Background

As an emerging paradigm in scientific machine learning (SciML), deep neural operators (DNOs) can learn nonlinear operators, via neural networks, that map between infinite-dimensional function spaces (i.e., operator learning), such as solution operators of partial differential equations (PDEs). However, training these SciML models requires collecting massive amounts of scientific data in a shared dataset, i.e., centralized training. Existing DNO models cannot be applied in critical DOE applications with large data volume or privacy concerns, as they lack the important capability for decentralized training and edge computing, where learning and modeling are performed alongside decentralized data generation at the edge.

Goals

Federated learning (FL) is a decentralized ML setting where many clients collaboratively train a common ML model under the orchestration of a central server, while keeping the training data decentralized. The first objective of this project is to develop a new paradigm for learning physics-informed and energy-aware DNOs from decentralized data in FL settings for scientific edge computing. Moreover, current DNOs are limited to learning an individual PDE, do not benefit from observations of similar systems, and cannot generalize to new PDEs. To further broaden the applicability and generalizability of our federated DNOs, the second objective is to develop the next generation of operator learning and DNOs---neural multi-operator learners (NeMOs)---that learn multiple operators simultaneously and work as scientific foundation models.

Recent News

• 04/2025: We are excited to announce the Yale/UNC-CH Geophysical Waveform Inversion Competition on Kaggle! This competition invites participants to develop machine learning algorithms for estimating subsurface properties, such as velocity maps, from seismic waveform data. We look forward to seeing your innovative solutions on Scientific Machine Learning to solve this challenging problem!

• 10/25/2024: We had the project kick-off meeting at Yale.

• 10/22/2024: FedNeMO at SIAM Conference on Mathematics of Data Science. Lu Lu and Zecheng Zhang co-organized a minisymposium on "Recent Advances of Operator Learning and Foundation-Model-Assisted Multi-Operator Learning"; Lu Lu, Zecheng Zhang, and Youzuo Lin gave talks and posters.

Six partner institutions

FedNeMO is supported by the U.S. Department of Energy Office of Advanced Scientific Computing Research.