Related papers: DiffusionNet: Accelerating the solution of Time-De…

Diffusion models have shown strong competitiveness in offline reinforcement learning tasks by formulating decision-making as sequential generation. However, the practicality of these methods is limited due to the lengthy inference processes…

Diffusion models have recently achieved great success in the synthesis of high-quality images and videos. However, the existing denoising techniques in diffusion models are commonly based on step-by-step noise predictions, which suffers…

The work presents an integral solution of the time-fractional subdiffusion through a preliminary defined profile with unknown coefficients and the concept of penetration layer well known from the heat diffusion The profile satisfies the…

In this paper, we present a novel diffusion-based model for lane detection, called DiffusionLane, which treats the lane detection task as a denoising diffusion process in the parameter space of the lane. Firstly, we add the Gaussian noise…

Diffusion models have significantly advanced the field of generative modeling. However, training a diffusion model is computationally expensive, creating a pressing need to adapt off-the-shelf diffusion models for downstream generation…

In this paper we study the time differential dual-phase-lag model of heat conduction incorporating the microstructural interaction effect in the fast-transient process of heat transport. We analyse the influence of the delay times upon some…

Deep Learning (DL) algorithms are emerging as a key alternative to computationally expensive CFD simulations. However, state-of-the-art DL approaches require large and high-resolution training data to learn accurate models. The size and…

The deep operator network (DeepONet) is a popular neural operator architecture that has shown promise in solving partial differential equations (PDEs) by using deep neural networks to map between infinite-dimensional function spaces. In the…

Decision Transformer (DT), a trajectory modelling method, has shown competitive performance compared to traditional offline reinforcement learning (RL) approaches on various classic control tasks. However, it struggles to learn optimal…

Nonlinear differential equations are challenging to solve numerically and are important to understanding the dynamics of many physical systems. Deep neural networks have been applied to help alleviate the computational cost that is…

In this paper, we present a novel trajectory prediction model for autonomous driving, combining a Characterized Diffusion Module and a Spatial-Temporal Interaction Network to address the challenges posed by dynamic and heterogeneous traffic…

Numerical simulation of steady-state heat conduction is common for thermal engineering. The simulation process usually involves mathematical formulation, numerical discretization and iteration of discretized ordinary or partial differential…

Known by many names and arising in many settings, the forced linear diffusion model is central to the modeling of power and influence within social networks (while also serving as the mechanistic justification for the widely used…

We employ Physics-Informed Neural Networks (PINNs) to solve the diffusion of heavy quarks within the expanding hot QCD medium generated in relativistic heavy-ion collisions. Due to the strong coupling between heavy quarks and the bulk…

We present a framework for recovering/approximating unknown time-dependent partial differential equation (PDE) using its solution data. Instead of identifying the terms in the underlying PDE, we seek to approximate the evolution operator of…

Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…

Diffusion models have emerged as the mainstream approach for visual generation. However, these models typically suffer from sample inefficiency and high training costs. Consequently, methods for efficient finetuning, inference and…

We present the partial evolutionary tensor neural networks (pETNNs), a novel framework for solving time-dependent partial differential equations with high accuracy and capable of handling high-dimensional problems. Our architecture…

Deep learning-based numerical schemes such as Physically Informed Neural Networks (PINNs) have recently emerged as an alternative to classical numerical schemes for solving Partial Differential Equations (PDEs). They are very appealing at…

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.…