# Parameter Flexible Wildfire Prediction Using Machine Learning Techniques: Forward and Inverse Modelling

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## Abstract

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## 1. Introduction

- We propose a parameter flexible data-driven algorithm scheme for burned area forecasting which can combine different approaches of ROM and ML prediction techniques with a large range of model parameters.
- We develop an inverse model to address the bottleneck of parameter identification in fire prediction models by using the recently developed GLA algorithm,
- We test the parameter flexible data-driven model and the inverse model for recent massive fire events in California where the data used for the assimilation are satellite observations (ORNL DAAC. 2018. MODIS and VIIRS Land Products Global Subsetting and Visualization Tool. ORNL DAAC, Oak Ridge, Tennessee, USA) of burned area.

## 2. Data Generation and Study Area

#### 2.1. Cellular Automata Fire Simulation

- state 1: the cell can not be burned;
- state 2: the cell is burnable but has not been ignited;
- state 3: the cell is burning;
- state 4: the cell has been burned.

#### 2.2. Study Area and Observation Data

## 3. A Parameter Flexible Data-Driven Model for Burned Area Forecasting: Methodology

#### 3.1. Reduced-Order Modelling

#### 3.1.1. Principle Component Analysis

#### 3.1.2. Convolutional Autoencoding

#### 3.1.3. Singular Value Decomposition Autoencoding

#### 3.2. Forward Problem: Machine Learning Prediction

#### 3.2.1. Random Forest Regression

#### 3.2.2. K-Nearest Neighbours Regression

#### 3.2.3. Multi Layer Perceptron

#### 3.3. Inverse Problem: Latent Data Assimilation

#### 3.3.1. Four Dimensional Variational Approach

#### 3.3.2. Generalised Latent Assimilation

Algorithm 1: 4Dvar GLA |

#### 3.4. Hyperparameter Tuning

## 4. Results and Analysis

#### 4.1. Reconstruction Accuracy of Reduced Order Modellings

#### 4.2. Prediction Performance of the Forward Model

#### 4.3. Parameter Estimation of the Inverse Model

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Acronyms

NN | Neural Network |

DNN | Deep Neural Network |

ML | Machine Learning |

LA | Latent Assimilation |

DA | Data Assimilation |

PR | Polynomial Regression |

AE | Autoencoder |

VAE | Variational Autoencoder |

CAE | Convolutional Autoencoder |

VAE | Variational Autoencoder |

BLUE | Best Linear Unbiased Estimator |

3D-Var | 3D Variational |

RNN | Recurrent Neural Network |

CNN | Convolutional Neural Network |

LSTM | long short-term memory |

POD | Proper Orthogonal Decomposition |

PCA | Principal Component Analysis |

PC | principal component |

SVD | Singular Value Decomposition |

ROM | reduced-order modelling |

CFD | computational fluid dynamics |

1D | one-dimensional |

2D | two-dimensional |

NWP | numerical weather prediction |

MSE | mean square error |

S2S | sequence-to-sequence |

R-RMSE | relative root mean square error |

BFGS | Broyden–Fletcher–Goldfarb–Shanno |

LHS | Latin Hypercube Sampling |

AI | artificial intelligence |

DL | Deep Learning |

PIV | Particle Image Velocimetry |

LIF | Laser Induced Fluorescence |

KNN | K-nearest Neighbours |

DT | Decision Tree |

RF | Random Forest |

KF | Kalman filter |

CART | Classification And Regression Tree |

CA | Cellular Automata |

MLP | Multi Layer Percepton |

GLA | Generalised Latent Assimilation |

3Dvar | Three-dimensional variational data assimilation |

4Dvar | Four-dimensional variational data assimilation |

MODIS | Moderate Resolution Imaging Spectroradiometer |

VIIRS | Visible Infrared Imaging Radiometer Suite |

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**Figure 2.**Flowchart of the forward prediction model with CA and ROM for a specific ecoregion. The data generation is performed with a set of parameters perturbed using LHS.

**Figure 4.**Relative reconstruction error of satellite observations and CA simulations in the test dataset against the dimension of the latent space.

**Figure 5.**Reconstruction of CA simulations for 2 examples in the test dataset of the Chimney fire at day 4.

**Figure 6.**Reconstruction of CA simulations for 2 examples in the test dataset of the Ferguson fire at day 4.

**Figure 7.**Reconstruction of the satellite observation for the Chimney (

**a**–

**h**) and the Ferguson (

**i**–

**p**) fire at day 4.

**Figure 8.**Prediction results of latent variables (with the highest variance in each case) for $q=30$ in the test dataset for both Chimney (C) and Ferguson (F) wildfires at day 4. The x-axis represents reordered samples according to their true latent values.

