When we talk about foundation models, what are we talking about? This is a reflection piece on foundation models by drawing an analogy from numerical solutions in fluid dynamics.

This paper explore the challenges in building these models for science and engineering and introduce a promising framework called the Data-Driven Finite Element Method (DD-FEM), which aims to bridge traditional numerical methods with modern AI to provide a rigorous foundation for this exciting new field.

Choi, Y., Cheung, S. W., Kim, Y., Tsai, P. H., Diaz, A. N., Zanardi, I., ... & Heinkenschloss, M. (2025). Defining Foundation Models for Computational Science: A Call for Clarity and Rigor. arXiv preprint arXiv:2505.22904.

IBM recently released the first-of-its-kind geospatial intelligence any-to-any model TerraMind. In this podcast, we feature this new generative model and learn its capability of multi-modality. I believe there is a lot of potential with such a model.

Jakubik, J., Yang, F., Blumenstiel, B., Scheurer, E., Sedona, R., Maurogiovanni, S., Bosmans, J., Dionelis, N., Marsocci, V., Kopp, N., Ramachandran, R., Fraccaro, P., Brunschwiler, T., Cavallaro, G., & Longépé, N. (2025). TerraMind: Large-Scale Generative Multimodality for Earth Observation. ArXiv. https://arxiv.org/abs/2504.11171

Today, we are featuring a geospatial foundation model Prithvi, produced by NASA and IBM, one of the first foundation model in this space.

Trained on a large global dataset of NASA’s Harmonized Landsat and Sentinel-2 data, Prithvi-EO-2.0 demonstrates significant improvements over its predecessor by incorporating temporal and location embeddings. Through extensive benchmarking using GEO-Bench, it outperforms other prominent GFMs across various remote sensing tasks and resolutions, highlighting its versatility. Furthermore, the model has been successfully applied to real-world downstream tasks led by subject matter experts in areas such as disaster response, land use and crop mapping, and ecosystem dynamics monitoring, showcasing its practical utility. Emphasising a Trusted Open Science approach, Prithvi-EO-2.0 is made available on Hugging Face and IBM TerraTorch to facilitate community adoption and customization, aiming to overcome limitations of previous GFMs related to multi-temporality, validation, and ease of use for non-AI experts.

This research article introduces HydroGraphNet, a novel physics-informed graph neural network for improved flood forecasting. Traditional hydrodynamic models are computationally expensive, while machine learning alternatives often lack physical accuracy and interpretability. HydroGraphNet integrates the Kolmogorov–Arnold Network (KAN) to enhance model interpretability within an unstructured mesh framework. By embedding mass conservation laws into its training and using a specific architecture, the model achieves more physically consistent and accurate predictions. Validation on real-world flood data demonstrates significant reductions in prediction error and improvements in identifying major flood events compared to standard methods.

Taghizadeh, M., Zandsalimi, Z., Nabian, M. A., Shafiee-Jood, M., & Alemazkoor, N. Interpretable physics-informed graph neural networks for flood forecasting. Computer-Aided Civil and Infrastructure Engineering. https://doi.org/10.1111/mice.13484

We are featuring three papers:

Mardani, M., Brenowitz, N., Cohen, Y., Pathak, J., Chen, C., Liu, C., Vahdat, A., Nabian, M. A., Ge, T., Subramaniam, A., Kashinath, K., Kautz, J., & Pritchard, M. (2025). Residual corrective diffusion modeling for km-scale atmospheric downscaling. Communications Earth & Environment, 6(1), 1-10. https://doi.org/10.1038/s43247-025-02042-5

Price, I., Alet, F., Andersson, T. R., Masters, D., Ewalds, T., Stott, J., Mohamed, S., Battaglia, P., Lam, R., & Willson, M. (2025). Probabilistic weather forecasting with machine learning. Nature, 637(8044), 84-90. https://doi.org/10.1038/s41586-024-08252-9

Lam, R., Sanchez-Gonzalez, A., Willson, M., Wirnsberger, P., Fortunato, M., Alet, F., Ravuri, S., Ewalds, T., Eaton-Rosen, Z., Hu, W., Merose, A., Hoyer, S., Holland, G., Vinyals, O., Stott, J., Pritzel, A., Mohamed, S., & Battaglia, P. (2023). Learning skillful medium-range global weather forecasting. Science. https://doi.org/adi2336