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While Bayesian neural networks (BNNs) have drawn increasing attention, their posterior inference remains challenging, due to the high-dimensional and over-parameterized nature. To address this issue, several highly flexible and scalable…

Machine Learning · Statistics 2019-05-10 Ziyu Wang , Tongzheng Ren , Jun Zhu , Bo Zhang

Convolutional neural networks (CNNs) provide flexible function approximations for a wide variety of applications when the input variables are in the form of images or spatial data. Although CNNs often outperform traditional statistical…

Methodology · Statistics 2024-05-24 Yeseul Jeon , Won Chang , Seonghyun Jeong , Sanghoon Han , Jaewoo Park

Large-scale numerical simulations are used across many scientific disciplines to facilitate experimental development and provide insights into underlying physical processes, but they come with a significant computational cost. Deep neural…

Large multilayer neural networks trained with backpropagation have recently achieved state-of-the-art results in a wide range of problems. However, using backprop for neural net learning still has some disadvantages, e.g., having to tune a…

Machine Learning · Statistics 2015-07-16 José Miguel Hernández-Lobato , Ryan P. Adams

Active learning (AL) has emerged as a powerful paradigm for accelerating materials discovery by iteratively steering experiments toward promising candidates, reducing the number of costly synthesis-and-characterization cycles needed to…

Materials Science · Physics 2026-03-25 Jeffrey Hu , Rongzhi Dong , Ying Feng , Ming Hu , Jianjun Hu

Gaussian processes are Bayesian non-parametric models used in many areas. In this work, we propose a Non-stationary Heteroscedastic Gaussian process model which can be learned with gradient-based techniques. We demonstrate the…

Machine Learning · Computer Science 2022-12-26 Zeel B Patel , Nipun Batra , Kevin Murphy

Bayesian neural networks utilize probabilistic layers that capture uncertainty over weights and activations, and are trained using Bayesian inference. Since these probabilistic layers are designed to be drop-in replacement of their…

Machine Learning · Computer Science 2021-06-28 Daniel T. Chang

Partial Bayesian neural networks (pBNNs) have been shown to perform competitively with fully Bayesian neural networks while only having a subset of the parameters be stochastic. Using sequential Monte Carlo (SMC) samplers as the inference…

Machine Learning · Computer Science 2026-01-30 Andrew Millard , Joshua Murphy , Simon Maskell , Zheng Zhao

This paper investigates two prominent probabilistic neural modeling paradigms: Bayesian Neural Networks (BNNs) and Mixture Density Networks (MDNs) for uncertainty-aware nonlinear regression. While BNNs incorporate epistemic uncertainty by…

Computation · Statistics 2025-10-30 Riddhi Pratim Ghosh , Ian Barnett

Bayesian learning is built on an assumption that the model space contains a true reflection of the data generating mechanism. This assumption is problematic, particularly in complex data environments. Here we present a Bayesian…

Machine Learning · Statistics 2018-11-05 S. P. Lyddon , S. G. Walker , C. C. Holmes

The rapidly increasing computational demands for artificial intelligence (AI) have spurred the exploration of computing principles beyond conventional digital computers. Physical neural networks (PNNs) offer efficient neuromorphic…

Neural networks and machine learning models for uncertainty quantification suffer from limited scalability and poor reliability compared to their deterministic counterparts. In industry-scale active learning settings, where generating a…

Numerical Analysis · Mathematics 2026-02-12 Chanwook Park , Brian Kim , Jiachen Guo , Wing Kam Liu

We propose stochastic, non-parametric activation functions that are fully learnable and individual to each neuron. Complexity and the risk of overfitting are controlled by placing a Gaussian process prior over these functions. The result is…

Machine Learning · Statistics 2017-12-01 Sebastian Urban , Marcus Basalla , Patrick van der Smagt

Bayesian method is capable of capturing real world uncertainties/incompleteness and properly addressing the over-fitting issue faced by deep neural networks. In recent years, Bayesian Neural Networks (BNNs) have drawn tremendous attentions…

Machine Learning · Computer Science 2020-05-11 Xiaotao Jia , Jianlei Yang , Runze Liu , Xueyan Wang , Sorin Dan Cotofana , Weisheng Zhao

Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding physical laws directly into neural network training. However, solving high-fidelity PDEs remains…

Machine Learning · Computer Science 2026-02-03 Olaf Yunus Laitinen Imanov

This work proposes a comprehensively progressive Bayesian neural network for robust continual learning of a sequence of tasks. A Bayesian neural network is progressively pruned and grown such that there are sufficient network resources to…

Machine Learning · Computer Science 2022-03-01 Guo Yang , Cheryl Sze Yin Wong , Ramasamy Savitha

Continual learning aims to learn new tasks without forgetting previously learned ones. This is especially challenging when one cannot access data from previous tasks and when the model has a fixed capacity. Current regularization-based…

Machine Learning · Computer Science 2020-02-21 Sayna Ebrahimi , Mohamed Elhoseiny , Trevor Darrell , Marcus Rohrbach

Accurate localization is a critical requirement for most robotic tasks. The main body of existing work is focused on passive localization in which the motions of the robot are assumed given, abstracting from their influence on sampling…

Robotics · Computer Science 2022-10-17 Daniel Honerkamp , Suresh Guttikonda , Abhinav Valada

In industrial machine learning pipelines, data often arrive in parts. Particularly in the case of deep neural networks, it may be too expensive to train the model from scratch each time, so one would rather use a previously learned model…

Machine Learning · Statistics 2018-03-29 Max Kochurov , Timur Garipov , Dmitry Podoprikhin , Dmitry Molchanov , Arsenii Ashukha , Dmitry Vetrov

This paper presents a deep learning strategy to simultaneously solve Partial Differential Equations (PDEs) and back-calculate their parameters in the context of deep tunnel excavation. A Physics-Informed Neural Network (PINN) model is…

Computational Physics · Physics 2026-05-29 Alec Tristani , Chloé Arson