https://github.com/psorlab/dynamicbounds.jl
Bounds and Relaxations of Parametric Differential Equations
https://github.com/psorlab/dynamicbounds.jl
Last synced: 4 months ago
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Bounds and Relaxations of Parametric Differential Equations
- Host: GitHub
- URL: https://github.com/psorlab/dynamicbounds.jl
- Owner: PSORLab
- License: other
- Created: 2020-02-27T21:24:33.000Z (over 5 years ago)
- Default Branch: master
- Last Pushed: 2022-03-18T03:48:39.000Z (over 3 years ago)
- Last Synced: 2025-01-20T17:54:47.812Z (5 months ago)
- Language: Julia
- Size: 249 KB
- Stars: 2
- Watchers: 2
- Forks: 2
- Open Issues: 7
-
Metadata Files:
- Readme: README.md
- License: LICENSE.md
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README
# DynamicBounds.jl: Validated Bounds and Relaxations of Differential Equations
| **Linux/OS/Windows** | **Coverage** | **Persistent DOI** |
|:--------------------------------------------------------------------------------:|:-------------------------------------------------------:|:-------------------------------------------------------:|
| [](https://github.com/PSORLab/DynamicBounds.jl/actions?query=workflow%3ACI) | [](https://codecov.io/gh/PSORLab/DynamicBounds.jl) | To Be Added (Zenodo) |
This package provides
An abstraction layer for constructing valid relaxations
and bounds on the solution sets (and numerical solutions of) parametric ODEs,
and DAEs. Evaluations of the parametric ODES/DAEs are made available by linking
the specific `integrator` to an equivalent evaluation using solvers present in
DifferentialEquations.jl.
## Example Usage
## The DynamicBounds.jl abstraction layer.
The abstraction layer for DynamicBounds is divided into three major parts. First, there are problems (`<:`) which hold all the information required to define a well-posed parametric differential equation problem. Second, there are integrators (`<:`) which hold all the information require to compute relaxations of the problem or `integrate` the parametric differential equation problem at a particular parameter value.
## Integrators available
- *DifferentialInequality*: Provides valid bounds and relaxations of the numerical solutions of systems of ODEs via second-order implicit methods.
- *DiscretizeRelax*: Provides valid bounds and relaxations of the numerical solutions of systems of ODEs via second-order implicit methods.
- *Wilhelm2019*: Provides valid bounds and relaxations of the numerical solutions of systems of ODEs via second-order implicit methods.
- *Wilhelm2019*: Provides valid bounds and relaxations of the numerical solutions of systems of ODEs via second-order implicit methods.
## Adding new problems/integrators
### Adding new integrators
- Define the new integrator structure and extend make.
- The integrator should be an abstract subtype of `AbstractODERelaxIntegator` for parametric systems of ODEs.
- The integrator should be an abstract subtype of `AbstractDAERelaxIntegator` for parametric systems of DAEs.
- Otherwise, it should be a subtype of abstract subtype of `AbstractDERelaxIntegator` associated with a specific problem form.
- Extend relax!
- Extend integrate!
- Extend the support/set/get/get!/getall! for all supported attributes
- Fully extending these functions for each attribute is desirable but also can
be a burden. We recommend the following as a minimal extension:
- For interval-only methods:
- get!(integrator, Value{Nominal}(), value)
- get!(integrator, Gradient{Nominal}(), value)
- get!(integrator, Gradient{Nominal}(), value)
- For relaxation methods:
-
- set!(integator, Gradient())
- set!(integrator, Value{Nominal}())
- Define new problems by adding a structure `<: AbstractDERelaxProblem`
- Add a corresponding structure `<: AbstractRelaxationAttribute` to hold the solution information.
- The extend the support and get functions for all supported attributes
## References
## Related Packages
- ReachabilityAnalysis.jl: A well-developed package in Julia for novel reachability
approaches. There is some overlap between the functionality enclosed in this
package and DynamicBounds.jl. Both packages provide methods for performing
reachability analysis. However, DynamicBounds.jl is meant to provide a specialized
interface to additionally query dynamic relaxations and supply optimization problems
with a structured abstraction layer such that optimizers may be written in a
reachability (or relaxation) algorithm agnostic fashion.