Structural Uncertainty Visualization of Morse Complexes for Time-Varying Data Prediction

Scientific simulations are essential for understanding complex physical systems, yet they are often computationally intensive and time-consuming. To address this challenge, researchers increasingly employ deep learning models to generate data efficiently and predict future system states. However, the uncertainty inherent in model outputs can undermine the reliability of these predictions, especially when analyzing structural patterns critical for scientific insight. While most existing approaches estimate uncertainty at the pixel or grid level, characterizing uncertainty in predicted topological structures provides a more intuitive and compact way to capture meaningful changes in the data. In this work, we quantify and visualize the uncertainty of Morse complexes during model prediction. Morse complexes, grounded in Morse theory, are gradient-based topological structures that offer concise abstractions of scalar fields. Given a time-varying scalar field, we use UNet-T, a U-Net-style convolutional architecture, to predict future timesteps. To assess the uncertainty of the resulting topological structures, we introduce MC-U, a joint-estimation graph neural network (GNN) that captures how uncertainty propagates into predicted Morse complexes. We demonstrate our approach on several 2D time-varying scientific datasets, showing that it effectively identifies regions of reduced structural reliability, thereby enhancing both the interpretability and the trustworthiness of the predictions.