Related papers: Efficient Manifold-Constrained Neural ODE for High…

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…

Datasets such as images, text, or movies are embedded in high-dimensional spaces. However, in important cases such as images of objects, the statistical structure in the data constrains samples to a manifold of dramatically lower…

Neural ordinary differential equations (neural ODEs) have emerged as a novel network architecture that bridges dynamical systems and deep learning. However, the gradient obtained with the continuous adjoint method in the vanilla neural ODE…

Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…

Measurement noise is an integral part while collecting data of a physical process. Thus, noise removal is necessary to draw conclusions from these data, and it often becomes essential to construct dynamical models using these data. We…

Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. In a previous work [arXiv:2104.13962], we explored the use of Neural Ordinary Differential Equations (NODE) as…

Learned denoisers play a fundamental role in various signal generation (e.g., diffusion models) and reconstruction (e.g., compressed sensing) architectures, whose success derives from their ability to leverage low-dimensional structure in…

Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise…

Neural Ordinary Differential Equations (ODEs) represent a significant advancement at the intersection of machine learning and dynamical systems, offering a continuous-time analog to discrete neural networks. Despite their promise, deploying…

Stiff systems of ordinary differential equations (ODEs) are pervasive in many science and engineering fields, yet standard neural ODE approaches struggle to learn them. This limitation is the main barrier to the widespread adoption of…

Algorithms proposed for solving high-dimensional optimization problems with no derivative information frequently encounter the "curse of dimensionality," becoming ineffective as the dimension of the parameter space grows. One feature of a…

A class of neural networks that gained particular interest in the last years are neural ordinary differential equations (neural ODEs). We study input-output relations of neural ODEs using dynamical systems theory and prove several results…

Artificial neural networks, widely recognised for their role in machine learning, are now transforming the study of ordinary differential equations (ODEs), bridging data-driven modelling with classical dynamical systems and enabling the…

Neural ODEs (NODEs) have emerged as powerful tools for modeling time series data, offering the flexibility to adapt to varying input scales and capture complex dynamics. However, they face significant challenges: first, their reliance on…

Normalizing flows are a powerful technique for obtaining reparameterizable samples from complex multimodal distributions. Unfortunately current approaches fall short when the underlying space has a non trivial topology, and are only…

Many successful methods to learn dynamical systems from data have recently been introduced. However, ensuring that the inferred dynamics preserve known constraints, such as conservation laws or restrictions on the allowed system states,…

Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. Here, we explore the use of Neural Ordinary Differential Equations, a recently introduced family of…

Neural ordinary differential equations (neural ODE) are powerful continuous-time machine learning models for depicting the behavior of complex dynamical systems, but their verification remains challenging due to limited reachability…

Neural Ordinary Differential Equations (NODEs) have proven to be a powerful modeling tool for approximating (interpolation) and forecasting (extrapolation) irregularly sampled time series data. However, their performance degrades…

The idea of neural Ordinary Differential Equations (ODE) is to approximate the derivative of a function (data model) instead of the function itself. In residual networks, instead of having a discrete sequence of hidden layers, the…