**Figure 9.**Machine learning (DL) prediction of burned area at day 6 for both fire events (Chimney (

**a**–

**h**) and Ferguson (

**i**–

**p**)) using original (${\mathbf{x}}_{b}$) and assimilated (${\mathbf{x}}_{a}$) parameters compared to CA simulations (considered as ground truth here) for 2 examples in the test dataset.

**Figure 10.**Machine learning (DL) prediction of burned area at day 6 for both fire events using original (${\mathbf{x}}_{b}$) and assimilated (${\mathbf{x}}_{a}$) parameters compared to satellite observations. The results of both CAE-MLP (

**a**,

**b**,

**f**,

**g**) and PCA-MLP (

**d**,

**e**,

**i**,

**j**) are demonstrated.

**Table 1.**Study areas of the Chimney and the Ferguson wildfire events in this work. The latitude and the longtitude represent the centre of the fires. The averaged wind speed of the first 6 days of fire propagation is also indicated.

Fire | Latitude | Longitude | Area | Duration | Start | Wind |
---|---|---|---|---|---|---|

Chimney | 37.6230 | −119.8247 | ≈$246\phantom{\rule{0.166667em}{0ex}}{\mathrm{km}}^{2}$ | 23 days | 13 August 2016 | 23.56 mph |

Ferguson | 35.7386 | −121.0743 | ≈$185\phantom{\rule{0.166667em}{0ex}}{\mathrm{km}}^{2}$ | 36 dyas | 13 July 2018 | 18.54 mph |

