Related papers: Continuous PDE Dynamics Forecasting with Implicit …

Accurate forecasting of spatiotemporal data remains challenging due to complex spatial dependencies and temporal dynamics. The inherent uncertainty and variability in such data often render deterministic models insufficient, prompting a…

Learning dynamics governed by differential equations is crucial for predicting and controlling the systems in science and engineering. Neural Ordinary Differential Equation (NODE), a deep learning model integrated with differential…

Temporal domain generalization is a promising yet extremely challenging area where the goal is to learn models under temporally changing data distributions and generalize to unseen data distributions following the trends of the change. The…

We extract data-driven, intrinsic spatial coordinates from observations of the dynamics of large systems of coupled heterogeneous agents. These coordinates then serve as an emergent space in which to learn predictive models in the form of…

Learning the solution operators of PDEs on arbitrary domains is challenging due to the diversity of possible domain shapes, in addition to the often intricate underlying physics. We propose an end-to-end graph neural network (GNN) based…

The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…

Deep learning has revolutionized the field of computer vision by introducing large scale neural networks with millions of parameters. Training these networks requires massive datasets and leads to intransparent models that can fail to…

The widespread deployment of sensing devices leads to a surge in data for spatio-temporal forecasting applications such as traffic flow, air quality, and wind energy. Although spatio-temporal graph neural networks have achieved success in…

Ocean current, fluid mechanics, and many other spatio-temporal physical dynamical systems are essential components of the universe. One key characteristic of such systems is that certain physics laws -- represented as ordinary/partial…

Solving partial differential equations (PDEs) by numerical methods meet computational cost challenge for getting the accurate solution since fine grids and small time steps are required. Machine learning can accelerate this process, but…

Many physical systems exhibit nonlocal spatiotemporal behaviors described by integro-differential equations (IDEs). Classical methods for solving IDEs require repeatedly evaluating convolution integrals, whose cost increases quickly with…

The extensive adoption of Deep Neural Networks has led to their increased utilization in challenging scientific visualization tasks. Recent advancements in building compressed data models using implicit neural representations have shown…

Identifying from observation data the governing differential equations of a physical dynamics is a key challenge in machine learning. Although approaches based on SINDy have shown great promise in this area, they still fail to address a…

Owing to the remarkable development of deep learning technology, there have been a series of efforts to build deep learning-based climate models. Whereas most of them utilize recurrent neural networks and/or graph neural networks, we design…

We propose a new class of parameterizations for spatio-temporal point processes which leverage Neural ODEs as a computational method and enable flexible, high-fidelity models of discrete events that are localized in continuous time and…

Engineering design problems often involve solving parametric Partial Differential Equations (PDEs) under variable PDE parameters and domain geometry. Recently, neural operators have shown promise in learning PDE operators and quickly…

Physics-informed neural operators (PINOs) have emerged as powerful tools for learning solution operators of partial differential equations (PDEs). Recent research has demonstrated that incorporating Lie point symmetry information can…

This paper introduces novel deep dynamical models designed to represent continuous-time sequences. Our approach employs a neural emission model to generate each data point in the time series through a non-linear transformation of a latent…

Current PINN implementations with sequential learning strategies often experience some weaknesses, such as the failure to reproduce the previous training results when using a single network, the difficulty to strictly ensure continuity and…

Data-driven methods for the identification of the governing equations of dynamical systems or the computation of reduced surrogate models play an increasingly important role in many application areas such as physics, chemistry, biology, and…