24 papers · ranked by Valyu relevance
Yiming Yang, Xiaoyuan Cheng, Yi Hai He, Kaiyu Li + 2 more
Diffusion models have recently emerged as powerful learned priors for Bayesian inverse problems (BIPs). Diffusion-based solvers rely on a presumed likelihood for the observations in BIPs to guide the generation process. However, the link between likelihood and recovery quality for BIPs is unclear in previous works. We…
Zhiliang Deng, Zhiyuan Wang, Xiaomei Yang, Xiaofei Guan
We present a novel Bayesian framework for inverse problems in which the posterior distribution is interpreted as the intensity measure of a Poisson point process (PPP). The posterior density is approximated using kernel density estimation, and the superposition property of PPPs is then exploited to enable efficient…
Bamdad Hosseini, Ziqi Huang
Data-driven methods for the solution of inverse problems have become widely popular in recent years thanks to the rise of machine learning techniques. A popular approach concerns the training of a generative model on additional data to learn a bespoke prior for the problem at hand. In this article we present an…
Haibo Li
Computing posterior distributions in large-scale Bayesian linear inverse problems is challenging due to the high dimensionality of the parameter space. In this work, we develop a data-informed framework that shifts the computational focus from the parameter space to the data space. We rigorously characterize an…
Piotr Gwiazda, Alexey Kazarnikov, Anna Marciniak-Czochra, Zuzanna Szymańska
Calibrating mathematical models of biological processes is essential for achieving predictive accuracy and gaining mechanistic insight. However, this task remains challenging due to limited and noisy data, significant biological variability, and the computational complexity of the models themselves. In this method’s…
Ray Zirui Zhang, Christopher E. Miles, Xiaohui Xie, John S. Lowengrub
Uncertainty quantification in PDE inverse problems is essential in many applications. Scientific machine learning and AI enable data-driven learning of model components while preserving physical structure, and provide the scalability and adaptability needed for emerging imaging technologies and clinical insights. We…
Ahmed Bilal, Makin, Joseph G.
Inverse problems are fundamental to science and engineering, where the goal is to infer an underlying signal or state from incomplete or noisy measurements. Recent approaches employ diffusion models as powerful implicit priors for such problems, owing to their ability to capture complex data distributions. However…
Laurenz Nagler, Martin Zach, Thomas Pock
Recently, diffusion models have attracted considerable attention for magnetic resonance image reconstruction due to their high sample quality. However, most existing methods rely on large networks with opaque time conditioning mechanisms and require offline coil sensitivity estimation. This results in limited…
Authors not listed
The political, social and economic consequences of climate change drastically influence the requirements of modern energy systems and its components. This includes not only energy production but also concepts and innovations for its storage, especially in magnitudes of gigawatt hours. Carnot batteries, which convert…
Yucong Liu, Zilai Si, Alexander Strang
Posterior distributions arising in ill-posed Bayesian inverse problems are often both analytically intractable and highly sensitive to parameters of the chosen prior family. We aim to understand the sensitivity of intractable posterior distributions to changes in prior assumptions by tracking how a sample…
Hojjat Kaveh, Ricardo Baptista, Andrew M. Stuart
We consider amortized Bayesian inference for nonlinear inverse problems in settings where only samples from the joint distribution of parameters and observations are available. Classical methods such as Markov chain Monte Carlo require solving a new inference problem for each observation, which can be computationally…
Yilai Li, Jing Yuan, Yi Zhou, Zhenghua Wang + 6 more
Single-particle cryo-electron microscopy (cryo-EM) enables structure determination of macromolecular complexes, yet reconstructions are often degraded by noise, anisotropic sampling and reconstruction artifacts. Correcting these effects is an ill-posed inverse problem that requires strong prior knowledge in addition to…
Ourania Giannopoulou
Magnetoencephalography (MEG) forward and inverse modeling is fundamental to neuroscientific discovery, yet the inversion of partial differential equations (PDEs) remains one of the most difficult challenges due to its inherent ill-posedness. While traditional numerical methods often struggle with the computational…
Ray Zirui Zhang, Christopher E. Miles, Xiaohui Xie, John S. Lowengrub
We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization problem. At the upper level, we minimize the data loss with respect to the PDE parameters. At the lower level, we train a neural network to…
Lukas Hecker
Electroencephalography (EEG) source imaging remains difficult to compare systematically because inverse solvers are distributed across different software packages, programming languages, and evaluation protocols. We present a frozen four-scenario EEG benchmark of 106 solvers evaluated on a shared BioSemi-32 / ico3…
Authors not listed
The rapid growth of worldwide computing power has transformed in silico chemistry into a discipline that is integrated into the daily work of many chemists. Nowadays, researchers find it increasingly straightforward to predict a wide range of molecular properties and chemi- cal processes at reasonable computational…
Mariya Mamajiwala, Cesare Corrado, Christopher W. Lanyon, Steven A. Niederer + 2 more
Atrial fibrillation (AF) is a common cardiac arrhythmia characterised by disordered electrical activity in the atria. The standard treatment is catheter ablation, which is invasive and irreversible. Recent advances in computational electrophysiology offer the potential for patient-specific models that can be used to…
Yukio-Pegio Gunji, Kyoko Nakamura, Kazuto Sasai, Iori Tani + 5 more
Artificial intelligence is typically formulated as an information-processing system composed of artificial neurons, where computation is understood as recursive operations connecting inputs and outputs. However, real neural systems are materially embodied and continuously reconfigured by metabolic and physical…
Daniela Calvetti, Erkki Somersalo
A central goal in many brain studies is the identification of those brain regions that are activated during an observation window that may correspond to a motor task, a stimulus, or simply a resting state. While functional MRI is currently the most commonly employed modality for such task, methods based on the…
Julia Sirock, Markus Vogel, Tina Seufert
Solving Bayesian problems poses many challenges, such as identifying relevant numerical information, classifying and translating it into mathematical formula language, and forming a mental representation. This triggers research on how to support the solving of Bayesian problems. The facilitating effect of using…
Rafał Brociek, Agata Wajda, Christian Napoli, Giacomo Capizzi + 4 more
This article presents an algorithm for solving the direct and inverse problem for a model consisting of a fractional differential equation with non-integer order derivatives with respect to time and space. The Caputo derivative was taken as the fractional derivative with respect to time, and the Riemann-Liouville…
Authors not listed
Surfactants are widely used for industrial applications, yet more environmentally-friendly surfactants with enhanced properties are demanded. A key thermodynamic property governing the behavior of a surfactant in an aqueous solution is its critical micelle concentration (CMC). Below the CMC, increasing the surfactant…
Authors not listed
Incorporating prior domain knowledge into Bayesian optimization (BO) remains difficult for statistical methods, which also typically suffer from limited interpretability. Large language models (LLMs) offer complementary strengths in reasoning and knowledge integration, but it remains unclear when and how they improve…
Authors not listed
Machine olfaction—the artificial replication of the sense of smell—faces significant challenges due to the absence of large, standardized training datasets. Unlike vision, language, and audio models, which benefit from extensive corpora such as ImageNet, GLUE, and AudioSet, olfaction lacks scaled equivalents and…