arXiv:2605. 07060v3 Announce Type: replace-cross Abstract: Physics-informed neural networks (PINNs) provide a mesh-free framework for solving PDE-constrained inverse problems, but their extension to Bayesian inversion still faces a fundamental difficulty: prior distributions are typically defined in the weight space of neural networks, whereas physically meaningful prior assumptions are more naturally expressed in function space.
By Ryoichiro Agata, Tomohisa Okazaki
arXiv:2601. 07944v2 Announce Type: replace-cross Abstract: Since the turn of the century, approximate Bayesian inference has steadily evolved as new computational techniques have been incorporated to handle increasingly complex, large-scale predictive problems.
By Roy Shivam Ram Shreshtth, Arnab Hazra, Gourab Mukherjee
arXiv:2503. 10496v2 Announce Type: replace-cross Abstract: Modeling natural phenomena with artificial neural networks (ANNs) often provides highly accurate predictions.
By Eirik H{\o}yheim, Lars Skaaret-Lund, Solve S{\ae}b{\o}, Aliaksandr Hubin
arXiv:2607. 21671v1 Announce Type: new Abstract: Neural network compression and interpretability remain open challenges in modern deep learn- ing, where billion-parameter architectures deliver impressive accuracy at the cost of trans- parency, computational efficiency, and reliable uncertainty quantification.
By Idris Karel Seunda Ekwe, Patrick Tenga Shako, Ernest Parfait Fokou\'e
arXiv:2508. 11657v2 Announce Type: replace-cross Abstract: Objective: Sparse Bayesian learning provides an effective framework to solve high-dimensional problems in brain signal decoding.
By Yuanhao Li, Badong Chen, Wenjun Bai, Yasuharu Koike, Okito Yamashita
arXiv:2602.01176v2 Announce Type: replace
Abstract: Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding physica...
By Olaf Yunus Laitinen Imanov
arXiv:2606. 13818v1 Announce Type: new Abstract: This thesis investigates how Bayesian principles can deepen our understanding of modern deep learning systems.
By Luis A. Ortega
arXiv:2502.16888v3 Announce Type: replace-cross
Abstract: Motivated by the remarkable success of Bayesian additive regression trees (BART) in regression modelling, we propose a novel nonparametric Ba...
By Jiahao Cao, Shiyuan He, Bohai Zhang
arXiv:2609.26867v1 Announce Type: cross
Abstract: This article is motivated by an imaging application from the Adolescent Brain Cognitive Development (ABCD) study, aiming to predict task-based brain...
By Rajarshi Guhaniyogi, Pritam Dey, Krishnendu Chandra, Aaron Scheffler, Bani K. Mallick
arXiv:2606. 16694v1 Announce Type: cross Abstract: Transformers are widely used as a general-purpose substrate for learning complex correlations between a large collection of coupled variables, but their internal mechanisms have remained mysterious.
By Ravin Raj, Gautam Reddy
The paper introduces the Local Gradient Neural Operator (LGNO), a lightweight and interpretable neural operator designed for field temporal evolution prediction and source identification in mechanical problems. LGNO leverages nonlinear gradient discretization priors and multilayer perceptron convolutional layers to learn translation‑invariant local kernels resembling discrete stencils, with a zero‑consistent stencil factorization that separates coefficient learning from field reconstruction. Experiments on a range of PDE benchmarks—including linear, nonlinear, static, dynamic, low‑ and high‑dimensional cases—demonstrate that LGNO achieves comparable accuracy to global neural operators while using fewer parameters and maintaining rollout stability across diffusion, flow, and quantum phenomena.
By Baiming Zhang, Jinsong Tang, Ying Xu, Lihua Chen, Shiying Xiong
Field temporal prediction and source identification constitute canonical problems in dynamical systems. Conventional approaches to these problems depend on a thorough understanding of the governing pa...