Related papers: Poseidon: Efficient Foundation Models for PDEs

Neural solvers for partial differential equations (PDEs) have great potential to generate fast and accurate physics solutions, yet their practicality is currently limited by their generalizability. PDEs evolve over broad scales and exhibit…

Surrogate modeling of body-driven fluid flows where immersed moving boundaries couple structural dynamics to chaotic, unsteady fluid phenomena remains a fundamental challenge for both computational physics and machine learning. We present…

The remarkable success of pretrain-then-finetune paradigm has led to a proliferation of available pre-trained models for vision tasks. This surge presents a significant challenge in efficiently choosing the most suitable pre-trained models…

Robust physics (e.g., governing equations and laws) discovery is of great interest for many engineering fields and explainable machine learning. A critical challenge compared with general training is that the term and format of governing…

Training foundation models on extensive datasets and then finetuning them on specific tasks has emerged as the mainstream approach in artificial intelligence. However, the model robustness, which is a critical aspect for safety, is often…

Modeling 3D dynamics is a fundamental problem in multi-body systems across scientific and engineering domains and has important practical implications in object trajectory prediction and simulation. While recent GNN-based approaches have…

Stochastic differential equations (SDEs) describe dynamical systems where deterministic flows, governed by a drift function, are superimposed with random fluctuations, dictated by a diffusion function. The accurate estimation (or discovery)…

There has been active investigation into deep learning approaches for time series analysis, including foundation models. However, most studies do not address significant scientific applications. This paper aims to identify key features in…

Traditional 2D hydraulic models face significant computational challenges that limit their applications that are time-sensitive or require many model evaluations. This study presents a physics-informed Deep Operator Network (DeepONet)…

Pretrained foundation models learn embeddings that can be used for a wide range of downstream tasks. These embeddings optimise general performance, and if insufficiently accurate at a specific task the model can be fine-tuned to improve…

Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…

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…

Controller tuning and parameter optimization are crucial in system design to improve closed-loop system performance. Bayesian optimization has been established as an efficient model-free controller tuning and adaptation method. However,…

In this work, we describe a novel approach to building a neural PDE solver leveraging recent advances in transformer based neural network architectures. Our model can provide solutions for different values of PDE parameters without any need…

Predictive dynamical models for marine ecosystems are used for a variety of needs. Due to sparse measurements and limited understanding of the myriad of ocean processes, there is however significant uncertainty. There is model uncertainty…

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…

In this paper, we combine deep learning concepts and some proper orthogonal decomposition (POD) model reduction methods for predicting flow in heterogeneous porous media. Nonlinear flow dynamics is studied, where the dynamics is regarded as…

We present two approaches to system identification, i.e. the identification of partial differential equations (PDEs) from measurement data. The first is a regression-based Variational System Identification procedure that is advantageous in…

Foundation models are deep neural networks (such as GPT-5, Gemini~3, and Opus~4) trained on large datasets that can perform diverse downstream tasks -- text and code generation, question answering, summarization, image classification, and…

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…