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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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The Sensitivity of Variational Bayesian Neural Network Performance to Hyperparameters

In scientific applications, predictive modeling is often of limited use without accurate uncertainty quantification (UQ) to indicate when a model may be extrapolating or when more data needs to be collected. Bayesian Neural Networks (BNNs) produce predictive uncertainty by propagating uncertainty in neural network (NN) weights and offer the promise of obtaining not only an accurate predictive model but also accurate UQ. However, in practice, obtaining accurate UQ with BNNs is difficult due in part to the approximations used for model training (such as those made in variational inference) and in part to the need to choose a suitable set of hyperparameters; these hyperparameters outnumber those needed for traditional NNs and often have opaque effects on the results. We aim to shed light on the effects of hyperparameter choices for variational BNNs by performing a global sensitivity analysis of variational BNN performance under varying hyperparameter settings. Our results indicate that many of the hyperparameters interact with each other to affect both predictive accuracy and UQ. For improved usage of variational BNNs in real-world applications, we suggest that thorough hyperparameter tuning, including tuning of prior hyperparameters and loss function parameters, is essential for accurate UQ in variational BNNs.

97 MATHEMATICS AND COMPUTING↗

Fast increased fidelity samplers for approximate Bayesian Gaussian process regression

Gaussian processes (GPs) are common components in Bayesian non-parametric models having a rich methodological literature and strong theoretical grounding. The use of exact GPs in Bayesian models is limited to problems containing several thousand observations due to their prohibitive computational demands. We develop a posterior sampling algorithm using H-matrix approximations that scales at O(n log 2 n). We show that this approximation’s Kullback-Leibler divergence to the true posterior can be made arbitrarily small. Though multidimensional GPs could be used with our algorithm, d-dimensional surfaces are modeled as tensor products of univariate GPs to minimize the cost of matrix construction and maximize computational efficiency. We illustrate the performance of this fast increased fidelity approximate GP, FIFA-GP, using both simulated and non-synthetic data sets

97 MATHEMATICS AND COMPUTING↗

The Effect of the Prior and the Experimental Design on the Inference of the Precision Matrix in Gaussian Chain Graph Models

Here, we investigate whether (and how) experimental design could aid in the estimation of the precision matrix in a Gaussian chain graph model, especially the interplay between the design, the effect of the experiment and prior knowledge about the effect. Estimation of the precision matrix is a fundamental task to infer biological graphical structures like microbial networks. We compare the marginal posterior precision of the precision matrix under four priors: flat, conjugate Normal-Wishart, Normal-MGIG and a general independent. Under the flat and conjugate priors, the Laplace-approximated posterior precision is not a function of the design matrix rendering useless any efforts to find an optimal experimental design to infer the precision matrix. In contrast, the Normal-MGIG and general independent priors do allow for the search of optimal experimental designs, yet there is a sharp upper bound on the information that can be extracted from a given experiment. We confirm our theoretical findings via a simulation study comparing (i) the KL divergence between prior and posterior and (ii) the Stein’s loss difference of MAPs between random and no experiment. Our findings provide practical advice for domain scientists conducting experiments to better infer the precision matrix as a representation of a biological network.

54 ENVIRONMENTAL SCIENCES↗

Quantum-Assisted Variational Segmentation for Image-to-Image Wildfire Detection Using Satellite Data

