Related papers: Universal Physics Simulation: A Foundational Diffu…
Diffusion models have recently emerged as powerful stochastic frameworks for high-dimensional inference and generation. However, existing applications to partial differential equations (PDEs) predominantly rely on physics-informed training…
Physics-Informed Neural Networks (PINNs) are a class of deep learning neural networks that learn the response of a physical system without any simulation data, and only by incorporating the governing partial differential equations (PDEs) in…
Physics-informed neural networks (PINNs) show great advantages in solving partial differential equations. In this paper, we for the first time propose to study conformable time fractional diffusion equations by using PINNs. By solving the…
Accurate vessel trajectory prediction is crucial for navigational safety, route optimization, traffic management, search and rescue operations, and autonomous navigation. Traditional data-driven models lack real-world physical constraints,…
The diffusion bridge, which is a diffusion process conditioned on hitting a specific state within a finite period, has found broad applications in various scientific and engineering fields. However, simulating diffusion bridges for modeling…
Climate simulations, at all grid resolutions, rely on approximations that encapsulate the forcing due to unresolved processes on resolved variables, known as parameterizations. Parameterizations often lead to inaccuracies in climate models,…
Physics-informed neural networks (PINNs) employed in fluid mechanics deal primarily with stationary boundaries. This hinders the capability to address a wide range of flow problems involving moving bodies. To this end, we propose a novel…
Inferring universal laws of the environment is an important ability of human intelligence as well as a symbol of general AI. In this paper, we take a step toward this goal such that we introduce a new challenging problem of inferring…
This study introduces a novel point-wise diffusion model that processes spatio-temporal points independently to efficiently predict complex physical systems with shape variations. This methodological contribution lies in applying forward…
Inverse problems involving differential equations often require identifying unknown parameters or functions from data. Existing approaches, such as Physics-Informed Neural Networks (PINNs), Universal Differential Equations (UDEs) and…
Due to the limited accuracy of 4D Magnetic Resonance Imaging (MRI) in identifying hemodynamics in cardiovascular diseases, the challenges in obtaining patient-specific flow boundary conditions, and the computationally demanding and…
Physics-informed neural networks (PINNs) impose known physical laws into the learning of deep neural networks, making sure they respect the physics of the process while decreasing the demand of labeled data. For systems represented by…
We investigate the use of Physics-Informed Neural Networks (PINNs) for solving the wave equation. Whilst PINNs have been successfully applied across many physical systems, the wave equation presents unique challenges due to the multi-scale,…
We introduce a universal diffusion-based downscaling framework that lifts deterministic low-resolution weather forecasts into probabilistic high-resolution predictions without any model-specific fine-tuning. A single conditional diffusion…
Physics-informed neural networks (PINNs) have been proposed to learn the solution of partial differential equations (PDE). In PINNs, the residual form of the PDE of interest and its boundary conditions are lumped into a composite objective…
The rapid development of AI highlights the pressing need for sustainable energy, a critical global challenge for decades. Nuclear fusion, generally seen as an ultimate solution, has been the focus of intensive research for nearly a century,…
Physics-Informed Neural Networks (PINNs) solve partial differential equations using deep learning. However, conventional PINNs perform pointwise predictions that neglect dependencies within a domain, which may result in suboptimal…
We introduce an evidence-driven Bayesian formulation of physics-informed neural networks that enables automatic optimization of loss weights between PDE residuals, boundary conditions, and observational data. Unlike existing Bayesian PINN…
Fictitious identical particle thermodynamics has emerged as a powerful tool to overcome the fermion sign problem, enabling highly accurate simulations of one thousand fermions in warm dense matter (T. Dornheim et al., J. Phys. Chem. Lett.…
In many scientific settings, acquiring complete observations of PDE coefficients and solutions can be expensive, hazardous, or impossible. Recent diffusion-based methods can reconstruct fields given partial observations, but require…