相关论文: Poseidon: Efficient Foundation Models for PDEs

Artificial Intelligence (AI) technologies have profoundly transformed the field of remote sensing, revolutionizing data collection, processing, and analysis. Traditionally reliant on manual interpretation and task-specific models, remote…

Partial differential equations (PDEs) are often computationally challenging to solve, and in many settings many related PDEs must be be solved either at every timestep or for a variety of candidate boundary conditions, parameters, or…

We consider small-data, large-scale decision problems in which a firm must make many operational decisions simultaneously (e.g., across a large product portfolio) while observing only a few, potentially noisy, data points per instance.…

Foundation models have demonstrated remarkable generalization, data efficiency, and robustness properties across various domains. In this paper, we explore the feasibility of foundation models for applications in the control domain. The…

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…

Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…

Time series forecasting drives operational decisions in areas like finance, transportation, and energy. While supervised learning approaches achieve strong performance, they require domain-specific training, feature engineering, and ongoing…

Species transport models typically combine partial differential equations (PDEs) with relations from hindered transport theory to quantify electromigrative, convective, and diffusive transport through complex nanoporous systems; however,…

In this work, we propose a method to learn the solution operators of PDEs defined on varying domains via MIONet, and theoretically justify this method. We first extend the approximation theory of MIONet to further deal with metric spaces,…

A computed approximation of the solution operator to a system of partial differential equations (PDEs) is needed in various areas of science and engineering. Neural operators have been shown to be quite effective at predicting these…

In the pursuit of accurate experimental and computational data while minimizing effort, there is a constant need for high-fidelity results. However, achieving such results often requires significant computational resources. To address this…

We develop a continual learning method for pretrained models that \emph{requires no access to old-task data}, addressing a practical barrier in foundation model adaptation where pretraining distributions are often unavailable. Our key…

Solving partial differential equations (PDEs) on fine spatio-temporal scales for high-fidelity solutions is critical for numerous scientific breakthroughs. Yet, this process can be prohibitively expensive, owing to the inherent complexities…

Neural operators have achieved strong performance in learning solution operators of partial differential equations (PDEs), but their inherently continuous representations struggle to capture discontinuities and sharp transitions. Existing…

Equations governing physico-chemical processes are usually known at microscopic spatial scales, yet one suspects that there exist equations, e.g. in the form of Partial Differential Equations (PDEs), that can explain the system evolution at…

Large amounts of digitized histopathological data display a promising future for developing pathological foundation models via self-supervised learning methods. Foundation models pretrained with these methods serve as a good basis for…

Physics-Informed Neural Networks (PINNs) have emerged as powerful tools for solving partial differential equations (PDEs). However, training PINNs from scratch is often computationally intensive and time-consuming. To address this problem,…

We introduce PPOPT - Proximal Policy Optimization using Pretraining, a novel, model-free deep-reinforcement-learning algorithm that leverages pretraining to achieve high training efficiency and stability on very small training samples in…

Is a deep learning model capable of understanding systems governed by certain first principle laws by only observing the system's output? Can deep learning learn the underlying physics and honor the physics when making predictions? The…

Advances in Earth observation (EO) foundation models have unlocked the potential of big satellite data to learn generic representations from space, benefiting a wide range of downstream applications crucial to our planet. However, most…