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stat.ML2025
Physics-Informed Neural Networks for Joint Source and Parameter Estimation in Advection-Diffusion Equations
Brenda Anague, Bamdad Hosseini, Issa Karambal +1
Recent studies have demonstrated the success of deep learning in solving forward and inverse problems in engineering and scientific computing domains, such as physics-informed neur…
stat.ML2025
Learning Paths for Dynamic Measure Transport: A Control Perspective
Aimee Maurais, Bamdad Hosseini, Youssef Marzouk
We bring a control perspective to the problem of identifying paths of measures for sampling via dynamic measure transport (DMT). We highlight the fact that commonly used paths may…
stat.ML2025
Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysis
Yasamin Jalalian, Juan Felipe Osorio Ramirez, Alexander Hsu +2
We introduce a novel kernel-based framework for learning differential equations and their solution maps that is efficient in data requirements, in terms of solution examples and am…