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Deep feedforward neural networks (DFNNs) are a powerful tool for functional approximation. We describe flexible versions of generalized linear and generalized linear mixed models incorporating basis functions formed by a DFNN. The…

Computation · Statistics 2018-05-28 Minh-Ngoc Tran , Nghia Nguyen , David Nott , Robert Kohn

Based on the back-propagation neural networks and density functional theory, a supervised learning is performed firstly to generate the nuclear charge density distributions. The charge density is further calibrated to the experimental…

Nuclear Theory · Physics 2023-11-23 Zu-Xing Yang , Xiao-Hua Fan , Tomoya Naito , Zhong-Ming Niu , Zhi-Pan Li , Haozhao Liang

We investigate uncertainty estimation and multimodality via the non-deterministic predictions of Bayesian neural networks (BNNs) in fluid simulations. To this end, we deploy BNNs in three challenging experimental test-cases of increasing…

Fluid Dynamics · Physics 2022-05-04 Maximilian Mueller , Robin Greif , Frank Jenko , Nils Thuerey

Uncertainties such as manufacturing tolerances cause performance variations in complex engineering systems, making robust design optimization (RDO) essential. However, simulation-based RDO faces high computational cost for statistical…

Optimization and Control · Mathematics 2026-02-10 Hyunho Jang , Dongjin Lee

The last decade witnessed a growing interest in Bayesian learning. Yet, the technicality of the topic and the multitude of ingredients involved therein, besides the complexity of turning theory into practical implementations, limit the use…

Machine Learning · Statistics 2023-02-01 Martin Magris , Alexandros Iosifidis

Current approximate posteriors in Bayesian neural networks (BNNs) exhibit a crucial limitation: they fail to maintain invariance under reparameterization, i.e. BNNs assign different posterior densities to different parametrizations of…

Machine Learning · Computer Science 2025-02-12 Hrittik Roy , Marco Miani , Carl Henrik Ek , Philipp Hennig , Marvin Pförtner , Lukas Tatzel , Søren Hauberg

This study introduces PV-RNN, a novel variational RNN inspired by the predictive-coding ideas. The model learns to extract the probabilistic structures hidden in fluctuating temporal patterns by dynamically changing the stochasticity of its…

Machine Learning · Computer Science 2019-06-26 Ahmadreza Ahmadi , Jun Tani

Nuclear masses are machine-learned as a function of proton and neutron numbers. The neural network with additive Gaussian process regression-optimized activation functions (GPR-NN) method is employed for the first time for this purpose.…

Nuclear Theory · Physics 2025-09-11 H. X. Liu , S. Manzhos , X. H. Wu

The vast quantity of strong galaxy-galaxy gravitational lenses expected by future large-scale surveys necessitates the development of automated methods to efficiently model their mass profiles. For this purpose, we train an approximate…

Instrumentation and Methods for Astrophysics · Physics 2021-06-30 James Pearson , Jacob Maresca , Nan Li , Simon Dye

Bayesian Neural Networks (BNNs) place priors over the parameters in a neural network. Inference in BNNs, however, is difficult; all inference methods for BNNs are approximate. In this work, we empirically compare the quality of predictive…

Machine Learning · Computer Science 2019-06-25 Jiayu Yao , Weiwei Pan , Soumya Ghosh , Finale Doshi-Velez

Machine learning is gaining growing momentum in various recent models for the dynamic analysis of information flows in data communications networks. These preliminary models often rely on off-the-shelf learning models to predict from…

Machine Learning · Computer Science 2023-04-04 Xiangle Cheng , James He , Shihan Xiao , Yingxue Zhang , Zhitang Chen , Pascal Poupart , Fenglin Li

Nuclear Reaction Analysis with ${}^{3}$He holds the promise to measure Deuterium depth profiles up to large depths. However, the extraction of the depth profile from the measured data is an ill-posed inversion problem. Here we demonstrate…

Accelerator Physics · Physics 2009-11-13 U. von Toussaint , T. Schwarz-Selinger , S. Gori

Binarization of neural network models is considered as one of the promising methods to deploy deep neural network models on resource-constrained environments such as mobile devices. However, Binary Neural Networks (BNNs) tend to suffer from…

Machine Learning · Computer Science 2021-03-31 Hyungjun Kim , Jihoon Park , Changhun Lee , Jae-Joon Kim

Bayesian neural networks (BNNs) have become a principal approach to alleviate overconfident predictions in deep learning, but they often suffer from scaling issues due to a large number of distribution parameters. In this paper, we discover…

Machine Learning · Computer Science 2021-12-14 Shiye Lei , Zhuozhuo Tu , Leszek Rutkowski , Feng Zhou , Li Shen , Fengxiang He , Dacheng Tao

Despite the promise of Convolutional neural network (CNN) based classification models for histopathological images, it is infeasible to quantify its uncertainties. Moreover, CNNs may suffer from overfitting when the data is biased. We show…

Computer Vision and Pattern Recognition · Computer Science 2021-11-09 Ponkrshnan Thiagarajan , Pushkar Khairnar , Susanta Ghosh

This work focuses on improving uncertainty estimation in the field of object classification from RGB images and demonstrates its benefits in two robotic applications. We employ a (BNN), and evaluate two practical inference techniques to…

The usual figure of merit characterizing the performance of neural networks applied to problems in the quantum domain is their accuracy, being the probability of a correct answer on a previously unseen input. Here we append this parameter…

Quantum Physics · Physics 2022-12-29 Jan Wasilewski , Tomasz Paterek , Karol Horodecki

Scientific machine learning has been successfully applied to inverse problems and PDE discovery in computational physics. One caveat concerning current methods is the need for large amounts of ("clean") data, in order to characterize the…

Numerical Analysis · Mathematics 2021-11-30 Christophe Bonneville , Christopher J. Earls

Intensive research has been conducted on the verification and validation of deep neural networks (DNNs), aiming to understand if, and how, DNNs can be applied to safety critical applications. However, existing verification and validation…

Machine Learning · Computer Science 2021-03-08 Nicolas Berthier , Amany Alshareef , James Sharp , Sven Schewe , Xiaowei Huang

Solving partial differential equations (PDEs) is the canonical approach for understanding the behavior of physical systems. However, large scale solutions of PDEs using state of the art discretization techniques remains an expensive…

Computational Engineering, Finance, and Science · Computer Science 2021-01-14 Xiaoxuan Zhang , Krishna Garikipati