Related papers: From Fourier to Neural ODEs: Flow Matching for Mod…

Solving complex fluid-structure interaction (FSI) problems, characterized by nonlinear partial differential equations, is crucial in various scientific and engineering applications. Traditional computational fluid dynamics (CFD) solvers are…

We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a…

Solving cell problems in homogenization is hard, and available deep-learning frameworks fail to match the speed and generality of traditional computational frameworks. More to the point, it is generally unclear what to expect of…

Neuroscientists fit morphologically and biophysically detailed neuron simulations to physiological data, often using evolutionary algorithms. However, such gradient-free approaches are computationally expensive, making convergence slow when…

We propose Characteristic-Neural Ordinary Differential Equations (C-NODEs), a framework for extending Neural Ordinary Differential Equations (NODEs) beyond ODEs. While NODEs model the evolution of a latent variables as the solution to an…

Ordinary differential equations (ODEs) are central to scientific modelling, but inferring their vector fields from noisy trajectories remains challenging. Current approaches such as symbolic regression, Gaussian process (GP) regression, and…

Neural operators can learn nonlinear mappings between function spaces and offer a new simulation paradigm for real-time prediction of complex dynamics for realistic diverse applications as well as for system identification in science and…

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…

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…

Deep learning has an increasing impact to assist research, allowing, for example, the discovery of novel materials. Until now, however, these artificial intelligence techniques have fallen short of discovering the full differential equation…

Neural ODEs (NODEs) are continuous-time neural networks (NNs) that can process data without the limitation of time intervals. They have advantages in learning and understanding the evolution of complex real dynamics. Many previous works…

Neural differential equation models have garnered significant attention in recent years for their effectiveness in machine learning applications.Among these, fractional differential equations (FDEs) have emerged as a promising tool due to…

This paper explores Neural Operators to predict turbulent flows, focusing on the Fourier Neural Operator (FNO) model. It aims to develop reduced-order/surrogate models for turbulent flow simulations using Machine Learning. Different model…

Learning continuous-time dynamics on complex networks is crucial for understanding, predicting and controlling complex systems in science and engineering. However, this task is very challenging due to the combinatorial complexities in the…

We propose a novel second-order optimization framework for training the emerging deep continuous-time models, specifically the Neural Ordinary Differential Equations (Neural ODEs). Since their training already involves expensive gradient…

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…

In this paper, we propose a way to solve partial differential equations (PDEs) by combining machine learning techniques and the finite element method called Phi-FEM. For that, we use the Fourier Neural Operator (FNO), a learning mapping…

Predicting scene dynamics from visual observations is challenging. Existing methods capture dynamics only within observed boundaries failing to extrapolate far beyond the training sequence. Node-RF (Neural ODE-based NeRF) overcomes this…

Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in…

Neural ordinary differential equations (NODEs) are geometric deep learning models based on dynamical systems and flows generated by vector fields on manifolds. Despite numerous successful applications, particularly within the flow matching…