Research

Research Interests

My research is motivated by the need for a concurrent theoretical and methodological development in the design of numerical schemes performing probabilistic inference and prediction. The design of algorithms optimally integrating dynamical models and observational data for state estimation and the solution of inverse problems is addressed by the field of data assimilation (DA). Machine learning (ML) has provided unprecedented capabilities in the computational sciences and engineering and offers a new avenue for probabilistic inference in DA. Yet, the development of firm theoretical foundations for the application of ML in scientific computation is at its infancy. 

My work focuses on addressing the theoretical and methodological challenges arising from the use of ML for DA. My interests also include the analysis and algorithmic development of data assimilation schemes, the design and theoretical analysis of novel methodology for scientific machine learning.

Preprints

• 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.

• E. Calvello, P. Monmarché, A. M. Stuart, U. Vaes, Accuracy of the Ensemble Kalman Filter in the Near-Linear Setting, 2024, https://arxiv.org/pdf/2409.09800.

• E. Calvello, N. B. Kovachki, M. E. Levine, A. M. Stuart, Continuum Attention for Neural Operators, 2024, https://arxiv.org/pdf/2406.06486. (code)

• E. Calvello, S. Reich, and A. M. Stuart, Ensemble Kalman Methods: A Mean Field Perspective, 2022, https://arxiv.org/abs/2209.11371. To Appear in Acta Numerica 2025. (code)

Talks 

• "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