Research Interests
My research develops machine learning methods for inference in partially observed dynamical systems, with the goal of grounding these methods in the mathematical structure of the underlying inference problem. I focus on forecasting, smoothing, filtering, and uncertainty quantification, aiming to design methodology for these tasks that is accurate and scalable in high-dimensional scientific applications.
To this end, I study operator learning as a framework for inference in dynamical systems, including neural operators for smoothing and forecasting, transformer-based neural operators, and neural operators acting on probability measures. My work is motivated by applications in weather forecasting, engineering design, and other large-scale scientific problems.
Preprints
E. Calvello, E. Carlson, N. Kovachki, M. Manta, A. Stuart, Operator Learning for Smoothing and Forecasting, 2026, https://arxiv.org/pdf/2603.20359
J. Kossaifi, N. Kovachki, M. Mardani, D. Leibovici, S. Ravuri, I. Shokar, E. Calvello, M. S. Abbas, P. Harrington, A. Subramaniam, N. Brenowitz, B. Bonev, W. Byeon, K. Kreis, D. Durran, A. Vahdat, M. Pritchard, and J. Kautz. Demystifying Data-Driven Probabilistic Medium-Range Weather Forecasting, 2026, https://arxiv.org/pdf/2601.18111.
A. Bacho, A. Sorokin, X. Yang, T. Bourdais, E. Calvello, M. Darcy, A. Hsu, B. Hosseini, H. Owhadi, Operator Learning at Machine Precision, 2025, https://arxiv.org/abs/2511.19980.
E. Calvello, J. A. Carrillo, F. Hoffmann, P. Monmarché, A. M. Stuart, U. Vaes, Statistical Accuracy of the Ensemble Kalman Filter in the Near-Linear Setting, 2025, https://arxiv.org/pdf/2503.16154.
R. Baptista, E. Calvello, M. Darcy, H. Owhadi, A. M. Stuart, X. Yang, Solving Roughly Forced Nonlinear PDEs via Misspecified Kernel Methods and Neural Network, 2025, https://arxiv.org/pdf/2501.17110. To Appear in AMS Mathematics of Computation.
Publications
E. Calvello, P. Monmarché, A. M. Stuart, U. Vaes, Accuracy of the Ensemble Kalman Filter in the Near-Linear Setting, SIAM Journal on Numerical Analysis (2026) 64:2, 391-429 (pdf)
E. Calvello, N. B. Kovachki, M. E. Levine, A. M. Stuart, Continuum Attention for Neural Operators, Journal of Machine Learning Research (2025) 300:1-52 (pdf, code)
E. Bach, R. Baptista, E. Calvello, B. Chen, A. Stuart, Learning Enhanced Ensemble Filters, Journal of Computational Physics, Volume 547, (2026) 114550. (pdf)
E. Calvello, S. Reich, and A. M. Stuart, Ensemble Kalman Methods: A Mean Field Perspective, Acta Numerica (2025), pp 123-291. (pdf, code)
Talks
"Operator Learning for Inference in Dynamical Systems" - SIAM UQ 2026, Minneapolis, MN, USA
"Transformers for Nonlinear Data Assimilation" - Applied Inverse Problems 2025, Rio de Janeiro, Brazil
"Transformers for Data Assimilation" - SIAM CSE 2025, Fort Worth, TX, USA
"Data Assimilation: From the Ensemble Kalman Filter to Operator Learning" - Control and Optimisation Seminar, Imperial College London, UK
"Transformers for Scientific Machine Learning" - MaLGa Seminar, University of Genova, Italy
"Ensemble Kalman Methods for Non-Linear Filtering: A Mean-Field Perspective - SIAM MDS 2024, Atlanta, GA, USA
"Transformers for Scientific Machine Learning" - Statistical Aspects of Non-linear Inverse Problems 2024, Cambridge, UK
"Transformers for Scientific Machine Learning" - Digital Twins for Inverse Problems in Earth Science 2024, Marseille, France - slides
"The Mean-Field Ensemble Kalman Filter: From Analysis To Algorithms" - SCICADE 2024, Singapore
"The Mean-Field Ensemble Kalman Filter: From Analysis To Algorithms" - SIAM AN 2024, Spokane, WA, USA
"The Mean-Field Ensemble Kalman Filter: Gaussian and Particle Approximations" - SIAM UQ 2024, Trieste, Italy
"The Mean-Field Ensemble Kalman Filter: Gaussian and Particle Approximations" - ISDA 2023, Bologna, Italy - slides
"Kernel Methods for Rough PDEs" - ICIAM 2023, Tokyo, Japan - slides coming soon
"Ensemble Kalman Methods: A Mean Field Perspective" - SIAM CSE 2023, Amsterdam, The Netherlands - slides
"Ensemble Kalman Methods: A Mean Field Perspective" - SIAM MDS 2022, San Diego, CA, USA - slides