Related papers: Physics-informed Neural Operator Learning for Nonl…

The physics-informed neural operator (PINO) is a machine learning paradigm that has demonstrated promising results for learning solutions to partial differential equations (PDEs). It leverages the Fourier Neural Operator to learn solution…

In multi-body dynamics, the motion of a complicated physical object is described as a coupled ordinary differential equation system with multiple unknown solutions. Engineers need to constantly adjust the object to meet requirements at the…

We present HyPINO, a multi-physics neural operator designed for zero-shot generalization across a broad class of PDEs without requiring task-specific fine-tuning. Our approach combines a Swin Transformer-based hypernetwork with mixed…

Engineering design problems often involve solving parametric Partial Differential Equations (PDEs) under variable PDE parameters and domain geometry. Recently, neural operators have shown promise in learning PDE operators and quickly…

Learning solution operators of partial differential equations (PDEs) from data has emerged as a promising route to fast surrogate models in multi-query scientific workflows. However, for geometric PDEs whose inputs and outputs transform…

Accurate modeling of personalized cardiovascular dynamics is crucial for non-invasive monitoring and therapy planning. State-of-the-art physics-informed neural network (PINN) approaches employ deep, multi-branch architectures with…

Physics-Informed Neural Operators provide efficient, high-fidelity simulations for systems governed by partial differential equations (PDEs). However, most existing studies focus only on multi-scale, multi-physics systems within a single…

Learning PDE dynamics from limited data with unknown physics is challenging. Existing neural PDE solvers either require large datasets or rely on known physics (e.g., PDE residuals or handcrafted stencils), leading to limited applicability.…

Neural operators have been explored as surrogate models for simulating physical systems to overcome the limitations of traditional partial differential equation (PDE) solvers. However, most existing operator learning methods assume that the…

Solving parametric partial differential equations (PDEs) and associated PDE-based, inverse problems is a central task in engineering and physics, yet existing neural operator methods struggle with high-dimensional, discontinuous inputs and…

We present the Physics-Informed Low-Rank Neural Operator (PILNO), a neural operator framework for efficiently approximating solution operators of partial differential equations (PDEs) on point cloud data. PILNO combines low-rank kernel…

Physics-informed Neural Networks (PINNs) have been shown as a promising approach for solving both forward and inverse problems of partial differential equations (PDEs). Meanwhile, the neural operator approach, including methods such as Deep…

Deep learning models trained on finite data lack a complete understanding of the physical world. On the other hand, physics-informed neural networks (PINNs) are infused with such knowledge through the incorporation of mathematically…

Accurate and efficient solutions of spatiotemporal partial differential equations (PDEs), such as phase-field models, are fundamental for understanding interfacial dynamics and microstructural evolution in materials science and fluid…

I provide an introduction to the application of deep learning and neural networks for solving partial differential equations (PDEs). The approach, known as physics-informed neural networks (PINNs), involves minimizing the residual of the…

Physics-informed neural networks (PINNs) have been proven as a promising way for solving various partial differential equations, especially high-dimensional ones and those with irregular boundaries. However, their capabilities in real…

Physics-informed neural networks (PINNs) and neural operators (NOs) for solving the problem of diffraction of Extreme Ultraviolet (EUV) electromagnetic waves from contemporary lithography masks are presented. A novel hybrid Waveguide Neural…

Physics-Informed Neural Networks (PINNs) have emerged as a promising paradigm for solving partial differential equations (PDEs) by embedding physical laws into neural network training objectives. However, their deployment on…

Neural operators have emerged as powerful deep learning frameworks for approximating solution operators of parameterized partial differential equations (PDE). However, current methods predominantly rely on multilayer perceptrons (MLPs) for…

PDEs arise ubiquitously in science and engineering, where solutions depend on parameters (physical properties, boundary conditions, geometry). Traditional numerical methods require re-solving the PDE for each parameter, making parameter…