Yasamin Jalalian
PhD Candidate in Applied and Computational Mathematics
California Institute of Technology
yjalalia [at] caltech [dot] edu
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Welcome!
I am a PhD candidate in Applied and Computational Mathematics at Caltech, advised by Professor Houman Owhadi and co-mentored by Professor Franca Hoffmann.
Research
I use tools from functional analysis and applied probability to study the theoretical foundations of data-driven methods for complex systems. In particular, I am interested in two broad categories:
Learning Differential Equations from Data
Theoretical and computational foundations for learning deterministic and stochastic governing equations, and their associated solution operators, in different data regimes
Function and Operator Approximation Theory
Error analysis for function and operator learning across different computational frameworks, including kernel methods and Gaussian processes
News
Upcoming: I will be giving talks at the 2026 New York–New Jersey–Pennsylvania Section of SIAM Annual Meeting, and organizing minisymposia and giving talks at SIAM MDS 2026 and SIAM CSE 2027.
July 2026: I gave a talk at SIAM Annual Meeting (AN26) on "Learning Differential Equations from Scarce Data: A Kernel-Based Approach".
April 2026: I gave a talk at Southern California Applied Mathematics Symposium (SOCAMS) on "Learning Differential Equations from Scarce Data: A Kernel-Based Approach".
September 2025: Our preprint on "Data-efficient Kernel Methods for Learning Hamiltonian Systems" is on arXiv.
March 2025: Our preprint on "Data-efficient Kernel Methods for Learning Differential Equations and their Solution Operators: Algorithms and Error Analysis" is on arXiv.
Preprints
Data-efficient Kernel Methods for Learning Differential Equations and their Solution Operators: Algorithms and Error Analysis
Yasamin Jalalian, Juan Felipe Osorio Ramirez, Alexander Hsu, Bamdad Hosseini, Houman Owhadi
Abstract
In this work, 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 amount of measurements from each example, and computational cost, in terms of training procedures.
Our approach is backed by rigorous theoretical guarantees in the form of quantitative worst-case error bounds for the learned equation.
Numerical benchmarks demonstrate significant improvements in computational complexity and robustness while achieving one to two orders of magnitude improvements in terms of accuracy compared to state-of-the-art algorithms.
In comparison to equivalent neural net methods, our approach is significantly more robust to the choice of hyperparameters and does not require close human supervision during training.
2025
Data-efficient Kernel Methods for Learning Hamiltonian Systems
Yasamin Jalalian, Mostafa Samir, Boumediene Hamzi, Peyman Tavallali, Houman Owhadi
Abstract
In this work, we propose kernel-based methods for identifying and forecasting Hamiltonian systems directly from data. We present two approaches: a two-step method that reconstructs trajectories before learning the Hamiltonian, and a one-step method that jointly infers both.
Across several benchmark systems, we demonstrate that our framework achieves accurate, data-efficient predictions and outperforms two-step kernel-based baselines, particularly in scarce-data regimes, while preserving the conservation properties of Hamiltonian dynamics.
We also prove theoretical a priori error estimates, ensuring reliability of the learned models.
2025
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