Related papers: Neural Manifold Ordinary Differential Equations

We introduce Statistical Flow Matching (SFM), a novel and mathematically rigorous flow-matching framework on the manifold of parameterized probability measures inspired by the results from information geometry. We demonstrate the…

Simulation of multiphase flow in porous media is crucial for the effective management of subsurface energy and environment related activities. The numerical simulators used for modeling such processes rely on spatial and temporal…

Normalizing flows (NFs) have become a prominent method for deep generative models that allow for an analytic probability density estimation and efficient synthesis. However, a flow-based network is considered to be inefficient in parameter…

Density regression models allow a comprehensive understanding of data by modeling the complete conditional probability distribution. While flexible estimation approaches such as normalizing flows (NF) work particularly well in multiple…

Flow-based generative models are composed of invertible transformations between two random variables of the same dimension. Therefore, flow-based models cannot be adequately trained if the dimension of the data distribution does not match…

Neural ordinary differential equations (Neural ODEs) is a class of machine learning models that approximate the time derivative of hidden states using a neural network. They are powerful tools for modeling continuous-time dynamical systems,…

Graph Neural Networks (GNNs) have gained popularity in various learning tasks, with successful applications in fields like molecular biology, transportation systems, and electrical grids. These fields naturally use graph data, benefiting…

Deep Learning research is advancing at a fantastic rate, and there is much to gain from transferring this knowledge to older fields like Computational Fluid Dynamics in practical engineering contexts. This work compares state-of-the-art…

Flow Matching enables simulation-free training of generative models on Riemannian manifolds, yet sampling typically still relies on numerically integrating a probability-flow ODE. We propose Riemannian MeanFlow (RMF), extending MeanFlow to…

Out-of-distribution (OOD) detection is crucial to safety-critical machine learning applications and has been extensively studied. While recent studies have predominantly focused on classifier-based methods, research on deep generative model…

Stochastic differential equations (SDEs) are well suited to modelling noisy and irregularly sampled time series found in finance, physics, and machine learning. Traditional approaches require costly numerical solvers to sample between…

Classical neural ODEs trained with explicit methods are intrinsically limited by stability, crippling their efficiency and robustness for stiff learning problems that are common in graph learning and scientific machine learning. We present…

Generative modelling has been a topic at the forefront of machine learning research for a substantial amount of time. With the recent success in the field of machine learning, especially in deep learning, there has been an increased…

Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…

Neural operators have emerged as a powerful data-driven paradigm for solving partial differential equations (PDEs), while their accuracy and scalability are still limited, particularly on irregular domains where fluid flows exhibit rich…

Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with some representative datasets. Recently, an augmented framework has been…

Normalizing flows are prominent deep generative models that provide tractable probability distributions and efficient density estimation. However, they are well known to fail while detecting Out-of-Distribution (OOD) inputs as they directly…

Chemically reacting flows are common in engineering, such as hypersonic flow, combustion, explosions, manufacturing processes and environmental assessments. For combustion, the number of reactions can be significant (over 100) and due to…

In this work, we investigate the use of normalizing flows to model conditional distributions. In particular, we use our proposed method to analyze inverse problems with invertible neural networks by maximizing the posterior likelihood. Our…

Accurate polyp segmentation remains challenging due to irregular lesion morphologies, ambiguous boundaries, and heterogeneous imaging conditions. While U-Net variants excel at local feature fusion, they often lack explicit mechanisms to…