Enhancing SPDEBench: An Extensive Benchmark for Learning Stochastic PDEs

[hello0630]

Your name, department, and University

Hao Ni, Department of Mathematics, UCL

Name(s) and department(s) of anyone else relevant to this project

Qi Meng, Chinese Academy of Mathematics and Systems Science, CAS

Please write a brief description of the application area of project

Machine learning for scientific computing, with potential applications in spatio-temporal data analysis

Please describe the project.

Stochastic Partial Differential Equations (SPDEs) are fundamental mathematical models for describing spatio-temporal dynamics in diverse domains such as finance, weather forecasting, and fluid dynamics. Leveraging machine learning (ML) for SPDEs offers the potential to significantly accelerate inference and improve scalability compared to traditional numerical solvers.

SPDEBench has been developed to facilitate the advancement of ML algorithms for learning SPDEs, encompassing both regular and singular cases. In this project, we aim to enhance SPDEBench along several key directions:

• Develop new ML architectures capable of efficiently learning and approximating SPDE solutions.

• Introduce additional benchmark tasks, including generative modeling of SPDE solution and inverse problem learning.

• Establish meta-learning tasks for SPDEs and explore foundational models that generalize across a wide range of SPDEs.

What will be the outputs of this project?

• Publication: A paper submitted to a top-tier machine learning conference.
• Competition: A competition on SPDE learning, aimed at encouraging further research and development in the field.
• Open-Source Repository: The updated SPDEBench repository, including additional datasets/tasks, models, and evaluation metrics.

Which programming language(s) will this project use?

Python

Links to any relevant existing software repositories, etc.

https://github.com/DeepIntoStreams/SPDE_hackathon

Links to any relevant papers, blog posts, etc.

https://arxiv.org/abs/2505.18511

Make project public

• I understand that this project proposal will be public

[benjaminstew]

Really interested in this project - part of my PhD is investigating how to train neural ODEs more efficiently, would love to work on learning SPDEs.

[hello0630]

@benjaminstew thanks for your interest! I'll set up the Discord channel and arrange the first meeting soon.

[joskelar]

Interested, too.

[benjaminstew]

As the software week begins on the 3rd, should we set up a meeting for this week?

[lewisodonnell]

I am also very interested and have discussed with @benjaminstew about working on this project together potentially

[OllieNash]

Hi - in my PhD, I am considering stochastics interacting particle systems and systems of SPDEs. I would be interested in joining the meeting this Thursday at 14:00 to see ML approaches and potentially get involved in the project if that is okay?