Partial differential equations (PDEs) are among the most universal and parsimonious
descriptions of natural physical laws, capturing a rich variety of phenomenology and …

The field of dynamical systems is being transformed by the mathematical tools and
algorithms emerging from modern computing and data science. First-principles derivations …

Global medium-range weather forecasting is critical to decision-making across many social
and economic domains. Traditional numerical weather prediction uses increased compute …

Graph neural networks have been extensively studied for learning with inter-connected data.
Despite this, recent evidence has revealed GNNs' deficiencies related to over-squashing …

Deep learning surrogate models have shown promise in solving partial differential
equations (PDEs). Among them, the Fourier neural operator (FNO) achieves good accuracy …

The two fields of machine learning and graphical causality arose and are developed
separately. However, there is, now, cross-pollination and increasing interest in both fields to …

Numerical simulation of fluids plays an essential role in modeling many physical
phenomena, such as weather, climate, aerodynamics, and plasma physics. Fluids are well …

We propose a generalization of transformer neural network architecture for arbitrary graphs.
The original transformer was designed for Natural Language Processing (NLP), which …

Mesh-based simulations are central to modeling complex physical systems in many
disciplines across science and engineering. Mesh representations support powerful …

We propose the geometry-informed neural operator (GINO), a highly efficient approach to
learning the solution operator of large-scale partial differential equations with varying …