Related papers: Poseidon: Efficient Foundation Models for PDEs

Over the last decade, data-driven methods have surged in popularity, emerging as valuable tools for control theory. As such, neural network approximations of control feedback laws, system dynamics, and even Lyapunov functions have attracted…

Neural operators have emerged as an efficient paradigm for solving PDEs, overcoming the limitations of traditional numerical methods and significantly improving computational efficiency. However, due to the diversity and complexity of PDE…

Recent advances in scientific machine learning have shed light on the modeling of pattern-forming systems. However, simulations of real patterns still incur significant computational costs, which could be alleviated by leveraging large…

Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. In a previous work [arXiv:2104.13962], we explored the use of Neural Ordinary Differential Equations (NODE) as…

Computational pathology needs whole-slide image (WSI) foundation models that transfer across diverse clinical tasks, yet current approaches remain largely slide-centric, often depend on private data and expensive paired-report supervision,…

We develop a novel data-driven approach to the inverse problem of classical statistical mechanics: given experimental data on the collective motion of a classical many-body system, how does one characterise the free energy landscape of that…

A large class of hyperbolic and advection-dominated PDEs can have solutions with discontinuities. This paper investigates, both theoretically and empirically, the operator learning of PDEs with discontinuous solutions. We rigorously prove,…

There has recently been increasing attention towards developing foundational neural Partial Differential Equation (PDE) solvers and neural operators through large-scale pretraining. However, unlike vision and language models that make use…

Most PDE foundation models are pretrained and fine-tuned on fluid-centric benchmarks. Their utility under extreme-loading material dynamics remains unclear. We benchmark out-of-distribution transfer on two discontinuity-dominated regimes in…

The spatiotemporal resolution of Partial Differential Equations (PDEs) plays important roles in the mathematical description of the world's physical phenomena. In general, scientists and engineers solve PDEs numerically by the use of…

Autoregressive next-step prediction models have become the de-facto standard for building data-driven neural solvers to forecast time-dependent partial differential equations (PDEs). Denoise training that is closely related to diffusion…

Partial differential equations (PDEs) that fit scientific data can represent physical laws with explainable mechanisms for various mathematically-oriented subjects, such as physics and finance. The data-driven discovery of PDEs from…

The rapid expansion of large foundation models within the pre-training and fine-tuning framework has underscored that larger models often yield better results. However, the scaling up of large foundation models has led to soaring costs in…

Foundation models for computational pathology are expected to facilitate the development of high-performing, generalisable deep learning systems. However, in addition to biologically relevant features, current foundation models also capture…

Deep Operator Networks are emerging as fundamental tools among various neural network types to learn mappings between function spaces, and have recently gained attention due to their ability to approximate nonlinear operators. In…

In recent years operator networks have emerged as promising deep learning tools for approximating the solution to partial differential equations (PDEs). These networks map input functions that describe material properties, forcing functions…

Deep learning models are widely used across computer vision and other domains. When working on the model induction, selecting the right architecture for a given dataset often relies on repetitive trial-and-error procedures. This procedure…

Many computer vision and image processing problems can be posed as solving partial differential equations (PDEs). However, designing PDE system usually requires high mathematical skills and good insight into the problems. In this paper, we…

We apply nonparametric Bayesian methods to study the problem of estimating the intensity function of an inhomogeneous Poisson process. We exhibit a prior on intensities which both leads to a computationally feasible method and enjoys…

Learning system dynamics from observations is a critical problem in many applications over various real-world complex systems, e.g., climate, ecology, and fluid systems. Recently, neural dynamics modeling method have become a prevalent…