Related papers: Poseidon: Efficient Foundation Models for PDEs

This paper addresses Bayesian inference related to partial differential equations (PDEs), particularly nonparametric regression constrained by PDEs. To effectively encode prior information, we propose a novel framework that learns a…

Multimodal foundation models are transformative in sequential recommender systems, leveraging powerful representation learning capabilities. While Parameter-efficient Fine-tuning (PEFT) is commonly used to adapt foundation models for…

This work describes the implementation of a data-driven approach for the reduction of the complexity of parametrical partial differential equations (PDEs) employing Proper Orthogonal Decomposition (POD) and Gaussian Process Regression…

Partial differential equation (PDE) simulation holds extensive significance in scientific research. Currently, the integration of deep neural networks to learn solution operators of PDEs has introduced great potential. In this paper, we…

Design and optimal control problems are among the fundamental, ubiquitous tasks we face in science and engineering. In both cases, we aim to represent and optimize an unknown (black-box) function that associates a performance/outcome to a…

We develop a new Bayesian framework based on deep neural networks to be able to extrapolate in space-time using historical data and to quantify uncertainties arising from both noisy and gappy data in physical problems. Specifically, the…

In this work, an efficient physics-constrained deep learning model is developed for solving multiphase flow in 3D heterogeneous porous media. The model fully leverages the spatial topology predictive capability of convolutional neural…

Many physics and engineering applications demand Partial Differential Equations (PDE) property evaluations that are traditionally computed with resource-intensive high-fidelity numerical solvers. Data-driven surrogate models provide an…

Foundation models are at the forefront of AI research, appealing for their ability to learn from vast datasets and cater to diverse tasks. Yet, their significant computational demands raise issues of environmental impact and the risk of…

Deep neural networks that approximate nonlinear function-to-function mappings, i.e., operators, which are called DeepONet, have been demonstrated in recent articles to be capable of encoding entire PDE control methodologies, such as…

In this manuscript, we introduce the tensor-train reduced basis method, a novel projection-based reduced-order model designed for the efficient solution of parameterized partial differential equations. While reduced-order models are widely…

Many-query computations, in which a computational model for an engineering system must be evaluated many times, are crucial in design and control. For systems governed by partial differential equations (PDEs), typical high-fidelity…

Operator learning has emerged as a promising tool for accelerating the solution of partial differential equations (PDEs). The Deep Operator Networks (DeepONets) represent a pioneering framework in this area: the "vanilla" DeepONet is valued…

Large-scale self-supervised pre-training has paved the way for one foundation model to handle many different vision tasks. Most pre-training methodologies train a single model of a certain size at one time. Nevertheless, various computation…

Deep operator networks (DeepONets) represent a powerful class of data-driven methods for operator learning, demonstrating strong approximation capabilities for a wide range of linear and nonlinear operators. They have shown promising…

Reinforcement learning-based quadruped robots excel across various terrains but still lack the ability to swim in water due to the complex underwater environment. This paper presents the development and evaluation of a data-driven…

Efficient and stable solution of partial differential equations (PDEs) is central to scientific and engineering applications, yet existing numerical solvers rely heavily on matrix based discretizations, while learning based methods require…

Proper orthogonal decomposition (POD) allows reduced-order modeling of complex dynamical systems at a substantial level, while maintaining a high degree of accuracy in modeling the underlying dynamical systems. Advances in machine learning…

Deep Operator Networks (DeepONets) have emerged as a powerful surrogate modeling framework for learning solution operators in PDE-governed systems. While their use is expanding across engineering disciplines, applications in geotechnical…

Fine-tuning pre-trained models for downstream tasks is a widely adopted technique known for its adaptability and reliability across various domains. Despite its conceptual simplicity, fine-tuning entails several troublesome engineering…