8 papers
Approximating Measures on Function Spaces: Transport and Truncation
Ricardo Baptista, Bamdad Hosseini, Alexander W. Hsu
Measures on function spaces arise throughout Bayesian inverse problems and generative modeling, often with low-dimensional structure relative to a tractable reference measure. We i…
Conditional Sampling via Wasserstein Autoencoders and Triangular Transport
Mohammad Al-Jarrah, Michele Martino, Marcus Yim +2
We present Conditional Wasserstein Autoencoders (CWAEs), a framework for conditional simulation that exploits low-dimensional structure in both the conditioned and the conditioning…
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…
Operator Learning at Machine Precision
Aras Bacho, Aleksei G. Sorokin, Xianjin Yang +6
Neural operator learning methods have garnered significant attention in scientific computing for their ability to approximate infinite-dimensional operators. However, increasing th…
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…
A joint optimization approach to identifying sparse dynamics using least squares kernel collocation
Alexander W. Hsu, Ike Griss Salas, Jacob M. Stevens-Haas +3
We develop an all-at-once modeling framework for learning systems of ordinary differential equations (ODE) from scarce, partial, and noisy observations of the states. The proposed…
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…
Score-based deterministic density sampling
Vasily Ilin, Peter Sushko, Jingwei Hu
We propose a deterministic sampling framework using Score-Based Transport Modeling for sampling an unnormalized target density given only its score . Our method…