Related papers: Learning Large Scale Ordinary Differential Equatio…

In this study, we present and validate the predictive capability of the Physics-Informed Neural Networks (PINNs) methodology for solving a variety of engineering and biological dynamical systems governed by ordinary differential equations…

The neural Ordinary Differential Equation (ODE) model has shown success in learning complex continuous-time processes from observations on discrete time stamps. In this work, we consider the modeling and forecasting of time series data that…

Equations, particularly differential equations, are fundamental for understanding natural phenomena and predicting complex dynamics across various scientific and engineering disciplines. However, the governing equations for many complex…

We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled…

We present a method to infer a dense depth map from a color image and associated sparse depth measurements. Our main contribution lies in the design of an annealing process for determining co-visibility (occlusions, disocclusions) and the…

The differentiable implementation of logic yields a seamless combination of symbolic reasoning and deep neural networks. Recent research, which has developed a differentiable framework to learn logic programs from examples, can even acquire…

We are interested in the numerical solution of coupled nonlinear partial differential equations (PDEs) in two and three dimensions. Under certain assumptions on the domain, we take advantage of the Kronecker structure arising in standard…

A variety of complex biological, natural and man-made systems exhibit non-Markovian dynamics that can be modeled through fractional order differential equations, yet, we lack sample comlexity aware system identification strategies. Towards…

We propose a simple algorithm to train stochastic neural networks to draw samples from given target distributions for probabilistic inference. Our method is based on iteratively adjusting the neural network parameters so that the output…

Increasing the layer number of on-chip photonic neural networks (PNNs) is essential to improve its model performance. However, the successively cascading of network hidden layers results in larger integrated photonic chip areas. To address…

Physics-informed neural networks (PINNs) have emerged as powerful tools for solving a wide range of partial differential equations (PDEs). However, despite their user-friendly interface and broad applicability, PINNs encounter challenges in…

Pixel-wise losses, e.g., cross-entropy or L2, have been widely used in structured prediction tasks as a spatial extension of generic image classification or regression. However, its i.i.d. assumption neglects the structural regularity…

Online Active Learning (OAL) aims to manage unlabeled datastream by selectively querying the label of data. OAL is applicable to many real-world problems, such as anomaly detection in health-care and finance. In these problems, there are…

Neural ordinary differential equations (Neural ODEs) are an effective framework for learning dynamical systems from irregularly sampled time series data. These models provide a continuous-time latent representation of the underlying…

We aim to identify the generating, ordinary differential equation (ODE) from a set of trajectories of a partially observed system. Our approach does not need prescribed basis functions to learn the ODE model, but only a rich set of Neural…

Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path…

This paper investigates a novel gradient algorithm, AGEM, using both energy and momentum, for addressing general non-convex optimization problems. The solution properties of the AGEM algorithm, including aspects such as uniformly…

Since the advent of the ``Neural Ordinary Differential Equation (Neural ODE)'' paper, learning ODEs with deep learning has been applied to system identification, time-series forecasting, and related areas. Exploiting the diffeomorphic…

Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…

The neural ordinary differential equation (ODE) framework has emerged as a powerful tool for developing accelerated surrogate models of complex physical systems governed by partial differential equations (PDEs). A popular approach for PDE…