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A fully Bayesian treatment of complicated predictive models (such as deep neural networks) would enable rigorous uncertainty quantification and the automation of higher-level tasks including model selection. However, the intractability of…

Dynamical systems modeling, particularly via systems of ordinary differential equations, has been used to effectively capture the temporal behavior of different biochemical components in signal transduction networks. Despite the recent…

Quantitative Methods · Quantitative Biology 2023-01-06 Nathaniel J. Linden , Boris Kramer , Padmini Rangamani

System inference for nonlinear dynamic models, represented by ordinary differential equations (ODEs), remains a significant challenge in many fields, particularly when the data are noisy, sparse, or partially observable. In this paper, we…

Machine Learning · Computer Science 2025-12-25 Hyunwoo Cho , Hyeontae Jo , Hyung Ju Hwang

We introduce the concept of numerical Gaussian processes, which we define as Gaussian processes with covariance functions resulting from temporal discretization of time-dependent partial differential equations. Numerical Gaussian processes,…

Machine Learning · Statistics 2017-03-31 Maziar Raissi , Paris Perdikaris , George Em Karniadakis

Computer simulations of differential equations require a time discretization, which inhibits to identify the exact solution with certainty. Probabilistic simulations take this into account via uncertainty quantification. The construction of…

Numerical Analysis · Mathematics 2020-10-15 Philipp Frank , Torsten A. Enßlin

Neural ordinary differential equations (NODE) have garnered significant attention for their design of continuous-depth neural networks and the ability to learn data/feature dynamics. However, for high-dimensional systems, estimating…

Machine Learning · Computer Science 2025-10-07 Muhao Guo , Haoran Li , Yang Weng

In multivariate time series analysis, understanding the underlying causal relationships among variables is often of interest for various applications. Directed acyclic graphs (DAGs) provide a powerful framework for representing causal…

Methodology · Statistics 2025-07-30 Arkaprava Roy , Anindya Roy , Subhashis Ghosal

This paper proposes a new formulation of functional Gaussian Process regression in manifolds, based on an Empirical Bayes approach, in the spatiotemporal random field context. We apply the machinery of tight Gaussian measures in separable…

Machine Learning · Statistics 2026-03-24 MD Ruiz-Medina , AE Madrid , A Torres-Signes , JM Angulo

We investigate the channel estimation for massive multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. We revisit the information geometry approach (IGA) for massive MIMO-OFDM channel estimation. By…

Information Theory · Computer Science 2024-06-05 Jiyuan Yang , Yan Chen , Mingrui Fan , An-An Lu , Wen Zhong , Xiqi Gao , Xiaohu You , Xiang-Gen Xia , Dirk Slock

Gait recognition aims to distinguish different walking patterns by analyzing video-level human silhouettes, rather than relying on appearance information. Previous research on gait recognition has primarily focused on extracting local or…

Computer Vision and Pattern Recognition · Computer Science 2023-07-26 Qian Wu , Ruixuan Xiao , Kaixin Xu , Jingcheng Ni , Boxun Li , Ziyao Xu

Event-based cameras asynchronously capture individual visual changes in a scene. This makes them more robust than traditional frame-based cameras to highly dynamic motions and poor illumination. It also means that every measurement in a…

Robotics · Computer Science 2023-09-14 Jianeng Wang , Jonathan D. Gammell

Time-Varying Bayesian Optimization (TVBO) is the go-to framework for optimizing a time-varying, expensive, noisy black-box function $f$. However, most of the asymptotic guarantees offered by TVBO algorithms rely on the assumption that…

Machine Learning · Statistics 2025-10-21 Anthony Bardou , Patrick Thiran

Recent machine learning advances have proposed black-box estimation of unknown continuous-time system dynamics directly from data. However, earlier works are based on approximative ODE solutions or point estimates. We propose a novel…

Machine Learning · Computer Science 2022-07-19 Pashupati Hegde , Çağatay Yıldız , Harri Lähdesmäki , Samuel Kaski , Markus Heinonen

Ordinary differential equations (ODEs) are widely used to model biological, (bio-)chemical and technical processes. The parameters of these ODEs are often estimated from experimental data using ODE-constrained optimisation. This article…

Optimization and Control · Mathematics 2015-11-06 Anna Fiedler , Fabian J. Theis , Jan Hasenauer

Statistical regression models whose mean functions are represented by ordinary differential equations (ODEs) can be used to describe phenomenons dynamical in nature, which are abundant in areas such as biology, climatology and genetics. The…

Methodology · Statistics 2017-05-15 Kyoungjae Lee , Jaeyong Lee , Sarat C. Dass

We propose classical interferometry with low-intensity thermal radiation for the estimation of nonclassical independent Gaussian processes in material samples. We generally determine the mean square error of the phase-independent parameters…

Quantum Physics · Physics 2017-02-14 László Ruppert , Radim Filip

Estimating time-varying graphical models are of paramount importance in various social, financial, biological, and engineering systems, since the evolution of such networks can be utilized for example to spot trends, detect anomalies,…

Machine Learning · Statistics 2023-02-07 Hang Yu , Songwei Wu , Justin Dauwels

We introduce a flexible, scalable Bayesian inference framework for nonlinear dynamical systems characterised by distinct and hierarchical variability at the individual, group, and population levels. Our model class is a generalisation of…

Machine Learning · Statistics 2019-10-03 Geoffrey Roeder , Paul K. Grant , Andrew Phillips , Neil Dalchau , Edward Meeds

A significant challenge in many fields of science and engineering is making sense of time-dependent measurement data by recovering governing equations in the form of differential equations. We focus on finding parsimonious ordinary…

Machine Learning · Computer Science 2024-10-04 Doris Voina , Steven Brunton , J. Nathan Kutz

The dynamics of systems biological processes are usually modeled by a system of ordinary differential equations (ODEs) with many unknown parameters that need to be inferred from noisy and sparse measurements. Here, we introduce…

Quantitative Methods · Quantitative Biology 2022-02-04 Mitchell Daneker , Zhen Zhang , George Em Karniadakis , Lu Lu