# Modeling Wildfire Spread with an Irregular Graph Network

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Area

#### 2.2. Variable-Scale Landscape with IGN

#### 2.2.1. Definition of the IGN

#### 2.2.2. IGN Initialization

#### 2.2.3. IGN Adaptive Optimization

#### 2.3. Deep Learning-Based Spread Model

#### 2.3.1. Definition of the IGN Spread

#### 2.3.2. Construction of Grid-Based Dataset

#### 2.3.3. Construction of IGN Dataset

#### 2.3.4. Design of Deep Neural Network

## 3. Results

#### 3.1. WFDNN Result

#### 3.2. Results of Getty Fire Case

## 4. Discussion

#### 4.1. Analysis of Getty Case

#### 4.2. Effect of Elevation Difference Threshold on IGN

#### 4.3. VSE Dataset Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

FARSITE | CA | IGN | |
---|---|---|---|

Theoretical principle | Thermal physics | Thermal physics | Deep learning |

Spread pattern | Huygens | Cellular automata | Graph network |

Landscape type | Vector | Grid | Vector |

Output format | Polygon or Grid | Grid | Graph |

- (1)
- Theoretical principle

- (2)
- Spread pattern

- (3)
- Landscape type

- (4)
- Output format

## Appendix B

Algorithm A1 Adaptive iteration process in IGN optimization. |

$\#\mathrm{INPUT}:{G}_{int}$, the initial IGN with uniform sampling and Delaunay algorithm $\#\mathrm{OUTPUT}:{G}_{opt}$, the optimized IGN $\left(\mathrm{V},\mathrm{E}\right)=$${G}_{int}$$$$$ is the edges of the graph network ${V}_{new}$ = null # To store newly inserted nodes Iter_counter = 0 # Count the time of iteration Iter_count_max = 1e3 # The maximum time of iteration # Adaptive iteration while True: # count the number of iteration Iter_counter += 1 $\mathrm{for}\mathrm{each}edg{e}^{i}\in E$: # Step 1: Edge interpolation. Use equally spaced interpolation to obtain a candidate node set $\{{n}_{0}^{i}$$,{n}_{1}^{i}$$,\dots {n}_{M}^{i}$$\}=\mathrm{Interpolate}(edg{e}^{i}$) $N{C}^{i}=\{{n}_{0}^{i}$$,{n}_{1}^{i}$$,\dots {n}_{M}^{i}\}$ # Candidate node set, containing M+1 nodes # Step 2: homogeneity check: fuel type and slope $\mathrm{for}\mathrm{each}{n}_{m}^{i}\in N{C}^{i}$: # fuel type $\mathrm{if}F{T}_{{n}_{m}^{i}}$$!=F{T}_{{n}_{m-1}^{i}}$: $\#\mathrm{The}\mathrm{fuel}\mathrm{type}\mathrm{changes}\mathrm{in}\mathrm{the}edg{e}^{i}$, thus we add the node to avoid the heterogeneity. ${V}_{new}$$.\mathrm{add}({n}_{m}^{i}$$)\#\mathrm{add}\mathrm{node}{n}_{m}^{i}$$\mathrm{into}{V}_{new}$ # Slope homogeneity. Here we use elevation difference to replace $E{D}_{N{C}^{i}}$$=\mathrm{Get}\_\mathrm{ED}(N{C}^{i}$) # Get elevation differences of neighboring nodes $\mathrm{for}\mathrm{each}E{D}_{m}\in E{D}_{N{C}^{i}}$ $\mathrm{if}E{D}_{m}-E{D}_{m-1}$$>{T}_{ed}$: # The elevation has a large wave, thus we add the node to eliminate it. ${V}_{new}$$.\mathrm{add}({n}_{m}^{i}$$)\#\mathrm{add}\mathrm{node}{n}_{m}^{i}$$\mathrm{into}{V}_{new}$ # Step 3: Reconstruct the IGN by Delaunay algorithm, ${V}_{c}$$=\mathrm{Concatenate}(\mathrm{V},{V}_{new}$) # Concatenate and generate new node set $\mathrm{G}=\mathrm{Delaunay}({V}_{c}$) # Update the G with new nodes $(\mathrm{V},\mathrm{E})=$ G # if no more new nodes or reaching the maximum iteration $\mathrm{If}\mathrm{is}\_\mathrm{null}({V}_{new}$) or Iter_counter> Iter_count_max: Break $\#\mathrm{Get}\mathrm{the}{G}_{opt}$ ${G}_{opt}$= G $\mathrm{Return}{G}_{opt}$ |

