Related papers: VNODE: A Piecewise Continuous Volterra Neural Netw…

Neural ordinary differential equations (NODEs) presented a new paradigm to construct (continuous-time) neural networks. While showing several good characteristics in terms of the number of parameters and the flexibility in constructing…

Ordinary differential equations (ODEs) are a conventional way to describe the observed dynamics of physical systems. Scientists typically hypothesize about dynamical behavior, propose a mathematical model, and compare its predictions to…

Reasoning over an instance composed of a set of vectors, like a point cloud, requires that one accounts for intra-set dependent features among elements. However, since such instances are unordered, the elements' features should remain…

Automated medical image segmentation plays a key role in quantitative research and diagnostics. Convolutional neural networks based on the U-Net architecture are the state-of-the-art. A key disadvantage is the hard-coding of the receptive…

A key appeal of the recently proposed Neural Ordinary Differential Equation (ODE) framework is that it seems to provide a continuous-time extension of discrete residual neural networks. As we show herein, though, trained Neural ODE models…

Neural ordinary differential equations (NODEs) have been proven useful for learning non-linear dynamics of arbitrary trajectories. However, current NODE methods capture variations across trajectories only via the initial state value or by…

Regression on medical image sequences can capture temporal image pattern changes and predict images at missing or future time points. However, existing geodesic regression methods limit their regression performance by a strong underlying…

The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here,…

One of the main open challenges in visual odometry (VO) is the robustness to difficult illumination conditions or high dynamic range (HDR) environments. The main difficulties in these situations come from both the limitations of the sensors…

Partial differential equations (PDEs) are indispensable for modeling many physical phenomena and also commonly used for solving image processing tasks. In the latter area, PDE-based approaches interpret image data as discretizations of…

This work proposes an extension of neural ordinary differential equations (NODEs) by introducing an additional set of ODE input parameters to NODEs. This extension allows NODEs to learn multiple dynamics specified by the input parameter…

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…

Neural Ordinary Differential Equations (NODEs) use a neural network to model the instantaneous rate of change in the state of a system. However, despite their apparent suitability for dynamics-governed time-series, NODEs present a few…

The inverse problem of supervised reconstruction of depth-variable (time-dependent) parameters in a neural ordinary differential equation (NODE) is considered, that means finding the weights of a residual network with time continuous…

Partial differential equation (PDE) models and their associated variational energy formulations are often rotationally invariant by design. This ensures that a rotation of the input results in a corresponding rotation of the output, which…

We combine vision transformers with operator learning to solve diverse inverse problems described by partial differential equations (PDEs). Our approach, named ViTO, combines a U-Net based architecture with a vision transformer. We apply…

Active Noise Control (ANC) systems are challenged by nonlinear distortions, which degrade the performance of traditional adaptive filters. While deep learning-based ANC algorithms have emerged to address nonlinearity, existing approaches…

Visual recognition has been dominated by convolutional neural networks (CNNs) for years. Though recently the prevailing vision transformers (ViTs) have shown great potential of self-attention based models in ImageNet classification, their…

We propose heavy ball neural ordinary differential equations (HBNODEs), leveraging the continuous limit of the classical momentum accelerated gradient descent, to improve neural ODEs (NODEs) training and inference. HBNODEs have two…

The technology for Visual Odometry (VO) that estimates the position and orientation of the moving object through analyzing the image sequences captured by on-board cameras, has been well investigated with the rising interest in autonomous…