Recurrent Convolutional Deep Neural Networks for Modeling Time-Resolved Wildfire Spread Behavior

Abstract

The increasing incidence and severity of wildfires underscores the necessity of accurately predicting their behavior. While high-fidelity models derived from first principles offer physical accuracy, they are too computationally expensive for use in real-time fire response. Low-fidelity models sacrifice some physical accuracy and generalizability via the integration of empirical measurements, but enable real-time simulations for operational use in fire response. Machine learning techniques have demonstrated the ability to bridge these objectives by learning first-principles physics while achieving computational speedups. While deep learning approaches have demonstrated the ability to predict wildfire propagation over large time periods, time-resolved fire-spread predictions are needed for active fire management. In this work, we evaluate the ability of deep learning approaches in accurately modeling the time-resolved dynamics of wildfires. We use an autoregressive process in which a convolutional recurrent deep learning model makes predictions that propagate a wildfire over 15 min increments. We apply the model to four simulated datasets of increasing complexity, containing both field fires with homogeneous fuel distribution as well as real-world topologies sampled from the California region of the United States. We show that even after 100 autoregressive predictions representing more than 24 h of simulated fire spread, the resulting models generate stable and realistic propagation dynamics, achieving a Jaccard score between 0.89 and 0.94 when predicting the resulting fire scar. The inference time of the deep learning models are examined and compared, and directions for future work are discussed.

Appendix 1: Deep Neural Network Transformations

While a full summary of deep neural networks is outside the scope of this paper, we provide a brief description of the transformations used in the DNNs described in this work. For a deeper background on DNNs, we refer the interested reader to [30].

The fundamental unit processed by a DNN is a tensor. A tensor is an n dimensional collection of scalar values, $n\ge 0$. For example, a single field specifying how much fuel exists in a 2D patch of ground could be stored in a 2D tensor with shape (H, W) where H is the height of the field and W is the width. That field represents a channel of information and if there are additional channels, they can be stored in a tensor of shape (H, W, C) where C is the number of channels. A time series of fields can be stored in a tensor of shape (T, H, W, C) where T is the number time points in the series. Training a DNN is usually done in batches, so a DNN that works on (T, H, W, C) data will actually take (B, T, H, W, C) data where B is the number of data points in a single batch.

DNNs are often said to predict some outcome based on a given data point though in reality, the output is merely the input after its been passed through a potentially large number of transformations. We sometimes refer to sets of transformations as a layer. Some layers contain parameters such that the process of training a DNN attempts to find the optimal set of values that result in transforming as much of the training input into as correct a set of output as possible. These are the primary transformations used in this work:

• fully connected: Every value in the output is a parameterized combination of every value in the input. Given an input shape (B, M) and output shape (B, N), there are $M \times N$ total parameters. This layer can be useful when many output values need to consider many input values, but can be particularly prone to overfitting and parameter bloat.

• convolutional (2D): This layer is appropriate for inputs that contain 2D fields. A 2D convolutional kernel is swept across both dimensions of the input field. At each location, the dot product between the kernel and the 2D field is computed, which generates a new field that is the convolution of the input field with the kernel. There can be multiple independent kernels, resulting in multiple field outputs. Given an input shape of (B, H, W, C), the output shape is (B, H, W, K) where K is the number of kernels.

• recurrent: A layer which explicitly considers temporal relationships in the input data when generating the output. Unlike spatial relationships, temporal relationships often cannot effectively be modeled by simply considering neighboring input. Temporal dynamics often require considering events that occurred at more distant times in the past. Recurrent layers build up a memory by iterating over individual time points one at a time. Cells in the output depend on the memory instead of actual time points in the past. If the input contains fields, the layers will also leverage convolutions such that an output cell can depend on the memory of itself, and the memory of neighboring cells. If the convolutions have K kernels and the input shape is (B, T, H, W, C), then the output shape will be (B, T, H, W, K). Given its wide-spread success at modeling image-to-image type tasks, we use the Convolutional Long-Short Term Memory layer (ConvLSTM) [37].

• activation: Passes each value in the input through an often non-linear and potentially parameterized function. The output shape is equal to the input shape.

• skip link: Taking the input for some transformation and concatenating (or adding) it with the output of the transformation. This effectively gives a path for the gradients of the model’s parameters to skip the transformation during training, significantly increasing the efficacy of training large networks.

• max pooling (2D): A field transformation that downsamples the spatial dimensions of the input and while typically doubling the number of channels. If the input has shape (B, H, W, C), then the output will have shape $(B, H/2, W/2, C \times 2)$.

• zero padding: This layer adds padding around the field. If the input shape is (B, H, W, C) and the padding size is P then the output shape will be $(B, H+2P, W+2P, C)$.

• one hot encoding: This layer transforms integer values in the input into a list of all zeros with the exception of a single element in the list corresponding to the integer value being given a value of one. If the input shape is (B, H, W, C), the output will be (B, H, W, C, E) where E is the maximum value the input can take.

• embedding: This layer converts a field that contains discrete valued cells into an field where each cell is replaced by a set of floating-point values. Values in the input that result in similar predictions are placed close to each other in the embedding space, which subsequent layers in the model can leverage more effectively than the discrete values alone. If the input has shape (B, H, W, 1) and the embedding space has rank E, then the output shape will be (B, H, W, E).