The quantum computing community has been searching for suitable applications to demonstrate the potential of near-term quantum devices. Quantum machine learning is a potential candidate, particularly using models that cannot be efficiently simulated with classical computers [1, 2]. This work focuses on a transition phase of quantum computers where the quantum machine learning model is still simulable classically but projected not to be simulable as the size of the model grows. Ultimately quantum computers may have advantages for high-dimensional real-world problems. Due to the limited number of qubits in current noisy intermediate-scale quantum (NISQ) devices, the direct application of quantum computers in high dimensional data is not feasible. To remedy this problem, an encoder-decoder architecture can be utilized. The encoder model would transform the high-dimensional data into a compact representation, to a level that small quantum computers can be used today (or in the near future), and the decoder would take the quantum processed outputs back to the high-dimensional space. Addressing the two challenges of quantum machine learning, this work investigates a hybrid supervised generative model with a quantum Ising Born machine embedded as the latent distribution. The model contains four main parts (Figure 1.a.): (1) a U-NET architecture responsible for learning segmentation flow, (2) a Prior network responsible for learning an encoded latent distribution of the input data, (3) a Born machine which represents the latent distribution, and (4) a Posterior network in charge of learning the joint encoded latent distribution of inputs and target data. The initial model, proposed by [3], is optimized by (1) maximizing the overlap of the prior and posterior latent distributions, and (2) minimizing the segmentation loss. The proposed model is designed to be investigated in a simulation environment applied to the real-world application of wildfire segmentation. Specifically, the model is designed to solve the patchy wildfire segmentations of Moderate Resolution Imaging Spectroradiometer (MODIS) by taking the MODIS observations and using Visible Infrared Imaging Radiometer Suite’s (VIIRS) consistent wildfire product as the target. The model solves patchy wildfire segmentations and provides insight into the epistemic errors sourced from model variation. The model utilizes the Born machine as a QUBO solver to represent the latent space as a Bernoulli distribution. The proposed configuration allows the variational segmentation model to leverage the true quantum probabilistic nature and derive a more expressive latent configuration, increasing the model performance in describing wildfire segmentations. The quantum probabilistic information of the Born machine is directly incorporated in the Kullback-Leibler divergence loss in the prior and posterior distributions, forcing the Bernoulli latent distribution to maximize the overlap of input and joint input-target distributions. The proposed model is then trained and compared with a baseline only consisting of direct Bernoulli latent distribution with no Born machine representing the latent space. The models are evaluated based on the segmentation metrics, such as precision, recall, intersect of union, with uncertainty boundaries accounting for the stochastic nature of the model. Our findings show that even in low latent-dimensional space (due to the limit in computational power of the classical quantum simulator), we are able to effectively capture the latent representation and hence the model performs better than the baseline. The findings are a projection for scaling the model into higher dimensional latent space with the Born machine surpassing the baseline performance. Figure 1. Sub-figure (a) demonstrates the architecture for the training phase. The model consists of a Prior and Posterior network that encode inputs and joint input-target data into compact representations, respectively. The Born machine represents the latent distribution, and the U-NET branch learns the segmentation patterns of the data. The stochasticity is introduced to the U-NET through its last layer to create meaningful but stochastic segmentations. Sub-figure (b) represents the inference phase where the model takes the stochastic behavior from the prior network and injects that into the U-NET. Each attempt of inference will generate different but similar segmentations from the same distribution of the wildfire event. REFERENCES [1] Coyle, B., Mills, D., Danos, V., & Kashefi, E. (2020). The Born supremacy: quantum advantage and training of an Ising Born machine. npj Quantum Information, 6(1), 1-11. [2] Liu, J. G., & Wang, L. (2018). Differentiable learning of quantum circuit born machines. Physical Review A, 98(6), 062324. [3] Kohl, S., Romera-Paredes, B., Meyer, C., De Fauw, J., Ledsam, J. R., Maier-Hein, K., ... & Ronneberger, O. (2018). A probabilistic u-net for segmentation of ambiguous images. Advances in neural information processing systems, 31.

quantum machine learning↗

Jensen–Shannon divergence based novel loss functions for Bayesian neural networks

Bayesian neural networks (BNNs) are state-of-the-art machine learning methods that can naturally regularize and systematically quantify uncertainties using their stochastic parameters. Kullback–Leibler (KL) divergence-based variational inference used in BNNs suffer from unstable optimization and challenges in approximating light-tailed posteriors due to the unbounded nature of the KL divergence. To resolve these issues, we formulate a novel loss function for BNNs based on a new modification to the generalized Jensen–Shannon (JS) divergence, which is bounded. In addition, we propose a Geometric JS divergence-based loss, which is computationally efficient since it can be evaluated analytically. We found that the JS divergence-based variational inference is intractable, and hence employed a constrained optimization framework to formulate these losses. Our theoretical analysis and empirical experiments on multiple regression and classification data sets suggest that the proposed losses perform better than the KL divergence-based loss, especially when the data sets are noisy or biased. Specifically, there are approximately 5% and 8% improvements in accuracy for a noise-added CIFAR-10 dataset and a regression dataset, respectively. There is about 13% reduction in false negative predictions of a biased histopathology dataset. Additionally, we quantify and compare the uncertainty metrics for the regression and classification tasks.

