MLMF_coastal

This repository provides a Python wrapper to implement the Multilevel Multifidelity Monte Carlo method (MLMF). It is the accompanying repository for "Clare, M. C., Leijnse, T. W., McCall, R. T., Diermanse, F. L., Cotter, C. J., & Piggott, M. D. (2022). Multilevel multifidelity Monte Carlo methods for assessing coastal flood risk." submitted to Natural Hazards and Earth System Sciences.

Here the Python wrapper has been implemented around the high fidelity model XBeach and the low fidelity model SFINCS to assess uncertainty in coastal problems.

The functions to implement MLMF are stored in mlmf_fns_multi.py, a copy of which is included in every test case folder. Note this wrapper is model independent and thus it can be easily implemented with different models simply by changing the fidelity_fns_*.py file.

This repository also contains python code to transform MLMF expectation outputs into cumulative distribution functions using the modified inverse transform sampling method. The code to do this for each test case is found in the python file *_dist.py in each folder.

Finally, the functions required for performing Monte Carlo to verify the MLMF method are stored in mc_fns.py

Software requirements

XBeach (https://oss.deltares.nl/web/xbeach/)
- In this work, we used version 1.23.5526 XBeachX release
SFINCS (Available on request. Please contact Deltares if you are interested in using this code.)
Python 3.5 or later

Simulation scripts

Carrier-Greenspan
1. MLMF/MLMC algorithm
```
#!bash
$ python carrier_mlmf.py
```
  Produces MLMF results if prelim_run = True; opt_sample = True; opt_hf=False, opt_lf=False;
  
  produces MLMC results for XBeach with prelim_run = True; opt_sample = False; opt_hf=True, opt_lf=False;
  
  produces MLMC results for SFINCS with prelim_run = True; opt_sample = False; opt_hf=False, opt_lf=True.
2. CDF
```
#!bash
$ python carrier_dist.py
```
  Post-processes the outputs of carrier_mlmf.py to produce the cumulative distribution function.
3. Monte Carlo
```
#!bash
$ python carrier_mc.py
```
  Produces Monte Carlo (MC) results to verify the MLMF/MLMC results. N.B. this file must be run multiple times to achieve a sufficient number of samples.
4. Analytical result
```
#!bash
$ python carrier_analytic.py
```
  Produces the analytical result to verify the MLMF/MLMC results for this test case.
Myrtle Beach
1. MLMF/MLMC algorithm
```
#!bash
$ python myrtle_mlmf.py
```
  Produces MLMF results if prelim_run = True; opt_sample = True; opt_hf=False, opt_lf=False;
  
  produces MLMC results for XBeach with prelim_run = True; opt_sample = False; opt_hf=True, opt_lf=False;
  
  produces MLMC results for SFINCS with prelim_run = True; opt_sample = False; opt_hf=False, opt_lf=True.
2. CDF
```
#!bash
$ python myrtle_dist.py
```
  Post-processes the outputs of myrtle_mlmf.py to produce the cumulative distribution function.
Non-breaking_wave
1. MLMF/MLMC algorithm
```
#!bash
$ python bates_mlmf.py
```
  Produces MLMF results if prelim_run = True; opt_sample = True; opt_hf=False, opt_lf=False;
  
  produces MLMC results for XBeach with prelim_run = True; opt_sample = False; opt_hf=True, opt_lf=False;
  
  produces MLMC results for SFINCS with prelim_run = True; opt_sample = False; opt_hf=False, opt_lf=True.
2. CDF
```
#!bash
$ python bates_dist.py
```
  Post-processes the outputs of bates_mlmf.py to produce the cumulative distribution function.
3. Monte Carlo
```
#!bash
$ python bates_mc.py
```
  Produces Monte Carlo (MC) results to verify the MLMF/MLMC results. N.B. this file must be run multiple times to achieve a sufficient number of samples.
4. Analytical result
```
#!bash
$ python bates_analytic.py
```
  Produces the analytical result to verify the MLMF/MLMC results for this test case.

mc4117/MLMF_coastal

MLMF_coastal

Software requirements

Simulation scripts