InverseProblems is a
- educational Inverse Problem or Numerical Method library. The goal is to provide students with a light-weighted code to explore these areas and interactive lectures with amazing Jupyter Notebook.
- benchmark repository originally designed to test unscented Kalman inversion and other derivative-free inverse methods. The goal is to provide reseachers with access to various inverse problems, while enabling researchers to quickly and easily develop and test novel inverse methods.
- All the inverse methods are in Inversion folder
- Each other folder contains one category of inverse problems
Let's start! (
- Overview
- What are inverse problems, why are they important?
- Bayesian inversion, Bayesian inference, and Bayesian calibration
- Probability density function space
- Probabilistic approaches
- Invariant and ergodic measures
- Langevin dynamics
- Markov Chain Monte Carlo methods
- Interacting particle methods
- Variational inference
- Coupling ideas
- When is posterior distribution close to Gaussian
- All models are wrong
- Invariant and ergodic measures
- Examples
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Linear inverse problems
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Chaotic systems
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Structure mechanics problems
- Damage detection of a "bridge"
- Consitutive modeling of a multiscale fiber-reinforced plate
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Fluid mechanics problems
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Fluid structure interaction problems
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Climate modeling
- Barotropic climate model
- Idealized general circulation model (Held-Suarez benchmark)
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Other posterior distribution estimations
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You are welcome to submit an issue for any questions related to InverseProblems.
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Daniel Zhengyu Huang, Tapio Schneider, and Andrew M. Stuart. "Iterated Kalman Methodology For Inverse Problems / Unscented Kalman Inversion."
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Daniel Zhengyu Huang, Jiaoyang Huang, Sebastian Reich, and Andrew M. Stuart. "Efficient Derivative-free Bayesian Inference for Large-Scale Inverse Problems."
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Shunxiang Cao, Daniel Zhengyu Huang. "Bayesian Calibration for Large-Scale Fluid Structure Interaction Problems Under Embedded/Immersed Boundary Framework."
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Yifan Chen, Daniel Zhengyu Huang, Jiaoyang Huang, Sebastian Reich, and Andrew M. Stuart. "Gradient Flows for Sampling: Mean-Field Models, Gaussian Approximations and Affine Invariance."
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Daniel Zhengyu Huang, Jiaoyang Huang, and Zhengjiang Lin. "Convergence Analysis of Probability Flow ODE for Score-based Generative Models."