Related papers: LeMON: Learning to Learn Multi-Operator Networks
Pretraining for partial differential equation (PDE) modeling has recently shown promise in scaling neural operators across datasets to improve generalizability and performance. Despite these advances, our understanding of how pretraining…
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…
In this paper, we present an initial attempt to learn evolution PDEs from data. Inspired by the latest development of neural network designs in deep learning, we propose a new feed-forward deep network, called PDE-Net, to fulfill two…
Gradient-based meta-learning methods have primarily been applied to classical machine learning tasks such as image classification. Recently, PDE-solving deep learning methods, such as neural operators, are starting to make an important…
Neural PDE solvers are often described as learning solution operators that map problem data to PDE solutions. In this work, we argue that this interpretation is generally incorrect when boundary conditions vary. We show that standard neural…
Learning solution operators for differential equations with neural networks has shown great potential in scientific computing, but ensuring their stability under input perturbations remains a critical challenge. This paper presents a robust…
Operator learning has become a powerful tool in machine learning for modeling complex physical systems governed by partial differential equations (PDEs). Although Deep Operator Networks (DeepONet) show promise, they require extensive data…
Operator learning techniques have recently emerged as a powerful tool for learning maps between infinite-dimensional Banach spaces. Trained under appropriate constraints, they can also be effective in learning the solution operator of…
Pre-training neural operators on diverse partial differential equation (PDE) datasets has emerged as a promising direction for building general-purpose surrogate models in scientific machine learning. However, the inherent complexity and…
In this paper, we investigate the applications of operator learning, specifically DeepONet, for solving nonlinear partial differential equations (PDEs). Unlike conventional function learning methods that require training separate neural…
Neural operator methods have emerged as powerful tools for learning mappings between infinite-dimensional function spaces, yet their potential in optimal control remains largely unexplored. We focus on multi-task control problems, whose…
Operator regression provides a powerful means of constructing discretization-invariant emulators for partial-differential equations (PDEs) describing physical systems. Neural operators specifically employ deep neural networks to approximate…
While it is widely known that neural networks are universal approximators of continuous functions, a less known and perhaps more powerful result is that a neural network with a single hidden layer can approximate accurately any nonlinear…
Operator learning refers to the application of ideas from machine learning to approximate (typically nonlinear) operators mapping between Banach spaces of functions. Such operators often arise from physical models expressed in terms of…
Inverse problems involving partial differential equations (PDEs) can be seen as discovering a mapping from measurement data to unknown quantities, often framed within an operator learning approach. However, existing methods typically rely…
Foundation models, such as large language models, have demonstrated success in addressing various language and image processing tasks. In this work, we introduce a multi-modal foundation model for scientific problems, named PROSE-PDE. Our…
Fast and accurate predictions for complex physical dynamics are a significant challenge across various applications. Real-time prediction on resource-constrained hardware is even more crucial in real-world problems. The deep operator…
Deep operator networks (DeepONets) are receiving increased attention thanks to their demonstrated capability to approximate nonlinear operators between infinite-dimensional Banach spaces. However, despite their remarkable early promise,…
We propose a novel data-lean operator learning algorithm, the Reduced Basis Neural Operator (ReBaNO), to solve a group of PDEs with multiple distinct inputs. Inspired by the Reduced Basis Method and the recently introduced Generative…
Neural networks have been applied to control problems, typically by combining data, differential equation residuals, and objective costs in the training loss or by incorporating auxiliary architectural components. Instead, we propose a…