Related papers: DeepONet as a Multi-Operator Extrapolation Model: …

In domains such as health care and finance, shortage of labeled data and computational resources is a critical issue while developing machine learning algorithms. To address the issue of labeled data scarcity in training and deployment of…

The recently introduced DeepONet operator-learning framework for PDE control is extended from the results for basic hyperbolic and parabolic PDEs to an advanced hyperbolic class that involves delays on both the state and the system output…

We present a novel framework combining Deep Operator Networks (DeepONets) with Physics-Informed Neural Networks (PINNs) to solve partial differential equations (PDEs) and estimate their unknown parameters. By integrating data-driven…

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…

Fine-tuning is a popular way of exploiting knowledge contained in a pre-trained convolutional network for a new visual recognition task. However, the orthogonal setting of transferring knowledge from a pretrained network to a visually…

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…

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…

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…

Most uses of machine learning today involve training a model from scratch for a particular task, or sometimes starting with a model pretrained on a related task and then fine-tuning on a downstream task. Both approaches offer limited…

In the present work, we introduce a novel approach to enhance the precision of reduced order models by exploiting a multi-fidelity perspective and DeepONets. Reduced models provide a real-time numerical approximation by simplifying the…

With the accumulation of resources in the era of big data and the rise of pre-trained models in deep learning, optimizing neural networks for various tasks often involves different strategies for fine-tuning pre-trained models versus…

Simulating and predicting multiscale problems that couple multiple physics and dynamics across many orders of spatiotemporal scales is a great challenge that has not been investigated systematically by deep neural networks (DNNs). Herein,…

A major challenge in machine learning is resilience to out-of-distribution data, that is data that exists outside of the distribution of a model's training data. Training is often performed using limited, carefully curated datasets and so…

Deep neural operators can learn operators mapping between infinite-dimensional function spaces via deep neural networks and have become an emerging paradigm of scientific machine learning. However, training neural operators usually requires…

The deep operator network (DeepONet) is a popular neural operator architecture that has shown promise in solving partial differential equations (PDEs) by using deep neural networks to map between infinite-dimensional function spaces. In the…

Developing neural operators that accurately predict the behavior of systems governed by partial differential equations (PDEs) across unseen parameter regimes is crucial for robust generalization in scientific and engineering applications.…

Accurately learning solution operators for time-dependent partial differential equations (PDEs) from sparse and irregular data remains a challenging task. Recurrent DeepONet extensions inherit the discrete-time limitations of…

Neural Operator Networks (ONets) represent a novel advancement in machine learning algorithms, offering a robust and generalizable alternative for approximating partial differential equations (PDEs) solutions. Unlike traditional Neural…

Finetuning a pretrained model has become a standard approach for training neural networks on novel tasks, resulting in fast convergence and improved performance. In this work, we study an alternative finetuning method, where instead of…

Operator learning for complex nonlinear systems is increasingly common in modeling multi-physics and multi-scale systems. However, training such high-dimensional operators requires a large amount of expensive, high-fidelity data, either…