相关论文: Homotopy-based training of NeuralODEs for accurate…

Accurately modelling the dynamics of complex systems and discovering their governing differential equations are critical tasks for accelerating scientific discovery. Using noisy, synthetic data from two damped oscillatory systems, we…

We propose a data-driven framework for learning reduced-order moment dynamics from PDE-governed systems using Neural ODEs. In contrast to derivative-based methods like SINDy, which necessitate densely sampled data and are sensitive to…

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…

Optimal control problems naturally arise in many scientific applications where one wishes to steer a dynamical system from a certain initial state $\mathbf{x}_0$ to a desired target state $\mathbf{x}^*$ in finite time $T$. Recent advances…

The order/dimension of models derived on the basis of data is commonly restricted by the number of observations, or in the context of monitored systems, sensing nodes. This is particularly true for structural systems (e.g., civil or…

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…

We propose heavy ball neural ordinary differential equations (HBNODEs), leveraging the continuous limit of the classical momentum accelerated gradient descent, to improve neural ODEs (NODEs) training and inference. HBNODEs have two…

Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an…

Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…

Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with some representative datasets. Recently, an augmented framework has been…

Forecasting system behaviour near and across bifurcations is crucial for identifying potential shifts in dynamical systems. While machine learning has recently been used to learn critical transitions and bifurcation structures from data,…

Dosing models often use differential equations to model biological dynamics. Neural differential equations in particular can learn to predict the derivative of a process, which permits predictions at irregular points of time. However, this…

Training dynamic models, such as neural ODEs, on long trajectories is a hard problem that requires using various tricks, such as trajectory splitting, to make model training work in practice. These methods are often heuristics with poor…

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…

Imaging Inverse problems aim to reconstruct an underlying image from undersampled, coded, and noisy observations. Within the wide range of reconstruction frameworks, the unrolling algorithm is one of the most popular due to the synergistic…

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…

Multiscale dynamical systems, modeled by high-dimensional stiff ordinary differential equations (ODEs) with wide-ranging characteristic timescales, arise across diverse fields of science and engineering, but their numerical solvers often…

The identification of a mathematical dynamics model is a crucial step in the designing process of a controller. However, it is often very difficult to identify the system's governing equations, especially in complex environments that…

Most machine learning methods are used as a black box for modelling. We may try to extract some knowledge from physics-based training methods, such as neural ODE (ordinary differential equation). Neural ODE has advantages like a possibly…

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…