97 MATHEMATICS AND COMPUTING↗

Approximate Bayesian Model Inversion for PDEs with Heterogeneous and State-Dependent Coefficients

We present two approximate Bayesian inference methods for parameter estimation in partial differential equation (PDE) models with space-dependent and state-dependent parameters. We demonstrate that these methods provide accurate and cost-effective alternatives to Markov Chain Monte Carlo simulation. We assume a parameterized Gaussian prior on the unknown functions, and approximate the posterior density by a parameterized multivariate Gaussian density. The parameters of the prior and posterior are estimated from sparse observations of the PDE model's states and the unknown functions themselves by maximizing the evidence lower bound (ELBO), a lower bound on the log marginal likelihood of the observations. The first method, Laplace-EM, employs the expectation maximization algorithm to maximize the ELBO, with a Laplace approximation of the posterior on the E-step, and minimization of a Kullback-Leibler divergence on the M-step. The second method, DSVI-EB, employs the doubly stochastic variational inference (DSVI) algorithm, in which the ELBO is maximized via gradient-based stochastic optimization, with nosiy gradients computed via simple Monte Carlo sampling and Gaussian backpropagation. We apply these methods to identifying diffusion coefficients in linear and nonlinear diffusion equations, and we find that both methods provide accurate estimates of posterior densities and the hyperparameters of Gaussian priors. While the Laplace-EM method is more accurate, it requires computing Hessians of the physics model. The DSVI-EB method is found to be less accurate but only requires gradients of the physics model.

approximate Bayesian inference, model inversion, v↗

Parameter uncertainties for imperfect surrogate models in the low-noise regime

Abstract Bayesian regression determines model parameters by minimizing the expected loss, an upper bound to the true generalization error. However, this loss ignores model form error, or misspecification, meaning parameter uncertainties are significantly underestimated and vanish in the large data limit. As misspecification is the main source of uncertainty for surrogate models of low-noise calculations, such as those arising in atomistic simulation, predictive uncertainties are systematically underestimated. We analyze the true generalization error of misspecified, near-deterministic surrogate models, a regime of broad relevance in science and engineering. We show that posterior parameter distributions must cover every training point to avoid a divergence in the generalization error and design a compatible ansatz which incurs minimal overhead for linear models. The approach is demonstrated on model problems before application to thousand-dimensional datasets in atomistic machine learning. Our efficient misspecification-aware scheme gives accurate prediction and bounding of test errors in terms of parameter uncertainties, allowing this important source of uncertainty to be incorporated in multi-scale computational workflows.

Swinburne, Thomas D. (ORCID:0000000232554257)↗

Beyond the Global Brain Differences: Intraindividual Variability Differences in 1q21.1 Distal and 15q11.2 BP1-BP2 Deletion Carriers

Carriers of the 1q21.1 distal and 15q11.2 BP1-BP2 copy number variants exhibit regional and global brain differences compared with noncarriers. However, interpreting regional differences is challenging if a global difference drives the regional brain differences. Intraindividual variability measures can be used to test for regional differences beyond global differences in brain structure. Magnetic resonance imaging data were used to obtain regional brain values for 1q21.1 distal deletion (n = 30) and duplication (n = 27) and 15q11.2 BP1-BP2 deletion (n = 170) and duplication (n = 243) carriers and matched noncarriers (n = 2350). Regional intra-deviation scores, i.e., the standardized difference between an individual’s regional difference and global difference, were used to test for regional differences that diverge from the global difference. For the 1q21.1 distal deletion carriers, cortical surface area for regions in the medial visual cortex, posterior cingulate, and temporal pole differed less and regions in the prefrontal and superior temporal cortex differed more than the global difference in cortical surface area. For the 15q11.2 BP1-BP2 deletion carriers, cortical thickness in regions in the medial visual cortex, auditory cortex, and temporal pole differed less and the prefrontal and somatosensory cortex differed more than the global difference in cortical thickness. We find evidence for regional effects beyond differences in global brain measures in 1q21.1 distal and 15q11.2 BP1-BP2 copy number variants. The results provide new insight into brain profiling of the 1q21.1 distal and 15q11.2 BP1-BP2 copy number variants, with the potential to increase understanding of the mechanisms involved in altered neurodevelopment.