## Appendix C

Algorithm A2 Grid-Graph matching algorithm. |

$\#$$\mathrm{graph}\mathrm{network};{L}_{grid}$ grid-based labels $\#\mathrm{OUTPUT}:{L}_{graph}$, graph-based labels $\#$$\mathrm{and}{L}_{grid}$ ${G}_{T}=$$\mathrm{Overlay}(\mathrm{G},{L}_{grid}$) $\#$$$$\mathrm{from}\mathrm{the}\mathrm{time}\mathrm{in}{L}_{grid}$ $\{{T}_{0}$$,{T}_{1}$$,\dots {T}_{K}$$\}={G}_{T}$$$ is the number of graph nodes # Set VSEs = null ${L}_{graph}$ = null # Search the VSE and VSN $\mathrm{For}\mathrm{each}{n}^{i}\in G$: # Get the spread time of each connected edge ${T}_{con}^{i}=\left\{{T}^{i}-{T}_{m}^{i}\right\}$$,\mathrm{m}=0,1,\dots ,\mathrm{M}.\#\mathrm{M}\mathrm{is}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{nodes}\mathrm{connected}\mathrm{with}{n}^{i}$ $\#\mathrm{Estimate}\mathrm{spread}\mathrm{time}\mathrm{with}\mathrm{an}\mathrm{empirical}\mathrm{formula}{f}_{emp}$ $t{s}^{i}={f}_{emp}\left(\theta \right)$$$ is the proprieties of graph edges # The minimum is taken as the VSE $\mathrm{j}=\mathrm{argmin}\left(\mathrm{abs}\right\{{T}_{con}^{i}-t{s}^{i}$}) # j is the index of the node with the minimum difference # Add the VSE $\mathrm{VSEs}.\mathrm{add}\left(\mathrm{pair}\right\{{n}^{i}$$,{n}^{j}$}) # Get the dataset ${L}_{graph}$= VSEs $\mathrm{Return}{L}_{graph}$ |

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**Figure 3.**IGN adaptive optimization. (

**a**) Homogeneity and heterogeneity in fuel and slope; (

**b**) adaptive iteration process for IGN optimization.

**Figure 7.**Experimental simulation results. (

**a**) FARSITE model [30 m]; (

**b**) FARSITE model [5 m]; (

**c**) CA model [30 m]; (

**d**) CA model [5 m]; (

**e**) IGN model; (

**f**) local IGN results.

**Figure 8.**Quantitative comparative analysis. (

**a**) Comparison of the burned area at different times; (

**b**) comparison of model performance.

**Figure 9.**Wildfire spread characteristics in IGN-based landscape. (

**a**) Spread rate; (

**b**) flame length; (

**c**) fire intensity.

**Figure 10.**IGN structure with different ${T}_{ed}$. (

**a**) ${T}_{ed}$ = 1 m; (

**b**) ${T}_{ed}$ = 3 m; (

**c**) ${T}_{ed}$ = 5 m.

**Figure 11.**Comparison of different VSE dataset construction. (

**a**) Training curve; (

**b**) test error; (

**c**) empirical method; (

**d**) maximum time method; (

**e**) all-extraction method.

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Jiang, W.; Wang, F.; Su, G.; Li, X.; Wang, G.; Zheng, X.; Wang, T.; Meng, Q. Modeling Wildfire Spread with an Irregular Graph Network. *Fire* **2022**, *5*, 185.
https://doi.org/10.3390/fire5060185

**AMA Style**

Jiang W, Wang F, Su G, Li X, Wang G, Zheng X, Wang T, Meng Q. Modeling Wildfire Spread with an Irregular Graph Network. *Fire*. 2022; 5(6):185.
https://doi.org/10.3390/fire5060185

**Chicago/Turabian Style**

Jiang, Wenyu, Fei Wang, Guofeng Su, Xin Li, Guanning Wang, Xinxin Zheng, Ting Wang, and Qingxiang Meng. 2022. "Modeling Wildfire Spread with an Irregular Graph Network" *Fire* 5, no. 6: 185.
https://doi.org/10.3390/fire5060185