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

Modeling nonlinear systems with Volterra series is challenging because the number of kernel coefficients grows exponentially with the model order. This work introduces Bayesian Tensor Network Volterra kernel machines (BTN-V), extending the…

We present Ordinary Differential Equation Variational Auto-Encoder (ODE$^2$VAE), a latent second order ODE model for high-dimensional sequential data. Leveraging the advances in deep generative models, ODE$^2$VAE can simultaneously learn…

Many physical processes such as weather phenomena or fluid mechanics are governed by partial differential equations (PDEs). Modelling such dynamical systems using Neural Networks is an active research field. However, current methods are…

Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…

We present PIVONet (Physically-Informed Variational ODE Neural Network), a unified framework that integrates Neural Ordinary Differential Equations (Neuro-ODEs) with Continuous Normalizing Flows (CNFs) for stochastic fluid simulation and…

A concept of using Neural Ordinary Differential Equations(NODE) for Transfer Learning has been introduced. In this paper we use the EfficientNets to explore transfer learning on CIFAR-10 dataset. We use NODE for fine-tuning our model. Using…

Non-linear spectral decompositions of images based on one-homogeneous functionals such as total variation have gained considerable attention in the last few years. Due to their ability to extract spectral components corresponding to objects…

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…

Deep learning has made a remarkable impact in the field of natural image processing over the past decade. Consequently, there is a great deal of interest in replicating this success across unsolved tasks in related domains, such as medical…

Neural networks have recently been used to analyze diverse physical systems and to identify the underlying dynamics. While existing methods achieve impressive results, they are limited by their strong demand for training data and their weak…

It was recently shown that neural ordinary differential equation models cannot solve fundamental and seemingly straightforward tasks even with high-capacity vector field representations. This paper introduces two other fundamental tasks to…

Visual Odometry (VO) accumulates a positional drift in long-term robot navigation tasks. Although Convolutional Neural Networks (CNNs) improve VO in various aspects, VO still suffers from moving obstacles, discontinuous observation of…

Recently deep residual learning with residual units for training very deep neural networks advanced the state-of-the-art performance on 2D image recognition tasks, e.g., object detection and segmentation. However, how to fully leverage…

Most existing vision encoders map images into a fixed-length sequence of tokens, overlooking the fact that different images contain varying amounts of information. For example, a visually complex image (e.g., a cluttered room) inherently…

The numerical determination of solitary states is an important topic for such research areas as Bose-Einstein condensates, nonlinear optics, plasma physics, etc. In this paper, we propose a data-driven approach for identifying solitons…

In optical fiber communication, optical and electrical components introduce nonlinearities, which require effective compensation to attain highest data rates. In particular, in short reach communication, components are the dominant source…

We present an end-to-end deep network for fine-grained visual categorization called Collaborative Convolutional Network (CoCoNet). The network uses a collaborative layer after the convolutional layers to represent an image as an optimal…

Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations.…

We propose a partial differential-integral equation (PDE) framework for deep neural networks (DNNs) and their associated learning problem by taking the continuum limits of both network width and depth. The proposed model captures the…

Consistency Training (CT) has recently emerged as a strong alternative to diffusion models for image generation. However, non-distillation CT often suffers from high variance and instability, motivating ongoing research into its training…