Related papers: When do neural ordinary differential equations gen…
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…
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…
Nonlinear ordinary differential equations (ODEs) are powerful tools for modeling real-world dynamical systems. However, propagating initial state uncertainty through nonlinear dynamics, especially when the ODE is unknown and learned from…
Neural ordinary differential equations (NODE) have been recently proposed as a promising approach for nonlinear system identification tasks. In this work, we systematically compare their predictive performance with current state-of-the-art…
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…
Distribution shifts on graphs -- the discrepancies in data distribution between training and employing a graph machine learning model -- are ubiquitous and often unavoidable in real-world scenarios. These shifts may severely deteriorate…
Ordinary differential equations (ODEs) are widely used to model complex dynamics that arises in biology, chemistry, engineering, finance, physics, etc. Calibration of a complicated ODE system using noisy data is generally very difficult. In…
The graph of a Bayesian Network (BN) can be machine learned, determined by causal knowledge, or a combination of both. In disciplines like bioinformatics, applying BN structure learning algorithms can reveal new insights that would…
There is a recent surge in the development of spatio-temporal forecasting models in the transportation domain. Long-range traffic forecasting, however, remains a challenging task due to the intricate and extensive spatio-temporal…
In complex physical systems, conventional differential equations often fall short in capturing non-local and memory effects, as they are limited to local dynamics and integer-order interactions. This study introduces a stepwise data-driven…
As an alternative to classical numerical solvers for partial differential equations (PDEs) subject to boundary value constraints, there has been a surge of interest in investigating neural networks that can solve such problems efficiently.…
Due to the performance degradation of graph neural networks (GNNs) under distribution shifts, the work on out-of-distribution (OOD) generalization on graphs has received widespread attention. A novel perspective involves distinguishing…
We propose a neural network based approach for extracting models from dynamic data using ordinary and partial differential equations. In particular, given a time-series or spatio-temporal dataset, we seek to identify an accurate governing…
Dissipative partial differential equations that exhibit chaotic dynamics tend to evolve to attractors that exist on finite-dimensional manifolds. We present a data-driven reduced order modeling method that capitalizes on this fact by…
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…
In this work, we investigate a method for simulation-free training of Neural Ordinary Differential Equations (NODEs) for learning deterministic mappings between paired data. Despite the analogy of NODEs as continuous-depth residual…
Graph-based spatio-temporal neural networks are effective to model the spatial dependency among discrete points sampled irregularly from unstructured grids, thanks to the great expressiveness of graph neural networks. However, these models…
Learning a graph topology to reveal the underlying relationship between data entities plays an important role in various machine learning and data analysis tasks. Under the assumption that structured data vary smoothly over a graph, the…
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…
Graph Neural Networks (GNNs) have demonstrated remarkable success in modeling complex relationships in graph-structured data. A recent innovation in this field is the family of Differential Equation-Inspired Graph Neural Networks (DE-GNNs),…