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Advanced Scientific Machine Learning

Modern Machine Learning Software
Uncertainty Propagation through Scientific Models
High-dimensional Uncertainty Propagation
- Functional Inputs to Scientific Models
- Operator Learning
Inverse Problems in Deterministic Scientific Models
Inverse Problems in Stochastic Scientific Models
- Stochastic Differential Equations
- Filtering and Smoothing
Physics-informed Neural Networks (PINNs)
Information Field Theory (IFT)

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Operator Learning

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Takeaways

Operator Learning#

Takeaways#

Scientific models are operators, i.e., functions that have functions as inputs.

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Example – Surrogate for stochastic Poisson equation with principal component analysis

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Inverse Problems in Deterministic Scientific Models

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By Ilias Bilionis

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