Discover the ideas shaping the future of trustworthy AI
Follow the project’s journey through accessible stories updates on our four research directions. Meet the mathematics, challenges, collaborations, and applications behind a new generation of Control theory and Machine Learning methods with analytical guarantees to discover how jointly address some of today’s most demanding scientific and technological questions.
Physics-Encoded Operator Learning: A Dynamical Systems Approach to Scientific Computing
Authors: Ziqian Li, Kang Liu, Yongcun Song, Hangrui Yue, and Enrique Zuazua Learning ...
The Geometry of How Transformers Process Long Sequences
Authors: Albert Alcalde, Giovanni Fantuzzi, Enrique Zuazua Modern machine learning systems often process ...
When Federated Learning Becomes a Game: How Incentives Trigger a Tipping Point
Authors: Kang Liu, Ziqi Wang, Enrique Zuazua A shared AI model needs more ...
The Deep Truncated FBSDE Method: A Robust Solver for High-Dimensional PDEs
Authors: Xinyu Cheng, Yunzhang Li, Weiran Xiong, Enrique Zuazua Partial differential equations (PDEs) ...
From fitting points to learning: generalization in neural ODEs
Author: Antonio Álvarez-López A model can remember every example in its training set ...
Nudging Simulations Toward Reality with Partial Observations
Author: Bo You Every forecast begins from an estimated state rather than nature’s ...
One Model, Many Outputs: Why Shapley Explanations refuse to Mix
Authors: Umberto Biccari, Roberto Morales, Enrique Zuazua Many artificial-intelligence systems make several predictions ...
Good Solutions, Bad Coordinates: The Coercivity Gap in Neural Partial Differential Equation Solvers
Author: Enrique Zuazua Read the complete contribution on SIAM News ...
The missing middle: following information through a Transformer
Authors: Umberto Biccari An accurate prediction does not reveal the path that produced ...
When averaging is not enough: coordinating distributed learning systems
Authors: Roberto Morales Modern machine learning often begins with an implicit assumption: somewhere, ...
Learning once, controlling many times: Neural Operators for fast feedback
Authors: Jun Chen, Umberto Biccari, Junmin Wang Imagine a system that must adapt ...