15q11.2 BP1-BP2↗

Source-Resolved Inversion of Elemental Carbon Emissions in California Using Log-Space Bayesian Inference

Elemental carbon (EC), operationally quantified by thermal-optical analysis, is widely used as a proxy for black carbon (BC) relevant to short-term climate forcing and public health. Current EC emission inventories remain highly uncertain, with persistent discrepancies between bottom-up and top-down estimates. In this study, we develop a source-resolved, log-space Bayesian inversion framework applied to estimate California’s statewide EC emissions in 2019. By integrating surface EC measurements from the EPA’s Air Quality System network with high-resolution source contributions simulated by a chemical transport model, we identify a one-third underestimation in the existing statewide EC inventory, requiring an increase of the total from a prior of 8.58 [5.49–13.75] Gg year–1 to a posterior estimate of 12.78 [10.71–15.37] Gg year–1. This discrepancy is primarily driven by substantial underestimations in the power and industrial and off-road mobile sectors. Furthermore, population-weighted exposure analysis reveals a marked sectoral divergence between emission mass and health burden: off-road mobile sources dominate both emissions and exposure, accounting for 31% of statewide exposure, while residential wood combustion contributes 26% of total exposure despite comprising only 19% of total emissions, due to its source proximity to population. These findings underscore the need to update sector-specific EC speciation profiles and demonstrate that mitigation strategies targeting off-road mobile sources and residential wood combustion are critical for reducing EC-related health impacts in California.

Zhang, Jie↗

Improved information criteria for Bayesian model averaging in lattice field theory

Bayesian model averaging is a practical method for dealing with uncertainty due to model specification. Use of this technique requires the estimation of model probability weights. Here, we revisit the derivation of estimators for these model weights. Use of the Kullback-Leibler divergence as a starting point leads naturally to a number of alternative information criteria suitable for Bayesian model weight estimation. We explore three such criteria, known to the statistics literature before, in detail: a Bayesian analog of the Akaike information criterion which we call the BAIC, the Bayesian predictive information criterion, and the posterior predictive information criterion (PPIC). We compare the use of these information criteria in numerical analysis problems common in lattice field theory calculations. We find that the PPIC has the most appealing theoretical properties and can give the best performance in terms of model-averaging uncertainty, particularly in the presence of noisy data, while the BAIC is a simple and reliable alternative.

97 MATHEMATICS AND COMPUTING↗

Expression of Prox1 defines regions of the avian otocyst that give rise to sensory or neural cells

The simple primordium of the inner ear (otocyst) differentiates into many cell types, including sensory neurons and hair cells. We examined expression of the divergent homeobox transcription factor, cProx1, during otocyst development in chickens. Nuclear cProx1 protein is not evident in the otic placode but emerges in the otic cup by stage 12. At stage 16, cProx1-positive nuclei are scattered continuously throughout the neuroepithelium, from anteroventral to posteromedial. These labeled cells are neural precursors; they express betaIII-tubulin and migrate to the cochleovestibular ganglion between stages 13 and 21. By stage 18, two areas develop a dense pattern of cProx1 expression in which every nucleus is labeled. These areas emerge at the anterior and posterior extremes of the band of scattered cProx1 expression and express the sensory markers cSerrate1 and Cath1 by stage 23. Four discrete patches of dense cProx1 expression appear by stage 23 that correspond to the future superior crista, lateral crista, saccular macula, and posterior crista, as confirmed by immunolabeling for hair cell antigen (HCA) by stage 29. The remaining sensory epithelia display a dense pattern of cProx1 expression and label for HCA by stage 29. In the basilar papilla, nuclear cProx1 expression is down-regulated in most hair cells by stage 37 and in many supporting cells by stage 40. Our findings show that regions of the otocyst that give rise to neurons or hair cells are distinguished by their relative density of cProx1-positive nuclei, and suggest a role for cProx1 in the genesis of these cell types.

NASA Discipline Developmental Biology↗