Related papers: U-Former ODE: Fast Probabilistic Forecasting of Ir…
Soil Organic Carbon (SOC) is a foundation of soil health and global climate resilience, yet its prediction remains difficult because of intricate physical, chemical, and biological processes. In this study, we explore a Scientific Machine…
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…
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…
Shape optimization under uncertainty (OUU) is computationally intensive for classical PDE-based methods due to the high cost of repeated sampling-based risk evaluation across many uncertainty realizations and varying geometries, while…
The dynamic trees problem is to maintain a tree under edge updates while supporting queries like connectivity queries or path queries. Despite the first data structure for this fundamental problem -- the link-cut tree -- being invented 40…
We introduce a novel modeling approach for time series imputation and forecasting, tailored to address the challenges often encountered in real-world data, such as irregular samples, missing data, or unaligned measurements from multiple…
Finite element analysis (FEA) has been widely used to generate simulations of complex and nonlinear systems. Despite its strength and accuracy, the limitations of FEA can be summarized into two aspects: a) running high-fidelity FEA often…
Effective data-driven PDE forecasting methods often rely on fixed spatial and / or temporal discretizations. This raises limitations in real-world applications like weather prediction where flexible extrapolation at arbitrary spatiotemporal…
Ordinary differential equations (ODEs) describe dynamical systems evolving deterministically in continuous time. Accurate data-driven modeling of systems as ODEs, a central problem across the natural sciences, remains challenging,…
Continuous normalizing flows (CNFs) and diffusion models (DMs) generate high-quality data from a noise distribution. However, their sampling process demands multiple iterations to solve an ordinary differential equation (ODE) with high…
Neural CDEs provide a natural way to process the temporal evolution of irregular time series. The number of function evaluations (NFE) is these systems' natural analog of depth (the number of layers in traditional neural networks). It is…
Generalist models have achieved remarkable success in both language and vision-language tasks, showcasing the potential of unified modeling. However, effectively integrating fine-grained perception tasks like detection and segmentation into…
We propose a method to reproduce dynamic appearance textures with space-stationary but time-varying visual statistics. While most previous work decomposes dynamic textures into static appearance and motion, we focus on dynamic appearance…
Neural ordinary differential equations (NODE) have been proposed as a continuous depth generalization to popular deep learning models such as Residual networks (ResNets). They provide parameter efficiency and automate the model selection…
Modeling complex systems using standard neural ordinary differential equations (NODEs) often faces some essential challenges, including high computational costs and susceptibility to local optima. To address these challenges, we propose a…
The advancement of human healthspan and bioengineering relies heavily on predicting the behavior of complex biological systems. While high-throughput multiomics data is becoming increasingly abundant, converting this data into actionable…
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…
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…
Time series data is ubiquitous in research as well as in a wide variety of industrial applications. Effectively analyzing the available historical data and providing insights into the far future allows us to make effective decisions. Recent…
Transient computational fluid dynamics (CFD) remains expensive when long horizons and multi-scale turbulence are involved. Data-driven surrogates promise relief, yet many degrade over multiple steps or drift from physical behavior. This…