## 1 Introduction
They incorporated a normalization-based attention module during feature extraction and adopted a multiscale deformable attention mechanism in the encoder-decoder structure to improve the detection of small-scale flames and smoke. Their proposed model achieved average precisions of 81.7% and 76.0% for flames and smoke, respectively. [PERSON] et al. [24] developed a lightweight fire segmentation model by integrating depth-wise separable convolutions and a novel confusion block architecture into a modified FusionNet. Their model achieved high segmentation accuracy and reduced computational costs; the results indicated that the intersection over union (IoU) scores were 0.79 and 0.91 on the FiSmo and Corsican fire datasets, respectively. [PERSON] et al. [25] developed a semantic fire segmentation model for outdoor images by improving the FusionNet architecture with input and output convolution layers and middle skip connections, resulting in a more precise pixel-level fire detection. [PERSON] [26] developed a \"flame tracker\" model using Python; this model automatically analyzes flame characteristics such as size, color, and temperature by extracting hue variations from flame images and videos in the RGB color space. This method highlights the potential of flame imagery as a versatile tool for HRR prediction in diverse fire scenarios. Recently, the prediction of transient HRR using AI models has gained increasing attention, and a limited number of studies have begun to explore this area [27; 28]. [PERSON] et al. [29] proposed a deep learning-based HRR prediction model by utilizing the VGG16 architecture designed for use in real fire environments, where conventional HRR measurement methods cannot be easily applied. The model was validated using both laboratory and real-world fire data, achieving a coefficient of determination \(R^{2}\) of 0.83 for low-HRR fires and an \(R^{2}\) of 0.68 for high-HRR fires. [PERSON] et al. [30] introduced a deep learning model to predict transient HRR using flame imagery and a hybrid Att-BiLSTM network. This model utilized attention mechanisms and bidirectional LSTM layers for capturing key temporal features from fire image sequences, which enabled accurate HRR forecasting, with an \(R^{2}\) of 0.997 for the validation datasets. [PERSON] [31] introduced a recurrent neural network (RNN)-based HRR prediction model using fire video data, demonstrating an improved predictive performance compared to that of traditional correlations, such as the Heskestad equation. The RNN model learned the temporal dynamics of flame patterns, capturing the evolving nature of fires and improving HRR estimation. The model was evaluated using fire video data from wood pallet and cardboard box fire experiments; the model yielded a mean absolute error (MAE) of around 115 kW, indicating robust prediction performance across diverse fire environments. A review of the existing literature indicates that many studies have focused on accurately measuring the HRR of various combustibles in laboratory environments using experimental equipment to improve measurement precision and reliability. Prior research on AI models for predicting fire characteristics has primarily focused on detecting and segmenting flames and smoke from fire images. However, a limited number of studies have explored HRR prediction using sequence modeling approaches. While such models demonstrate promising real-time prediction performance, they typically require large-scale paired datasets of fire image sequences and corresponding HRR values for training. Moreover, purely data-driven models are limited in identifying the underlying physical behavior of flames. Thus, this study proposes a real-time HRR prediction model that predicts the HRR from fire images by extracting flame features such as flame height and fire diameter using a deep learning- and image processing-based segmentation technique.