Related papers: Foundation Inference Models for Ordinary Different…

Outlier detection (OD) has a vast literature as it finds numerous real-world applications. Being an unsupervised task, model selection is a key bottleneck for OD without label supervision. Despite a long list of available OD algorithms with…

In this paper, we propose an innovative learning-based channel prediction scheme so as to achieve higher prediction accuracy and reduce the requirements of huge amounts and strict sequential format of channel data. Inspired by the idea of…

Deformable image registration (DIR) is crucial in medical image analysis, enabling the exploration of biological dynamics such as organ motions and longitudinal changes in imaging. Leveraging Neural Ordinary Differential Equations (ODE) for…

Machine learning techniques have recently been of great interest for solving differential equations. Training these models is classically a data-fitting task, but knowledge of the expression of the differential equation can be used to…

One of the most popular recent areas of machine learning predicates the use of neural networks augmented by information about the underlying process in the form of Partial Differential Equations (PDEs). These physics-informed neural…

Poverty is a complex dynamic challenge that cannot be adequately captured using predefined differential equations. Nowadays, artificial machine learning (ML) methods have demonstrated significant potential in modelling real-world dynamical…

Learning models of dynamical systems with external inputs, which may be, for example, nonsmooth or piecewise, is crucial for studying complex phenomena and predicting future state evolution, which is essential for applications such as…

Ordinary differential equation (ODE) models are widely used to describe systems in many areas of science. To ensure these models provide accurate and interpretable representations of real-world dynamics, it is often necessary to infer…

Efficient modeling of High Temperature Superconductors (HTSs) is crucial for real-time quench monitoring; however, full-order electromagnetic simulations remain prohibitively costly due to the strong nonlinearities. Conventional…

Parameter estimation and associated uncertainty quantification is an important problem in dynamical systems characterized by ordinary differential equation (ODE) models that are often nonlinear. Typically, such models have analytically…

Neural ordinary differential equations (ODEs) are an emerging class of deep learning models for dynamical systems. They are particularly useful for learning an ODE vector field from observed trajectories (i.e., inverse problems). We here…

System inference for nonlinear dynamic models, represented by ordinary differential equations (ODEs), remains a significant challenge in many fields, particularly when the data are noisy, sparse, or partially observable. In this paper, we…

In recent years we have witnessed a growth in mathematics for deep learning, which has been used to solve inverse problems of partial differential equations (PDEs). However, most deep learning-based inversion methods either require paired…

Neural Ordinary Differential Equations (ODEs) are elegant reinterpretations of deep networks where continuous time can replace the discrete notion of depth, ODE solvers perform forward propagation, and the adjoint method enables efficient,…

Diffusion models achieve state-of-the-art image quality. However, sampling is costly at inference time because it requires a large number of function evaluations (NFEs). To reduce NFEs, classical ODE numerical methods have been adopted.…

This paper proposes the use of spectral element methods \citep{canuto_spectral_1988} for fast and accurate training of Neural Ordinary Differential Equations (ODE-Nets; \citealp{Chen2018NeuralOD}) for system identification. This is achieved…

Sampling from diffusion models can be treated as solving the corresponding ordinary differential equations (ODEs), with the aim of obtaining an accurate solution with as few number of function evaluations (NFE) as possible. Recently,…

Gradient matching with Gaussian processes is a promising tool for learning parameters of ordinary differential equations (ODE's). The essence of gradient matching is to model the prior over state variables as a Gaussian process which…

The present project aims to use machine learning, specifically neural networks (NN), to learn the trajectories of a set of coupled ordinary differential equations (ODEs) and decrease compute times for obtaining ODE solutions by using this…

Often the regression function appearing in fields like economics, engineering, biomedical sciences obeys a system of higher order ordinary differential equations (ODEs). The equations are usually not analytically solvable. We are interested…