ALGORITHMIC AND SOFTWARE METHOD FOR PREDICTING DATA WITH MULTIMODAL DISTRIBUTION BASED ON THE MDN MODEL

The development of machine learning models capable of accurately predicting data with multimodal distributions is a critical direction in modern data analysis. Such data commonly arise in practical applications where a single input can correspond to multiple valid outputs, for example, in robotic control systems, image processing, or pattern recognition. Traditional neural network models, which rely on deterministic prediction strategies, are often limited in their ability to capture this variability and uncertainty. To address this limitation, this paper presents a modified algorithmic and software method based on the Mixture Density Network (MDN), incorporating a probabilistic method into the loss function calculation during training. Applying a numerical integral into the proposed probabilistic method, making the model more stable and interpretable during training. The study includes a comparative analysis of the classical MDN and the proposed method using synthetic datasets with clearly defined multimodal characteristics, as well as a real-world simulation of a robotic arm positioning task, where multiple angle configurations can achieve the same target coordinates. Additional complexity is introduced by modeling the simultaneous operation of two robotic arms, further emphasizing the model’s capacity to resolve multiple overlapping outcomes. The experimental results demonstrate that the modified MDN achieves a consistent reduction in prediction error and training loss across all test scenarios, outperforming both the original MDN and a conventional least-squares method. Despite an increase in training time, the computational efficiency of the final model remains unaffected. These findings highlight the practical relevance and scalability of the proposed method for improving prediction accuracy in complex multimodal systems, offering valuable potential for broader applications in intelligent automation and decision-making systems.