Differential equations are one of the main reasons automatic differentiation matters in scientific computing. Many scientific models are not written as closed-form functions....
| Section | Title |
|---|---|
| 1 | Chapter 14. Scientific Computing Applications |
| 2 | Sensitivity Analysis |
| 3 | Inverse Problems |
| 4 | Computational Fluid Dynamics |
| 5 | Molecular Simulation |
| 6 | Computational Finance |
| 7 | Signal Processing |
| 8 | Robotics and Control |
| 9 | Probabilistic Programming |
Chapter 14. Scientific Computing ApplicationsDifferential equations are one of the main reasons automatic differentiation matters in scientific computing. Many scientific models are not written as closed-form functions....
Sensitivity AnalysisSensitivity analysis studies how changes in inputs affect the outputs of a system. In differential equations, optimization, simulation, and machine learning, the main object...
Inverse ProblemsAn inverse problem asks for causes from effects. A forward model predicts observations from parameters. An inverse model tries to recover parameters from observations.
Computational Fluid DynamicsComputational fluid dynamics studies fluid motion by solving discretized forms of the governing equations. Automatic differentiation enters CFD when we want gradients of...
Molecular SimulationMolecular simulation models the behavior of atoms and molecules using physical interaction laws. Automatic differentiation is important because many molecular methods require...
Computational FinanceComputational finance uses numerical models to price contracts, measure risk, and optimize portfolios. Automatic differentiation is useful because most financial computations...
Signal ProcessingSignal processing studies how information is represented, transformed, filtered, compressed, reconstructed, and estimated from signals. A signal may be a time series, an...
Robotics and ControlRobotics and control systems interact with the physical world through sensing, estimation, planning, and actuation. Automatic differentiation is important because modern...
Probabilistic ProgrammingProbabilistic programming represents uncertainty using executable probabilistic models. A probabilistic program defines a distribution rather than only a deterministic computation.