Model/Hyperparameters | Grid Search Space | Final Set |
---|---|---|

CAE | ||

Filter, Strides, Pooling size | / | Table 3 |

Activation | {ReLu, LeakyReLu, Sigmoid} | Table 3 |

Optimizer | {Adam, SGD} | Adam |

Batch size | $\{16,32,64\}$ | 32 |

RF | ||

split criteria | {‘gini’, ‘entropy’} | ‘gini’ |

${n}_{\mathrm{DT}}$ | $\{10,50,100\}$ | 100 |

${n}_{\mathrm{features}}$ | {‘log2’, ‘sqrt’} | ‘sqrt’ |

KNN | ||

k | {5, 10, 20} | 5 |

Metric | $\{{L}_{1},{L}_{2}\}$ | ${L}_{2}$ |

MLP | ||

${n}_{\mathrm{MLP},1}$ | {10, 20, 30} | 20 |

${n}_{\mathrm{MLP},2}$ | {30, 40, 50} | 30 |

Activation | {ReLu, LeakyReLu, Sigmoid} | |

Optimizer | {Adam, SGD} | Adam |

GLA | ||

${d}_{p}$ | 2–6 | 4 |

${n}_{s}$ | $\{200,500,1000,2000\}$ | 1000 |

${r}_{s}$ | 50–200% | $80\%$ |

**Table 3.**NN structure of the CAE with ordered meshes where the latent dimension $q\in \{10,20,30,40,50\}$.

Layer (Type) | Output Shape | Activation |
---|---|---|

Encoder | ||

Input | $(899,982,1)$ | |

Conv 2D (10 × 10) | $(899,982,4)$ | ReLu |

MaxPooling 2D (5 × 5) | $(180,197,4)$ | |

Conv 2D (4 × 4) | $(180,197,4)$ | ReLu |

MaxPooling 2D (3 × 3) | $(60,66,8)$ | |

Conv 2D (3 × 3) | $(60,66,8)$ | ReLu |

MaxPooling 2D (3 × 3) | $(20,22,8)$ | |

Conv 2D (2 × 2) | $(20,22,8)$ | ReLu |

MaxPooling 2D (2 × 2) | $(10,11,8)$ | |

Flatten | 880 | |

Dense $\left(q\right)$ | q | LeakyReLu (0.3) |

Decoder | ||

Input | q | |

Dense $\left(110\right)$ | 110 | LeakyReLu (0.3) |

Reshape | $(10,11,1)$ | |

Conv 2D (2 × 2) | $(10,11,8)$ | ReLu |

Upsampling 2D (2 × 2) | $(20,22,8)$ | |

Conv 2D (3 × 3) | $(10,11,8)$ | ReLu |

Upsampling 2D (3 × 3) | $(60,66,8)$ | |

Conv 2D (4 × 4) | $(60,66,8)$ | ReLu |

Upsampling 2D (3 × 3) | $(180,198,8)$ | |

Conv 2D (5 × 5) | $(180,198,4)$ | ReLu |

Upsampling 2D (5 × 5) | $(900,990,4)$ | |

Cropping 2D $(1,8)$ | $(899,982,4)$ | |

Conv 2D (8 × 8) | $(899,982,1)$ | Sigmoid |

**Table 4.**Averaged prediction error for Chimney and Ferguson fires at day 4 in the full physical space after decoding. The dimension of the latent space is fixed as $q=30$.

ML Approache | Chimney | Ferguson | ||||
---|---|---|---|---|---|---|

PCA | CAE | SVD AE | PCA | CAE | SVD AE | |

KNN | 1.87% | 4.95% | 1.88% | 2.00 % | 3.30% | 2.73% |

RF | 1.70% | 4.91% | 1.80% | 1.89% | 3.27% | 2.45% |

MLP | 1.71% | 4.54% | 1.59% | 2.13% | 3.11% | 2.54% |

**Table 5.**Averaged computational time for offline training (on the training dataset of 1000 samples) and online prediction(for each sample including decoding) for different ROMs using RF. The dimension of the latent space is fixed as $q=30$.

Fire | Offline ROM and ML Training | Online Prediction | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

PCA | CAE | SVD AE | KNN | RF | MLP | CA | PCA | CAE | SVD AE | |

Chimney | 101.06 s | ≈1 h 38 min | 414.55 s | 0.02 s | 0.67 s | 108 s | ≈35 min | 0.52 s | 0.41 s | 14.47 s |

Ferguson | 97.50 s | ≈1 h 29 min | 316.61 s | 0.02 s | 0.54 s | 116 s | ≈29 min | 0.25 s | 0.31 s | 18.62 s |

**Table 6.**Relative prediction error and the averaged computational time (only the LA for parameter estimation) for the Chimney and the Ferguson fire at day 6 with assimilated parameters.

Fire | Data | Forward | PCA | CAE | ||||
---|---|---|---|---|---|---|---|---|

Prior | Posterior | Time | Prior | Posterior | Time | |||

Chimney | CA(test) | KNN | 10.1% | 6.0% | 0.98 s | 11.1% | 7.5% | 0.52 s |

RF | 10.4% | 5.7% | 0.78 s | 10.2% | 6.6% | 0.45 s | ||

MLP | 10.9% | 6.3% | 1.25 s | 10.6% | 5.0% | 0.46 s | ||

observation | MLP | 8.3% | 5.0% | 9.65% | 6.5% | |||

Ferguson | CA(test) | KNN | 30.5% | 20.3% | 0.74 s | 21.3% | 9.4% | 0.60 s |

RF | 27.0% | 22.5% | 0.60 s | 23.1% | 13.6% | 0.58 s | ||

MLP | 30.7% | 17.9% | 0.76 s | 22.4% | 12.6% | 0.88 s | ||

observation | MLP | 41.6% | 14.8% | 23.8% | 11.9% |

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## Share and Cite

**MDPI and ACS Style**

Cheng, S.; Jin, Y.; Harrison, S.P.; Quilodrán-Casas, C.; Prentice, I.C.; Guo, Y.-K.; Arcucci, R.
Parameter Flexible Wildfire Prediction Using Machine Learning Techniques: Forward and Inverse Modelling. *Remote Sens.* **2022**, *14*, 3228.
https://doi.org/10.3390/rs14133228

**AMA Style**

Cheng S, Jin Y, Harrison SP, Quilodrán-Casas C, Prentice IC, Guo Y-K, Arcucci R.
Parameter Flexible Wildfire Prediction Using Machine Learning Techniques: Forward and Inverse Modelling. *Remote Sensing*. 2022; 14(13):3228.
https://doi.org/10.3390/rs14133228

**Chicago/Turabian Style**

Cheng, Sibo, Yufang Jin, Sandy P. Harrison, César Quilodrán-Casas, Iain Colin Prentice, Yi-Ke Guo, and Rossella Arcucci.
2022. "Parameter Flexible Wildfire Prediction Using Machine Learning Techniques: Forward and Inverse Modelling" *Remote Sensing* 14, no. 13: 3228.
https://doi.org/10.3390/rs14133228