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

Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…

In dynamic and uncertain environments, robotic path planning demands accurate spatiotemporal environment understanding combined with robust decision-making under partial observability. However, current deep reinforcement learning-based path…

Neural surrogates for partial differential equations (PDEs) have become popular due to their potential to quickly simulate physics. With a few exceptions, neural surrogates generally treat the forward evolution of time-dependent PDEs as a…

In this paper, authors successfully construct a new algorithm for the new higher order scheme of weak approximation of SDEs. The algorithm presented here is based on [1][2]. Although this algorithm shares some features with the algorithm…

Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics and engineering to medicine and economics. These systems cannot be properly modelled and simulated with standard…

We apply Runge-Kutta methods to linear partial differential-algebraic equations of the form $Au_t(t,x) + B(u_{xx}(t,x)+ru_x(t,x))+Cu(t,x) = f(t,x)$, where $A,B,C\in\R^{n,n}$ and the matrix $A$ is singular. We prove that under certain…

Differential equations are important tools to portray dynamic problems, and are widely used in finance, engineering and biology. Here, multiple dynamic differential models were built innovatively, and discretized with the Runge-Kutta…

A new deep-learning neural network architecture based on high-order weak approximation algorithms for stochastic differential equations (SDEs) is proposed. The architecture enables the efficient learning of martingales by deep learning…

We propose a novel Transformer-based architecture for the task of generative modelling of 3D human motion. Previous work commonly relies on RNN-based models considering shorter forecast horizons reaching a stationary and often implausible…

This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…

Human motion prediction from motion capture data is a classical problem in the computer vision, and conventional methods take the holistic human body as input. These methods ignore the fact that, in various human activities, different body…

Similar to conventional video generation, current deep learning-based weather prediction frameworks often lack explicit physical constraints, leading to unphysical outputs that limit their reliability for operational forecasting. Among…

Air quality prediction and modelling plays a pivotal role in public health and environment management, for individuals and authorities to make informed decisions. Although traditional data-driven models have shown promise in this domain,…

Neural networks, especially the recent proposed neural operator models, are increasingly being used to find the solution operator of differential equations. Compared to traditional numerical solvers, they are much faster and more efficient…

This paper introduces an adaptive physics-guided neural network (APGNN) framework for predicting quality attributes from image data by integrating physical laws into deep learning models. The APGNN adaptively balances data-driven and…

This paper addresses the limitations of Physics-Informed Neural Networks for time-dependent problems by introducing a tangent bundle learning framework. Instead of directly approximating the solution, we parameterize its temporal derivative…

Accurate time-series forecasting is crucial in various scientific and industrial domains, yet deep learning models often struggle to capture long-term dependencies and adapt to data distribution shifts over time. We introduce Future-Guided…

Trajectory estimation of maneuvering objects is applied in numerous tasks like navigation, path planning and visual tracking. Many previous works get impressive results in the strictly controlled condition with accurate prior statistics and…

Spatial-temporal forecasting is crucial and widely applicable in various domains such as traffic, energy, and climate. Benefiting from the abundance of unlabeled spatial-temporal data, self-supervised methods are increasingly adapted to…

Motion Planning (MP) is a critical challenge in robotics, especially pertinent with the burgeoning interest in embodied artificial intelligence. Traditional MP methods often struggle with high-dimensional complexities. Recently neural…