相关论文: Physics-informed Spectral Learning: the Discrete H…

Physics-informed machine learning typically integrates physical priors into the learning process by minimizing a loss function that includes both a data-driven term and a partial differential equation (PDE) regularization. Building on the…

A novel physics-informed operator learning technique based on spectral methods is introduced to model the complex behavior of heterogeneous materials. The Lippmann-Schwinger operator in Fourier space is employed to construct physical…

We propose a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of parametric partial differential equations (PDEs) conditioned on partial observations, which includes,…

Deep kernel learning is a promising combination of deep neural networks and nonparametric function learning. However, as a data driven approach, the performance of deep kernel learning can still be restricted by scarce or insufficient data,…

Physics-Informed Neural Networks have become a powerful mesh-free method for solving partial differential equations, but their performance is often limited by spectral bias. Specifically, in standard MLPs used in PINNs, the global parameter…

Mode conversion in non-homogeneous elastic media makes it challenging to interpret physical properties accurately. Decomposing these modes correctly is crucial across various scientific areas. Recent machine learning approaches have been…

We use a space-time discretization based on physics informed deep learning (PIDL) to approximate solutions of a class of rate-dependent strain gradient plasticity models. The differential equation governing the plastic flow, the so-called…

Physics-informed machine learning (PIML) integrates partial differential equations (PDEs) into machine learning models to solve inverse problems, such as estimating coefficient functions (e.g., the Hamiltonian function) that characterize…

We propose the Physics-Informed Neural Network-driven Sparse Field Discretization method (PINN-SFD), a novel self-supervised, physics-informed deep learning approach for addressing the Near-Field Acoustic Holography (NAH) problem. Unlike…

Partial differential equations (PDEs) are fundamental for modeling complex natural and physical phenomena. In many real-world applications, however, observational data are extremely sparse, which severely limits the applicability of both…

Dynamical systems are typically governed by a set of linear/nonlinear differential equations. Distilling the analytical form of these equations from very limited data remains intractable in many disciplines such as physics, biology, climate…

Diffusion models provide expressive priors for forecasting trajectories of dynamical systems, but are typically unreliable in the sparse data regime. Physics-informed machine learning (PIML) improves reliability in such settings; however,…

This paper introduces a hybrid computational framework for the multi-frequency inverse source problem governed by the Helmholtz equation. By integrating a classical Fourier method with a deep convolutional neural network, we address the…

We introduce variational spectral learning (VSL), a machine learning framework for solving partial differential equations (PDEs) that operates directly in the coefficient space of spectral expansions. VSL offers a principled bridge between…

High-fidelity simulation of complex physical systems is exorbitantly expensive and inaccessible across spatiotemporal scales. Recently, there has been an increasing interest in leveraging deep learning to augment scientific data based on…

To address the sensitivity of parameters and limited precision for physics-informed extreme learning machines (PIELM) with common activation functions, such as sigmoid, tangent, and Gaussian, in solving high-order partial differential…

We apply physics-informed machine learning (PIML) to solve inverse problems in holography and classical mechanics, focusing on neural ordinary differential equations (Neural ODEs) and physics-informed neural networks (PINNs) for solving…

Partial differential equations (PDEs) are commonly employed to model complex industrial systems characterized by multivariable dependence. Existing physics-informed neural networks (PINNs) excel in solving PDEs in a homogeneous medium.…

This paper presents a new method for learning dissipative Hamiltonian dynamics from a limited and noisy dataset. The method uses the Helmholtz decomposition to learn a vector field as the sum of a symplectic and a dissipative vector field.…

Accurate blur estimation is essential for high-performance imaging across various applications. Blur is typically represented by the point spread function (PSF). In this paper, we propose a physics-informed PSF learning framework for…