Scientific Machine Learning

Physics-informed and operator-learning methods for scientific computing.

frontier tier

Scientific Machine Learning. Physics-informed and operator-learning methods for scientific computing.

Recent technical contributions

A handful of recent papers carry the methodological frontier of scientific machine learning forward. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations (Raissi et al., 2019) is a primary reference for this area and develops new techniques or results that downstream work builds on. Scientific machine learning through physics-informed neural networks: Where we are and what’s next (Cuomo et al., 2022) pushes the technical state of the art and is widely cited in subsequent work on the topic.

Open methodological questions for scientific machine learning include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.

Prerequisites

Sources

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  1. 01

    Physics-Informed Neural Networks

    PINNs for forward and inverse PDE problems.
  2. 02

    Neural Operators

    Fourier, DeepONet, and graph neural operators for PDE solution maps.
  3. 03

    Reduced-Order Modeling

    POD, DEIM, and data-driven reduced models.
  4. 04

    Sparse Identification of Dynamics

    SINDy and operator learning from data.
  5. 05

    Differentiable Scientific Programming

    Adjoint sensitivity, automatic differentiation through ODE/PDE solvers.

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