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

Neural Networks (NNs) can be used to solve Ordinary and Partial Differential Equations (ODEs and PDEs) by redefining the question as an optimization problem. The objective function to be optimized is the sum of the squares of the PDE to be…

Neural ordinary differential equations (neural ODEs) can effectively learn dynamical systems from time series data, but their behavior on graph-structured data remains poorly understood, especially when applied to graphs with different size…

By interpreting the forward dynamics of the latent representation of neural networks as an ordinary differential equation, Neural Ordinary Differential Equation (Neural ODE) emerged as an effective framework for modeling a system dynamics…

Analyzing large volumes of high-dimensional data requires dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. Such practice is needed in atomistic simulations of complex…

Deep neural network (DNN) generally takes thousands of iterations to optimize via gradient descent and thus has a slow convergence. In addition, softmax, as a decision layer, may ignore the distribution information of the data during…

Continuous deep learning architectures have recently re-emerged as Neural Ordinary Differential Equations (Neural ODEs). This infinite-depth approach theoretically bridges the gap between deep learning and dynamical systems, offering a…

Dynamic brain data, teeming with biological and functional insights, are becoming increasingly accessible through advanced measurements, providing a gateway to understanding the inner workings of the brain in living subjects. However, the…

The neural dynamics underlying brain activity are critical to understanding cognitive processes and mental disorders. However, current voxel-based whole-brain dimensionality reduction techniques fall short of capturing these dynamics,…

Complex design problems are common in the scientific and industrial fields. In practice, objective functions or constraints of these problems often do not have explicit formulas, and can be estimated only at a set of sampling points through…

Manifold optimization is ubiquitous in computational and applied mathematics, statistics, engineering, machine learning, physics, chemistry and etc. One of the main challenges usually is the non-convexity of the manifold constraints. By…

Modeling dynamical systems is crucial across the science and engineering fields for accurate prediction, control, and decision-making. Recently, machine learning (ML) approaches, particularly neural ordinary differential equations (NODEs),…

Causal inference in continuous-time sequential decision problems is challenged by hidden confounders. We show that, in latent state-space models with time-varying interventions, observability of the latent dynamics from observed data is…

Recently, Neural Ordinary Differential Equations has emerged as a powerful framework for modeling physical simulations without explicitly defining the ODEs governing the system, but instead learning them via machine learning. However, the…

The manifold hypothesis suggests that high-dimensional neural time series lie on a low-dimensional manifold shaped by simpler underlying dynamics. To uncover this structure, latent dynamical variable models such as state-space models,…

Brain network analysis is vital for understanding the neural interactions regarding brain structures and functions, and identifying potential biomarkers for clinical phenotypes. However, widely used brain signals such as Blood Oxygen Level…

The data-driven discovery of interpretable models approximating the underlying dynamics of a physical system has gained attraction in the past decade. Current approaches employ pre-specified functional forms or basis functions and often…

Purpose: To develop a neural ordinary differential equation (ODE) model for visualizing deep neural network (DNN) behavior during multi-parametric MRI (mp-MRI) based glioma segmentation as a method to enhance deep learning explainability.…

Flow matching has emerged as a simulation-free alternative to diffusion-based generative modeling, producing samples by solving an ODE whose time-dependent velocity field is learned along an interpolation between a simple source…

We describe a framework that can integrate prior physical information, e.g., the presence of kinematic constraints, to support data-driven simulation in multi-body dynamics. Unlike other approaches, e.g., Fully-connected Neural Network…

Graph Neural Networks (GNNs) with equivariant properties have achieved significant success in modeling complex dynamic systems and molecular properties. However, their expressiveness ability is limited by: (1) Existing methods often…