scatter. This new framework is based on the conditional probability distribution of the level of physical inconsistency given the obtained value of the measure. We use the index of inconsistency as a case study to illustrate the new interpretation framework, but this can be generalized to other metrics. Importantly, there are two aspects in the quantification of inconsistency that behave differently as the number of model parameters increases. The first is the probability for the level of physical inconsistency to reach a threshold which drops with the increase of the number of parameters under consideration. The second is the actual level of physical inconsistency which remains rather insensitive to such an increase in parameters. The difference between these two aspects is often overlooked, which leads to a long-standing ambiguity: when a given inconsistency is found between two constraints, its “significance” seems to be lower when considered in a higher-dimensional parameter space. This ambiguity is resolved by the Bayesian interpretation we introduce in this work because the conditional probability distribution includes all the statistical information of the level of physical inconsistency. Finally, we apply the Bayesian interpretation to examine the (in)consistency between Planck versus the Cepheid-based local measurement, the Dark Energy Survey (DES), the Atacama Cosmology Telescope (ACT) and WMAP. We confirm and revisit the degrees of previous physical inconsistencies and show the stability of the new interpretation with respect to the number of cosmological parameters compared to the commonly used n-σ interpretation when applied to cosmological tensions in multi-parameter spaces.

Astronomy & Astrophysics↗

Event generator tuning using Bayesian optimization

Monte Carlo event generators contain a large number of parameters that must be determined by comparing the output of the generator with experimental data. Generating enough events with a fixed set of parameter values to enable making such a comparison is extremely CPU intensive, which prohibits performing a simple brute-force grid-based tuning of the parameters. Bayesian optimization is a powerful method designed for such black-box tuning applications. In this article, we show that Monte Carlo event generator parameters can be accurately obtained using Bayesian optimization and minimal expert-level physics knowledge. A tune of the PYTHIA 8 event generator using $e^+e^-$ events, where 20 parameters are optimized, can be run on a modern laptop in just two days. Combining the Bayesian optimization approach with expert knowledge should enable producing better tunes in the future, by making it faster and easier to study discrepancies between Monte Carlo and experimental data.

47 OTHER INSTRUMENTATION↗

Sparse Bayesian mass mapping with uncertainties: peak statistics and feature locations

ABSTRACT Weak lensing convergence maps – upon which higher order statistics can be calculated – can be recovered from observations of the shear field by solving the lensing inverse problem. For typical surveys this inverse problem is ill-posed (often seriously) leading to substantial uncertainty on the recovered convergence maps. In this paper we propose novel methods for quantifying the Bayesian uncertainty in the location of recovered features and the uncertainty in the cumulative peak statistic – the peak count as a function of signal-to-noise ratio (SNR). We adopt the sparse hierarchical Bayesian mass-mapping framework developed in previous work, which provides robust reconstructions and principled statistical interpretation of reconstructed convergence maps without the need to assume or impose Gaussianity. We demonstrate our uncertainty quantification techniques on both Bolshoi N-body (cluster scale) and Buzzard V-1.6 (large-scale structure) N-body simulations. For the first time, this methodology allows one to recover approximate Bayesian upper and lower limits on the cumulative peak statistic at well-defined confidence levels.

79 ASTRONOMY AND ASTROPHYSICS↗