LaplaceSalesNet: A Neural Laplace-Transformer Framework for Continuous-Time Sales Forecasting

Sales forecasting is critical for effective inventory management, revenue optimization, and strategic planning in dynamic retail markets. Traditional time-series models struggle to handle irregularly spaced data and abrupt sales fluctuations. In this paper, we propose LaplaceSalesNet, a novel neural architecture combining Neural Laplace Models with Transformer-based time-aware attention, to perform continuous-time sales forecasting. LaplaceSalesNet represents sales as a continuous function in the Laplace domain, enabling accurate predictions at arbitrary future time points. The model was evaluated on three datasets, Superstore Sales Dataset, Retail Sales Forecasting, and Walmart Sales Forecast. It outperformed state-of-the-art models, achieving a 9.87 RMSE on SSD, an 11.15 RMSE on RSF, and a 10.02 RMSE on WSF, showing an average improvement of 12% over N-BEATS and 18% over Transformer. Furthermore, With 10% of the SSD's data missing, LaplaceSalesNet maintained a low MAE of 7.89, demonstrating its resilience to missing data. These results highlight the effectiveness of LaplaceSalesNet in capturing complex temporal dependencies and irregular sales patterns, making it a reliable solution for modern retail forecasting challenges.