Related papers: A physics-informed transformer neural operator 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…
Elliptic partial differential equations (PDEs) are a major class of time-independent PDEs that play a key role in many scientific and engineering domains such as fluid dynamics, plasma physics, and solid mechanics. Recently, neural…
Recently deep learning surrogates and neural operators have shown promise in solving partial differential equations (PDEs). However, they often require a large amount of training data and are limited to bounded domains. In this work, we…
We present an end-to-end framework to learn partial differential equations that brings together initial data production, selection of boundary conditions, and the use of physics-informed neural operators to solve partial differential…
Neural operators effectively solve PDE problems from data without knowing the explicit equations, which learn the map from the input sequences of observed samples to the predicted values. Most existing works build the model in the original…
Neural operator models for solving partial differential equations (PDEs) often rely on global mixing mechanisms-such as spectral convolutions or attention-which tend to oversmooth sharp local dynamics and introduce high computational cost.…
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…
Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work…
Scientific machine learning has enabled the extraction of physical insights and data-driven modeling of high-dimensional spatiotemporal data, yet achieving physically interpretable latent representations and computationally efficient…
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.…
Physics-Informed Neural Network (PINN) is a novel multi-task learning framework useful for solving physical problems modeled using differential equations (DEs) by integrating the knowledge of physics and known constraints into the…
Although neural operators are widely used in data-driven physical simulations, their training remains computationally expensive. Recent advances address this issue via downstream learning, where a model pretrained on simpler problems is…
This paper presents an efficient mesh deformation method based on boundary integration and neural operators, formulating the problem as a linear elasticity boundary value problem (BVP). To overcome the high computational cost of traditional…
We combine vision transformers with operator learning to solve diverse inverse problems described by partial differential equations (PDEs). Our approach, named ViTO, combines a U-Net based architecture with a vision transformer. We apply…
We propose the geometry-informed neural operator (GINO), a highly efficient approach to learning the solution operator of large-scale partial differential equations with varying geometries. GINO uses a signed distance function and…
Physics informed neural networks (PINNs) are nowadays used as efficient machine learning methods for solving differential equations. However, vanilla-PINNs fail to learn complex problems as ones involving stiff ordinary differential…
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…
Partial differential equations (PDEs) govern a wide range of physical phenomena, but their numerical solution remains computationally demanding, especially when repeated simulations are required across many parameter settings. Recent…
Industrial design evaluation often relies on high-fidelity simulations of governing partial differential equations (PDEs). While accurate, these simulations are computationally expensive, making dense exploration of design spaces…
Physics-informed neural networks (PINNs) are a new tool for solving boundary value problems by defining loss functions of neural networks based on governing equations, boundary conditions, and initial conditions. Recent investigations have…