Related papers: Adaptive Runge-Kutta Dynamics for Spatiotemporal P…

An important class of spatio-temporal models is constructed by leveraging the hierarchical structure of dynamical (or, state-space) models. This paper proposes a new statistical dynamical model for spatio-temporal processes motivated by…

Video prediction aims to predict future frames by modeling the complex spatiotemporal dynamics in videos. However, most of the existing methods only model the temporal information and the spatial information for videos in an independent…

Physics-Informed Neural Networks (PINNs) often suffer from slow convergence, training instability, and reduced accuracy on challenging partial differential equations due to the anisotropic and rapidly varying geometry of their loss…

In this contribution, a novel spatio-temporal prediction algorithm for video coding is introduced. This algorithm exploits temporal as well as spatial redundancies for effectively predicting the signal to be encoded. To achieve this, the…

Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for modelling spatiotemporal PDE-dynamics under the influence of randomness. Based on the notion of mild solution of an SPDE, we introduce a novel neural…

This paper tackles video prediction from a new dimension of predicting spacetime-varying motions that are incessantly changing across both space and time. Prior methods mainly capture the temporal state transitions but overlook the complex…

The aim of this paper is to construct and analyze exponential Runge-Kutta methods for the temporal discretization of a class of semilinear parabolic problems with arbitrary state-dependent delay. First, the well-posedness of the problem is…

The design of numerical integrators for solving stochastic dynamics with high weak order relies on tedious calculations and is subject to a high number of order conditions. The original approaches from the literature consider strong…

We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems. Starting from a model trained on low-fidelity or observational data, we apply a…

Simulating the time evolution of Partial Differential Equations (PDEs) of large-scale systems is crucial in many scientific and engineering domains such as fluid dynamics, weather forecasting and their inverse optimization problems.…

Exploring spatial-temporal dependencies from observed motions is one of the core challenges of human motion prediction. Previous methods mainly focus on dedicated network structures to model the spatial and temporal dependencies. This paper…

Mixed precision Runge--Kutta methods have been recently developed and used for the time-evolution of partial differential equations. Two-derivative Runge--Kutta schemes may offer enhanced stability and accuracy properties compared to…

Robot navigation in dense human crowds poses a significant challenge due to the complexity of human behavior in dynamic and obstacle-rich environments. In this work, we propose a dynamic weight adjustment scheme using a neural network to…

Physics-informed neural networks solve partial differential equations by training neural networks. Since this method approximates infinite-dimensional PDE solutions with finite collocation points, minimizing discretization errors by…

Neural differential equations offer a powerful approach for learning dynamics from data. However, they do not impose known constraints that should be obeyed by the learned model. It is well-known that enforcing constraints in surrogate…

In this work, we present a machine learning approach for reducing the error when numerically solving time-dependent partial differential equations (PDE). We use a fully convolutional LSTM network to exploit the spatiotemporal dynamics of…

Predicting high-fidelity future human poses, from a historically observed sequence, is decisive for intelligent robots to interact with humans. Deep end-to-end learning approaches, which typically train a generic pre-trained model on…

A recent line of work in the machine learning community addresses the problem of predicting high-dimensional spatiotemporal phenomena by leveraging specific tools from the differential equations theory. Following this direction, we propose…

Embedding physical knowledge into neural network (NN) training has been a hot topic. However, when facing the complex real-world, most of the existing methods still strongly rely on the quantity and quality of observation data. Furthermore,…

Spatiotemporal dynamics models are fundamental for various domains, from heat propagation in materials to oceanic and atmospheric flows. However, currently available neural network-based spatiotemporal modeling approaches fall short when…